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+ +.. toctree:: + :maxdepth: 2 + :glob: + + modeling/index + optimizers/index + problems/index + tolerances diff --git a/_sources/api/modeling/Annotation.rst.txt b/_sources/api/modeling/Annotation.rst.txt new file mode 100644 index 00000000..cede135e --- /dev/null +++ b/_sources/api/modeling/Annotation.rst.txt @@ -0,0 +1,4 @@ +Annotation +========== + +.. doxygenclass:: idol::Annotation diff --git a/_sources/api/modeling/Column.rst.txt b/_sources/api/modeling/Column.rst.txt new file mode 100644 index 00000000..4f16f907 --- /dev/null +++ b/_sources/api/modeling/Column.rst.txt @@ -0,0 +1,6 @@ +.. _api_Column: + +Column +====== + +.. doxygenclass:: idol::Column diff --git a/_sources/api/modeling/Constant.rst.txt b/_sources/api/modeling/Constant.rst.txt new file mode 100644 index 00000000..910e997b --- /dev/null +++ b/_sources/api/modeling/Constant.rst.txt @@ -0,0 +1,6 @@ +.. _api_Constant: + +Constant +======== + +.. doxygenclass:: idol::Constant diff --git a/_sources/api/modeling/Ctr.rst.txt b/_sources/api/modeling/Ctr.rst.txt new file mode 100644 index 00000000..483b7feb --- /dev/null +++ b/_sources/api/modeling/Ctr.rst.txt @@ -0,0 +1,6 @@ +.. _api_Ctr: + +Ctr +=== + +.. doxygenclass:: idol::Ctr diff --git a/_sources/api/modeling/Env.rst.txt b/_sources/api/modeling/Env.rst.txt new file mode 100644 index 00000000..1eee279a --- /dev/null +++ b/_sources/api/modeling/Env.rst.txt @@ -0,0 +1,4 @@ +Env +=== + +.. doxygenclass:: idol::Env diff --git a/_sources/api/modeling/Expr.rst.txt b/_sources/api/modeling/Expr.rst.txt new file mode 100644 index 00000000..89fb9869 --- /dev/null +++ b/_sources/api/modeling/Expr.rst.txt @@ -0,0 +1,6 @@ +.. _api_Expr: + +Expr +==== + +.. doxygenclass:: idol::Expr diff --git a/_sources/api/modeling/LinExpr.rst.txt b/_sources/api/modeling/LinExpr.rst.txt new file mode 100644 index 00000000..4068df68 --- /dev/null +++ b/_sources/api/modeling/LinExpr.rst.txt @@ -0,0 +1,22 @@ +LinExpr +======= + +This class is used to represent linear expressions in the modeling interface of idol. + +It consists in a set of linear terms which represent products of keys (typically, variables) and scalars. + +.. admonition:: Example + + In this example, we create a linear expression representing the following linear expression. + + .. math:: + + 3 x_0 + 2 x_1 + + .. code-block:: cpp + + auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x"); + + LinExpr lin_expr = 3 * x[0] + 2 * x[1]; + +.. doxygenclass:: idol::LinExpr diff --git a/_sources/api/modeling/Model.rst.txt b/_sources/api/modeling/Model.rst.txt new file mode 100644 index 00000000..e02e8fac --- /dev/null +++ b/_sources/api/modeling/Model.rst.txt @@ -0,0 +1,55 @@ +.. _api_model: + +Model +===== + +The Model class is probably the most central of idol. It is used to represent a mathematical optimization problem of the +following general form. + +.. math:: + + \begin{array}{lll} + \textrm{minimize } & \displaystyle \sum_{j=1}^n a_{0j}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^0x_jx_k + b_0\\ + \textrm{subject to } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\ + & l_j \le x_j \le u_j & j=1,...,m \\ + & x_j\in\mathbb Z & j\in J_I, + \end{array} + +Here, :math:`x_1, ..., x_n` are the decision variables with bounds :math:`[l_1,u_1],...,[l_n,u_n]` (possibly, +:math:`l_j = -\infty` or :math:`u_j = +\infty`). Note that some variables have integrality requirements (i.e., those whose +indices are in :math:`J_I`). Other entities are input parameters of the problem and must typically have real values +(e.g., :math:`c_j, a_{ij}, q_{jk}^i` and :math:`b_i\in\mathbb R`). Alternatively, optimization problems can also be maximization +problems. + +.. admonition:: Example: + + Here is a short example which builds and solves the following optimization problem. + + .. math:: + + \begin{array}{ll} + \textrm{minimize } & -x_0 - 1.5 x_1 + 3 \\ + \textrm{subject to } & x_0 + 2 x_1 \le 1.5 \\ + & 0 \le x_0 \le 1 \\ + & 0 \le x_1 \le 1 + \end{array} + + .. code-block:: cpp + + Env env; + + Model model(env); + + auto x = model.add_vars(Dim<1>(2), 0, 1, Continuous, "x"); + + auto c = model.add_ctr(x[0] + 2 * x[1] <= 1.5); + + model.set_obj_expr(-x[0] - 1.5 * x[1] + 3); + + model.use(Gurobi()); + + model.optimize(); + + std::cout << "Best obj = " << model.get_best_obj() << std::endl; + +.. doxygenclass:: idol::Model diff --git a/_sources/api/modeling/Param.rst.txt b/_sources/api/modeling/Param.rst.txt new file mode 100644 index 00000000..1684f2f3 --- /dev/null +++ b/_sources/api/modeling/Param.rst.txt @@ -0,0 +1,6 @@ +.. _api_Param: + +Param +===== + +.. doxygenclass:: idol::Param diff --git a/_sources/api/modeling/QuadExpr.rst.txt b/_sources/api/modeling/QuadExpr.rst.txt new file mode 100644 index 00000000..ba0e9a74 --- /dev/null +++ b/_sources/api/modeling/QuadExpr.rst.txt @@ -0,0 +1,4 @@ +QuadExpr +======== + +.. doxygenclass:: idol::QuadExpr diff --git a/_sources/api/modeling/Row.rst.txt b/_sources/api/modeling/Row.rst.txt new file mode 100644 index 00000000..c3f40773 --- /dev/null +++ b/_sources/api/modeling/Row.rst.txt @@ -0,0 +1,6 @@ +.. _api_Row: + +Row +=== + +.. doxygenclass:: idol::Row diff --git a/_sources/api/modeling/SolutionDual.rst.txt b/_sources/api/modeling/SolutionDual.rst.txt new file mode 100644 index 00000000..60b141e7 --- /dev/null +++ b/_sources/api/modeling/SolutionDual.rst.txt @@ -0,0 +1,6 @@ +.. _api_SolutionDual: + +Solution::Dual +================ + +.. doxygenclass:: idol::Solution::Dual diff --git a/_sources/api/modeling/SolutionPrimal.rst.txt b/_sources/api/modeling/SolutionPrimal.rst.txt new file mode 100644 index 00000000..1d5a4242 --- /dev/null +++ b/_sources/api/modeling/SolutionPrimal.rst.txt @@ -0,0 +1,6 @@ +.. _api_SolutionPrimal: + +Solution::Primal +================ + +.. doxygenclass:: idol::Solution::Primal diff --git a/_sources/api/modeling/TempCtr.rst.txt b/_sources/api/modeling/TempCtr.rst.txt new file mode 100644 index 00000000..ee27bcce --- /dev/null +++ b/_sources/api/modeling/TempCtr.rst.txt @@ -0,0 +1,6 @@ +.. _api_TempCtr: + +TempCtr +======= + +.. doxygenclass:: idol::TempCtr diff --git a/_sources/api/modeling/TempVar.rst.txt b/_sources/api/modeling/TempVar.rst.txt new file mode 100644 index 00000000..d6b70635 --- /dev/null +++ b/_sources/api/modeling/TempVar.rst.txt @@ -0,0 +1,6 @@ +.. _api_TempVar: + +TempVar +======= + +.. doxygenclass:: idol::TempVar diff --git a/_sources/api/modeling/Var.rst.txt b/_sources/api/modeling/Var.rst.txt new file mode 100644 index 00000000..431108bb --- /dev/null +++ b/_sources/api/modeling/Var.rst.txt @@ -0,0 +1,6 @@ +.. _api_var: + +Var +=== + +.. doxygenclass:: idol::Var diff --git a/_sources/api/modeling/index.rst.txt b/_sources/api/modeling/index.rst.txt new file mode 100644 index 00000000..7727b861 --- /dev/null +++ b/_sources/api/modeling/index.rst.txt @@ -0,0 +1,10 @@ +.. _api_modeling: + +Modeling +======== + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/api/optimizers/branch-and-bound/BranchAndBound.rst.txt b/_sources/api/optimizers/branch-and-bound/BranchAndBound.rst.txt new file mode 100644 index 00000000..b44abddf --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/BranchAndBound.rst.txt @@ -0,0 +1,31 @@ +.. _api_BranchAndBound: + +BranchAndBound +============== + +This class is an optimizer factory which creates a new branch-and-bound algorithm. +It can be used to create customized branch-and-bound algorithms with a large degree of freedom. + +.. seealso:: + + If you are not familiar with optimizers and optimizer factories, please refer to :ref:`this page `. + +.. admonition:: Example + + Here, we create a simple branch-and-bound algorithm where branching is done on integer variables which are being + relaxed. Each node is solved by the external solver GLPK. Nodes are selected according to the "best-bound" + rule while variables are selected according to the "most-infeasible" branching rule. + + The created algorithm also incorporates sub-tree exploration of maximum depth 2. + + .. code-block:: + + model.use( + BranchAndBound() + .with_node_optimizer( GLPK::ContinuousRelaxation() ) + .with_branching_rule( MostInfeasible() ) + .with_node_selection_rule( BestBound() ) + .with_subtree_depth(2) + ); + +.. doxygenclass:: idol::BranchAndBound diff --git a/_sources/api/optimizers/branch-and-bound/BranchAndBoundCallback.rst.txt b/_sources/api/optimizers/branch-and-bound/BranchAndBoundCallback.rst.txt new file mode 100644 index 00000000..5432eb88 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/BranchAndBoundCallback.rst.txt @@ -0,0 +1,74 @@ +.. _api_BranchAndBoundCallback: + +BranchAndBoundCallback +====================== + +This class can be used to create callbacks to run on idol's :ref:`branch-and-bound implementation `. + +.. warning:: + + BranchAndBoundCallback-s is an *advanced* feature. + + Please, make sure that what you are trying do cannot be done with + a :ref:`solver-independent callback ` first, or with pre-existing callbacks, e.g., + :ref:`UserCutCallback ` or :ref:`LazyCutCallback `. + + The advantage of using a :ref:`BranchAndBoundCallback ` instead of a standard + solver-independent :ref:`Callback ` lies in the possibility to access specific information regarding + the execution of the branch-and-bound algorithm. For instance, accessing a node's information, or the current + relaxation model being solved. + +.. admonition:: Example + + Here is an example of callback which prints out the event triggering it and, when the event corresponds to `NodeLoaded`, + prints the node's model to be solved. + + .. code-block:: + + class MyCallback : public BranchAndBoundCallbackFactory { + public: + class Strategy : public BranchAndBoundCallback { + protected: + void operator()(CallbackEvent t_event) override { + + std::cout << "MyCallback is called for " << t_event << std::endl; + + if (t_event != NodeLoaded) { + return; + } + + std::cout << "The problem being solve at node " << node().id() << std::endl; + std::cout << relaxation() << std::endl; + + } + }; + + BranchAndBoundCallback *operator()() override { + return new Strategy(); + } + + [[nodiscard]] BranchAndBoundCallbackFactory *clone() const override { + return new MyCallback(*this); + } + }; + + Then, this callback can be used as follows. + + .. code-block:: + + model.use( + BranchAndBound() + .with_node_optimizer(GLPK::ContinuousRelaxation()) + .with_branching_rule(MostInfeasible()) + .with_node_selection_rule(DepthFirst()) + .with_callback(MyCallback()); + ); + +.. hint:: + + By default, most of the objects returned by BranchAndBoundCallback methods are const. If you wish to access non-const + versions (e.g., if you want to perform non-standard updates to the relaxed model or want to change the node's current + information manually), you should use the advanced interface obtained by calling ``BranchAndBoundCallback::advanced_interface``. + +.. doxygenclass:: idol::BranchAndBoundCallback + :protected-members: diff --git a/_sources/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.rst.txt b/_sources/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.rst.txt new file mode 100644 index 00000000..8024dfe2 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.rst.txt @@ -0,0 +1,6 @@ +.. _api_MostInfeasible: + +MostInfeasible +============== + +.. doxygenclass:: idol::MostInfeasible diff --git a/_sources/api/optimizers/branch-and-bound/branching-rules/index.rst.txt b/_sources/api/optimizers/branch-and-bound/branching-rules/index.rst.txt new file mode 100644 index 00000000..fc91078b --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/branching-rules/index.rst.txt @@ -0,0 +1,10 @@ +.. _api_branching_rules: + +Branching rules +=============== + +.. toctree:: + :maxdepth: 2 + :glob: + + MostInfeasible \ No newline at end of file diff --git a/_sources/api/optimizers/branch-and-bound/index.rst.txt b/_sources/api/optimizers/branch-and-bound/index.rst.txt new file mode 100644 index 00000000..20b843b9 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/index.rst.txt @@ -0,0 +1,13 @@ +.. _api_branch_and_bound: + +Branch-And-Bound algorithms +=========================== + +.. toctree:: + :maxdepth: 2 + :glob: + + BranchAndBound + branching-rules/index + node-selection-rules/index + BranchAndBoundCallback \ No newline at end of file diff --git a/_sources/api/optimizers/branch-and-bound/node-selection-rules/BestBound.rst.txt b/_sources/api/optimizers/branch-and-bound/node-selection-rules/BestBound.rst.txt new file mode 100644 index 00000000..06d82014 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/node-selection-rules/BestBound.rst.txt @@ -0,0 +1,6 @@ +.. _api_BestBound: + +BestBound +========= + +.. doxygenclass:: idol::BestBound diff --git a/_sources/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.rst.txt b/_sources/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.rst.txt new file mode 100644 index 00000000..dd8e6551 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.rst.txt @@ -0,0 +1,6 @@ +.. _api_BreadthFirst: + +BreadthFirst +============ + +.. doxygenclass:: idol::BreadthFirst diff --git a/_sources/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.rst.txt b/_sources/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.rst.txt new file mode 100644 index 00000000..933582f3 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.rst.txt @@ -0,0 +1,6 @@ +.. _api_DepthFirst: + +DepthFirst +========== + +.. doxygenclass:: idol::DepthFirst diff --git a/_sources/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.rst.txt b/_sources/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.rst.txt new file mode 100644 index 00000000..29068ea0 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.rst.txt @@ -0,0 +1,6 @@ +.. _api_WorstBound: + +WorstBound +========== + +.. doxygenclass:: idol::WorstBound diff --git a/_sources/api/optimizers/branch-and-bound/node-selection-rules/index.rst.txt b/_sources/api/optimizers/branch-and-bound/node-selection-rules/index.rst.txt new file mode 100644 index 00000000..290f71a7 --- /dev/null +++ b/_sources/api/optimizers/branch-and-bound/node-selection-rules/index.rst.txt @@ -0,0 +1,13 @@ +.. _api_node_selection_rules: + +Node selection rules +==================== + +.. toctree:: + :maxdepth: 2 + :glob: + + BestBound + WorstBound + DepthFirst + BreadthFirst \ No newline at end of file diff --git a/_sources/api/optimizers/callbacks/Callback.rst.txt b/_sources/api/optimizers/callbacks/Callback.rst.txt new file mode 100644 index 00000000..63c00d3a --- /dev/null +++ b/_sources/api/optimizers/callbacks/Callback.rst.txt @@ -0,0 +1,85 @@ +.. _api_Callback: + +Callback +======== + +Callbacks are user-defined functions which are invoked during the execution of branch-and-bound algorithms at certain +key steps of the procedure. These key points are called :ref:`events ` in idol. +Callback functions can be used to monitor the algorithm's progress, control its behavior, or perform additional processing. + +UserCutCallback and LazyCutCallback +----------------------------------- + +A common use of callbacks is to implement custom cut generation procedures at each node of the branch-and-bound tree. Note that +idol offers out-of-the-box callback routines for cut separation. Namely, :ref:`UserCutCallback ` +and :ref:`LazyCutCallback `. Yet, it is totally possible to define your own cut generation procedure +by using the ``Callback::add_user_cut`` and ``Callback::add_lazy_cut`` methods inside your callback. + +In a nutshell, :ref:`UserCutCallback ` (or, similarly, ``Callback::add_user_cut``) are intended for +cuts which have a potential to improve the quality of the relaxation but whose presence in the model is not necessary for the +branch-and-bound to converge to an optimal solution. :ref:`UserCutCallback ` callbacks are called when +a non-valid solution has been found. + +:ref:`LazyCutCallback ` (or, similarly, ``Callback::add_lazy_cut``), +instead, are intended to generate constraints which should be part of the model but which were omitted in the model for some reason. +A typical reason for omitting constraints in a model's definition is the large number of such constraints. +:ref:`LazyCutCallback ` callbacks are called when a valid solution has been found. + +Creating your own callback +-------------------------- + +If you want to create your own callback, you should first create a new class which inherits the ``Callback`` class and +overrides the ``operator()(CallbackEvent)`` method. + +Note that callbacks cannot be given "as-is" to an optimizer but must be passed through a ``CallbackFactory``. A callback +factory is a class whose role is to create a new callback object whenever it is needed. Every callback factories must be +a child (or little child) of the ``CallbackFactory`` class. + +.. admonition:: Example + + We now give an example of callback which prints out every valid solution found. + + .. code-block:: + + class MyCallback : public CallbackFactory { + public: + + class Strategy { // Real callback implementation + protected: + void operator()(CallbackEvent t_event) { + + if (t_event != IncumbentSolution) { + return; + } + + std::cout << primal_solution() << std::endl; + } + } + + Callback* operator()() { // Creates a new callback object + return new Strategy(); + } + + CallbackFactory* clone() const { // Creates a copy of the callback factory + return new MyCallback(*this); + } + + } + + Later, it is then possible to use this callback in compliant optimizers like :ref:`Gurobi ` or :ref:`BranchAndBound `. + + .. code-block:: + + model.use( + Gurobi().with_callback(MyCallback(); + ); + + model.optimize(); + +.. hint:: + + Note that there also exists more advanced callbacks which are specific to idol's branch-and-bound implementation. + For these advanced feature, see :ref:`BranchAndBoundCallback `. + +.. doxygenclass:: idol::Callback + :protected-members: diff --git a/_sources/api/optimizers/callbacks/CallbackEvent.rst.txt b/_sources/api/optimizers/callbacks/CallbackEvent.rst.txt new file mode 100644 index 00000000..823233be --- /dev/null +++ b/_sources/api/optimizers/callbacks/CallbackEvent.rst.txt @@ -0,0 +1,6 @@ +.. _api_CallbackEvent: + +Events +====== + +.. doxygenenum:: idol::CallbackEvent \ No newline at end of file diff --git a/_sources/api/optimizers/callbacks/LazyCutCallback.rst.txt b/_sources/api/optimizers/callbacks/LazyCutCallback.rst.txt new file mode 100644 index 00000000..2197b5f0 --- /dev/null +++ b/_sources/api/optimizers/callbacks/LazyCutCallback.rst.txt @@ -0,0 +1,60 @@ +.. _api_LazyCutCallback: + +LazyCutCallback +=============== + +Lazy cuts are essentially constraints which are part of an optimization model but which have been omitted in the current +definition of the model. Lazy cuts typically arise in models with a large number of constraints. Instead of enumerating +then all, it may be judicious to omit some of them to get a smaller optimization model. Then, the returned solution is +checked for feasibility against the whole set of constraints. If a violated constraint is identified, we add the +constraint to the model and resolve. If not, then all the constraints are satisfied and the solution is optimal for the +original model in which all constraints materializes. + +The LazyCutCallback can be used to implement lazy cut constraint generation on the fly, during the optimization process. + +Consider the following optimization problem: + +.. math:: + + \begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X, \\ + & \xi^\top x \le \xi_0 \quad (\xi_0,\xi) \in \Xi, + \end{align} + +in which assume that :math:`|\Xi|` is large (potentially infinite). The idea is to start by solving the following +relaxed master problem in which constraints associated to :math:`(\xi_0,\xi)` have been omitted. + +.. math:: + + \begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X. + \end{align} + +If we assume that this problem is feasible and bounded, we can denote by :math:`x^*` a solution of this problem. Then, +we search for a violated constraint ":math:`\xi^\top x \le \xi_0`" for some :math:`(\xi_0,\xi)\in\Xi`. Observe that +a constraint is violated if, and only if, the following holds: + +.. math:: + + \left(\exists(\xi_0,\xi)\in\Xi, \ \xi^\top x^* > \xi_0\right) + \Leftrightarrow + \left(\max_{(\xi_0,\xi)\in\Xi} \xi_0 - \xi^\top x^* < 0\right). + +Thus, the LazyCutCallback automatically solve the optimization problem on the right handside and checks for its value. +A new constraint is added if, and only if, + +.. math:: + \max_{\xi\in\Xi} \xi_0 - \xi^\top x^* < -\varepsilon, + +with :math:`\varepsilon` a given tolerance (by default, :code:`Tolerance::Feasibility`). + + +.. hint:: + + You may also be interested by a tutorial showing how you can implement a simple Benders Decomposition using lazy + cuts. :ref:`See Benders Decomposition tutorial `. + + +.. doxygenclass:: idol::LazyCutCallback \ No newline at end of file diff --git a/_sources/api/optimizers/callbacks/UserCutCallback.rst.txt b/_sources/api/optimizers/callbacks/UserCutCallback.rst.txt new file mode 100644 index 00000000..cf10e6e1 --- /dev/null +++ b/_sources/api/optimizers/callbacks/UserCutCallback.rst.txt @@ -0,0 +1,6 @@ +.. _api_UserCutCallback: + +UserCutCallback +=============== + +.. doxygenclass:: idol::UserCutCallback \ No newline at end of file diff --git a/_sources/api/optimizers/callbacks/index.rst.txt b/_sources/api/optimizers/callbacks/index.rst.txt new file mode 100644 index 00000000..fa5c54a9 --- /dev/null +++ b/_sources/api/optimizers/callbacks/index.rst.txt @@ -0,0 +1,16 @@ +.. _api_callbacks: + +Callbacks +========= + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 4 + :glob: + + CallbackEvent + Callback + LazyCutCallback + UserCutCallback diff --git a/_sources/api/optimizers/column-generation/ColumnGeneration.rst.txt b/_sources/api/optimizers/column-generation/ColumnGeneration.rst.txt new file mode 100644 index 00000000..69b0e769 --- /dev/null +++ b/_sources/api/optimizers/column-generation/ColumnGeneration.rst.txt @@ -0,0 +1,13 @@ +.. _api_ColumnGeneration: + +ColumnGeneration +================ + +.. danger:: + + Currently, the master problem must have a "convexity constraint" for the algorithm to converge. + Problems without this property will lead to undefined behavior. + + We strongly advise you to use :ref:`DantzigWolfeDecomposition ` instead. + +.. doxygenclass:: idol::ColumnGeneration diff --git a/_sources/api/optimizers/column-generation/DantzigWolfeDecomposition.rst.txt b/_sources/api/optimizers/column-generation/DantzigWolfeDecomposition.rst.txt new file mode 100644 index 00000000..167b82a2 --- /dev/null +++ b/_sources/api/optimizers/column-generation/DantzigWolfeDecomposition.rst.txt @@ -0,0 +1,12 @@ +.. _api_DantzigWolfeDecomposition: + +DantzigWolfeDecomposition +========================= + +.. hint:: + + This page documents on the DantzigWolfeDecomposition optimizer factory. Note that there is also a + :ref:`Dantzig-Wolfe decomposition tutorial ` which shows how to solve a + Generalized Assignment Problem by using a branch-and-price algorithm. + +.. doxygenclass:: idol::DantzigWolfeDecomposition diff --git a/_sources/api/optimizers/column-generation/index.rst.txt b/_sources/api/optimizers/column-generation/index.rst.txt new file mode 100644 index 00000000..7c842979 --- /dev/null +++ b/_sources/api/optimizers/column-generation/index.rst.txt @@ -0,0 +1,14 @@ +.. _api_column_generation: + +Column-Generation algorithms +============================ + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 4 + :glob: + + ColumnGeneration + DantzigWolfeDecomposition diff --git a/_sources/api/optimizers/glpk/GLPK.rst.txt b/_sources/api/optimizers/glpk/GLPK.rst.txt new file mode 100644 index 00000000..24b1b493 --- /dev/null +++ b/_sources/api/optimizers/glpk/GLPK.rst.txt @@ -0,0 +1,4 @@ +GLPK +==== + +.. doxygenclass:: idol::GLPK diff --git a/_sources/api/optimizers/glpk/index.rst.txt b/_sources/api/optimizers/glpk/index.rst.txt new file mode 100644 index 00000000..fa8cd3ab --- /dev/null +++ b/_sources/api/optimizers/glpk/index.rst.txt @@ -0,0 +1,13 @@ +.. _api_GLPK: + +GLPK interface +============== + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 2 + :glob: + + GLPK \ No newline at end of file diff --git a/_sources/api/optimizers/gurobi/Gurobi.rst.txt b/_sources/api/optimizers/gurobi/Gurobi.rst.txt new file mode 100644 index 00000000..06c2f356 --- /dev/null +++ b/_sources/api/optimizers/gurobi/Gurobi.rst.txt @@ -0,0 +1,4 @@ +Gurobi +====== + +.. doxygenclass:: idol::Gurobi diff --git a/_sources/api/optimizers/gurobi/index.rst.txt b/_sources/api/optimizers/gurobi/index.rst.txt new file mode 100644 index 00000000..400aeae9 --- /dev/null +++ b/_sources/api/optimizers/gurobi/index.rst.txt @@ -0,0 +1,13 @@ +.. _api_Gurobi: + +Gurobi interface +================ + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 2 + :glob: + + Gurobi \ No newline at end of file diff --git a/_sources/api/optimizers/index.rst.txt b/_sources/api/optimizers/index.rst.txt new file mode 100644 index 00000000..e36df96c --- /dev/null +++ b/_sources/api/optimizers/index.rst.txt @@ -0,0 +1,134 @@ +.. _api_optimizers: + +Optimizers +========== + +Introduction +------------ + +Optimizers denote the algorithms which are being used by idol to solve a given ``Model``. +They are set by using the ``Model::use`` method, as done in the following example. + +.. code-block:: cpp + + Env env; + + Model my_model(env); + + my_model.use( Gurobi() ); // setting the optimizer of my_model to Gurobi() + +Here, ``Gurobi`` is actually an ``OptimizerFactory`` which will eventually create an optimizer to solve our model. Indeed, +the "real" optimizer in this case will be an instance of ``Optimizers::Gurobi`` which will be created when necessary. + +This mechanism is what allows idol to create complex algorithms by combining optimizers together. Here is a second example +which creates a nested branch-and-price algorithm. + +.. code-block:: cpp + + auto nested_branch_and_price = + + /* The overall algorithm is a branch-and-bound */ + BranchAndBound() + + /* Each node is solved with a Dantzig-Wolfe decomposition algorithm */ + .with_node_solver( + + /* The annotation "decomposition1" is used to automatically decompose the problem */ + DantzigWolfeDecomposition(decomposition1) + + /* The master problem is solved using Gurobi */ + .with_master_optimizer(Gurobi::ContinuousRelaxation()) + + /* Each pricing problem is solved by a (nested) branch-and-bound algorithm */ + .with_pricing_solver( + + BranchAndBound() + + /* Each node is solved by a dantzig-wolfe decomposition algorithm */ + .with_nodes_solver( + + /* The annotation "decomposition2" is used to decompose the sub-problem again */ + DantzigWolfeDecomposition(decomposition2) + + /* The master problem is solved using Mosek */ + .with_master_optimizer(Mosek::ContinuousRelaxation()) + + /* The sub-problem is solved by a (nested) branch-and-bound algorithm [we could have used, e.g., Gurobi instead] */ + .with_pricing_optimizer( + + BranchAndBound() + + /* Each node is solved by GLPK */ + .with_node_solver(GLPK::ContinuousRelaxation()) + + /* Variables are selected for branching using the most-infeasible rule */ + .with_branching_rule(MostInfeasible()) + + /* Nodes are selected using the worst-bound rule */ + .with_node_selection_rule(WorstBound()) + + ) + + /* Branching constraints are applied to the pricing problem */ + .with_branching_on_master(false) + ) + /* Variables are selected for branching using the most-infeasible rule */ + .with_branching_rule(MostInfeasible()) + + /* Nodes are selected using the depth-first rule */ + .with_node_selection_rule(DepthFirst()) + ) + + /* Column generation is stabilized by dual-price smoothing */ + .with_dual_price_smoothing_stabilization(.3) + + /* Infeasible master problem are dealt with using Farkas pricing */ + .with_farkas_pricing() + + /* Branching constraints are applied to the master problem */ + .with_branching_on_master() + ) + /* Variables are selected for branching using the most-infeasible rule */ + .with_branching_rule(MostInfeasible()) + + /* Nodes are selected using the best-bound rule */ + .with_node_selection_rule(BestBound() + + /* Only informational logs will be printed (in blue) */ + .with_log_level(Info, Blue) + + /* The algorithm will run with a time limit of 3600 */ + .with_time_limit(3600) + ) + + my_model.use(nested_branch_and_price); + +Once an optimizer, or rather, an optimizer factory, has been given, the ``Model::optimize`` method can be called to actually +solve the model. + +.. code-block:: + + my_model.optimize(); + +Optimizer factories +------------------- + +Typically, a user mostly works with optimizer factories rather than with optimizers. Optimizer factories are like +"building plans" for creating actual optimizers. They usually can be recognized by their ``with_*`` functions allowing +the user to customize this plan. For instance, the ``BranchAndBound`` optimizer factory has a method ``with_node_optimizer`` +allowing the user to pass yet another optimizer factory which will be used to create optimizers for the branch-and-bound +nodes. + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 4 + :glob: + + branch-and-bound/index + column-generation/index + glpk/index + gurobi/index + mosek/index + callbacks/index diff --git a/_sources/api/optimizers/mosek/Mosek.rst.txt b/_sources/api/optimizers/mosek/Mosek.rst.txt new file mode 100644 index 00000000..ce11678d --- /dev/null +++ b/_sources/api/optimizers/mosek/Mosek.rst.txt @@ -0,0 +1,4 @@ +Mosek +===== + +.. doxygenclass:: idol::Mosek diff --git a/_sources/api/optimizers/mosek/index.rst.txt b/_sources/api/optimizers/mosek/index.rst.txt new file mode 100644 index 00000000..fde2b541 --- /dev/null +++ b/_sources/api/optimizers/mosek/index.rst.txt @@ -0,0 +1,13 @@ +.. _api_Mosek: + +Mosek interface +=============== + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 2 + :glob: + + Mosek \ No newline at end of file diff --git a/_sources/api/problems/ProblemsFLP.rst.txt b/_sources/api/problems/ProblemsFLP.rst.txt new file mode 100644 index 00000000..ed8155a7 --- /dev/null +++ b/_sources/api/problems/ProblemsFLP.rst.txt @@ -0,0 +1,4 @@ +Facility Location Problem (FLP) +=============================== + +.. doxygennamespace:: idol::Problems::FLP diff --git a/_sources/api/problems/ProblemsGAP.rst.txt b/_sources/api/problems/ProblemsGAP.rst.txt new file mode 100644 index 00000000..f550c328 --- /dev/null +++ b/_sources/api/problems/ProblemsGAP.rst.txt @@ -0,0 +1,4 @@ +Generalized Assignment Problem (GAP) +==================================== + +.. doxygennamespace:: idol::Problems::GAP diff --git a/_sources/api/problems/ProblemsKP.rst.txt b/_sources/api/problems/ProblemsKP.rst.txt new file mode 100644 index 00000000..4ce82f7f --- /dev/null +++ b/_sources/api/problems/ProblemsKP.rst.txt @@ -0,0 +1,4 @@ +Knapsack Problem (KP) +===================== + +.. doxygennamespace:: idol::Problems::KP diff --git a/_sources/api/problems/ProblemsMKP.rst.txt b/_sources/api/problems/ProblemsMKP.rst.txt new file mode 100644 index 00000000..0adce681 --- /dev/null +++ b/_sources/api/problems/ProblemsMKP.rst.txt @@ -0,0 +1,4 @@ +Multiple Knapsack Problem (MKP) +=============================== + +.. doxygennamespace:: idol::Problems::MKP diff --git a/_sources/api/problems/ProblemsSRP.rst.txt b/_sources/api/problems/ProblemsSRP.rst.txt new file mode 100644 index 00000000..793ffc56 --- /dev/null +++ b/_sources/api/problems/ProblemsSRP.rst.txt @@ -0,0 +1,4 @@ +Staff Rostering Problem (SRP) +=============================== + +.. doxygennamespace:: idol::Problems::SRP diff --git a/_sources/api/problems/index.rst.txt b/_sources/api/problems/index.rst.txt new file mode 100644 index 00000000..c3886b36 --- /dev/null +++ b/_sources/api/problems/index.rst.txt @@ -0,0 +1,10 @@ +.. _api_problems: + +Problems +======== + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/api/tolerances.rst.txt b/_sources/api/tolerances.rst.txt new file mode 100644 index 00000000..d90896c9 --- /dev/null +++ b/_sources/api/tolerances.rst.txt @@ -0,0 +1,4 @@ +Tolerances +========== + +.. doxygennamespace:: idol::Tolerance diff --git a/_sources/developer_guide/build-the-doc.rst.txt b/_sources/developer_guide/build-the-doc.rst.txt new file mode 100644 index 00000000..4d331aef --- /dev/null +++ b/_sources/developer_guide/build-the-doc.rst.txt @@ -0,0 +1,61 @@ +.. highlight:: sh +.. _dev_build_the_doc: + +Build the doc! +============== + +This page explains how to build the documentation on a local machine. + +Dependencies +------------ + +Description +^^^^^^^^^^^ + +The documentation is built using `doxygen`_ and a bunch of other tools, in particular: + +* `doxygen`_ the C++ documentation generator; +* `Sphinx`_ the python documentation generator; +* `sphinx-rtd-theme `_ a Sphinx theme used to render the + HTML version of the documentation; +* `sphinx-sitemap `_ a Sphinx extension + to generate multi-version and multi-language sitemaps.org compliant sitemaps for the HTML version + of a Sphinx documentation; +* `sphinx-copybutton `_ a Sphinx extension which + automatically adds buttons on code-blocks environments to copy its content; +* `Breathe`_ the Sphinx plugin for integrating doxygen outputs into Sphinx. + +For a detailed description on how these tools interact, please refer to `this article `_. + +Installation guide (Ubuntu) +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +:: + + sudo apt-get install doxygen # installs the last version of doxygen + + sudo apt-get install python3-sphinx # installs the last version of Sphinx + + sudo apt-get install python3-breathe # installs the last version of Breathe + + pip3 install sphinx-sitemap sphinx-rtd-theme sphinx-copybutton # installs theme and extensions + +Build instructions +------------------ + +By default, CMake automatically creates a ``doc`` target. All you have to do to build the documentation website +is to build this target. For instance, inside a ``build`` directory, the following command can be used. + +:: + + cmake .. && make doc + +Note that you do not need to use ``make`` and use the following generic command. + +:: + + cmake --build . --target doc + +.. _doxygen: https://doxygen.nl/ +.. _Sphinx: https://www.sphinx-doc.org/en/master/ +.. _Breathe: https://github.com/breathe-doc/breathe \ No newline at end of file diff --git a/_sources/developer_guide/index.rst.txt b/_sources/developer_guide/index.rst.txt new file mode 100644 index 00000000..e222b3ee --- /dev/null +++ b/_sources/developer_guide/index.rst.txt @@ -0,0 +1,11 @@ +.. _dev: + +Developer guide +=============== + +.. toctree:: + :maxdepth: 2 + :glob: + + build-the-doc + tests \ No newline at end of file diff --git a/_sources/developer_guide/tests.rst.txt b/_sources/developer_guide/tests.rst.txt new file mode 100644 index 00000000..bd9cfb10 --- /dev/null +++ b/_sources/developer_guide/tests.rst.txt @@ -0,0 +1,91 @@ +.. _tests: + +Unit and integration tests +========================== + +This page explains how to build the unit and integration tests on a local machine. + +Dependencies +------------ + +Tests are managed by the C++ unit testing framework `Catch2 `_. + +When CMake is told to create test targets, it will automatically look for an installation of Catch2 on your +machine. If it cannot be found, CMake will attempt to download Catch2 from its GitHub repository. + + +Installation guide (Ubuntu) +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: shell + + git clone https://github.com/catchorg/Catch2.git # Clone Catch2 repository + + cd Catch2 # go inside the new directory + + cmake -Bbuild -H. -DBUILD_TESTING=OFF # Create install target + + sudo cmake --build build/ --target install # Build and install + + +Build instructions +------------------ + +By default, CMake will not create test targets nor look for Catch2. To tell CMake to generate them, you +need to set the CMake option ``BUILD_TESTS`` to ``YES``. + + +.. admonition:: Example + + The following will tell CMake to create targets for tests. + + .. code-block:: + + cmake -DBUILD_TESTS=YES .. + + For instance, we can now build all the existing tests + + .. code-block:: + + make tests + + and run them. + + .. code-block:: + + ./tests/tests + +Code coverage options +--------------------- + +Code coverage is done via ``gcov``. + +If you want to active code coverage options, you shall set the CMake option ``WITH_TEST_COVERAGE`` to ``YES``. +Note that this only has an effect when ``BUILD_TESTS`` is also set to ``YES``. + +.. admonition:: Example + + The following command will tell CMake to generate targets for tests with code coverage options. + + .. code-block:: + + cmake -DBUILD_TESTS=YES -DWITH_CODE_COVERAGE=YES .. + + Then, you should build and run the tests. + + .. code-block:: + + make tests && ./tests/tests + + Once you are there, you may generate a report to a file called ``coverage.info`` by using ``gcov``. + + .. code-block:: + + lcov --directory . --capture --output-file coverage.info + +Also note that this forces ``g++`` to be used for compiling. + +.. tip:: + + Code coverage reports are also automatically generated at every push action on idol's GitHub repository and + are available on `codecov `_. diff --git a/_sources/examples/facility-location-problem.rst.txt b/_sources/examples/facility-location-problem.rst.txt new file mode 100644 index 00000000..ebd29f63 --- /dev/null +++ b/_sources/examples/facility-location-problem.rst.txt @@ -0,0 +1,6 @@ +Facility Location Problem / Branch-and-Bound +============================================ + + +.. literalinclude:: ../../examples/facility-location-problem/main.cpp + :language: cpp diff --git a/_sources/examples/generalized-assignment-problem.rst.txt b/_sources/examples/generalized-assignment-problem.rst.txt new file mode 100644 index 00000000..b48f2d98 --- /dev/null +++ b/_sources/examples/generalized-assignment-problem.rst.txt @@ -0,0 +1,5 @@ +Generalized Assignment Problem / Branch-and-Price +================================================= + +.. literalinclude:: ../../examples/generalized-assignment-problem/main.cpp + :language: cpp diff --git a/_sources/examples/index.rst.txt b/_sources/examples/index.rst.txt new file mode 100644 index 00000000..91935202 --- /dev/null +++ b/_sources/examples/index.rst.txt @@ -0,0 +1,14 @@ +.. _examples: + +Examples +======== + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 2 + + knapsack-problem + facility-location-problem + generalized-assignment-problem \ No newline at end of file diff --git a/_sources/examples/knapsack-problem.rst.txt b/_sources/examples/knapsack-problem.rst.txt new file mode 100644 index 00000000..3a2f4187 --- /dev/null +++ b/_sources/examples/knapsack-problem.rst.txt @@ -0,0 +1,5 @@ +Knapsack Problem / Gurobi +========================= + +.. literalinclude:: ../../examples/knapsack-problem/main.cpp + :language: cpp diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 00000000..1410bdfa --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,151 @@ +Welcome to idol! +================ + +.. image:: https://img.shields.io/github/license/hlefebvr/idol +.. image:: https://img.shields.io/github/v/tag/hlefebvr/idol?label=version +.. image:: https://img.shields.io/github/actions/workflow/status/hlefebvr/idol/cmake.yml?branch=main +.. image:: https://img.shields.io/github/issues-raw/hlefebvr/idol +.. image:: https://www.repostatus.org/badges/latest/wip.svg +.. image:: https://codecov.io/github/hlefebvr/idol/branch/main/graph/badge.svg?token=BWMH5522QP)](https://app.codecov.io/gh/hlefebvr/idol + +.. toctree:: + :maxdepth: 2 + :caption: Contents: + +Idol is a C++ library for implementing complex decomposition algorithms for +mathematical optimization. + +Its main goal is to ease the development of new mathematical optimization techniques to +solve complex optimization problems. It offers a user-friendly interface to build new algorithms +on top of state-of-the-art methods like Dantzig-Wolfe decomposition, Benders decomposition or +column-and-constraint generation. + +New to idol? +------------ + +If you are new to idol, I advise you to visit our :ref:`installation guideline `. +In particular, have a look at the :ref:`local installation guideline `. +It is the easiest installation process one could think of since it automatically downloads the latest version of idol and +installs it in a local folder. It's really a mater of seconds before you can start using idol. + +.. admonition:: Example + + Idol has a user-friendly interface which should look natural to people working in optimization. For instance, + here is how one solves a Knapsack Problem using the `Gurobi `_ solver. + + .. code:: cpp + + using namespace idol; + + const unsigned int n_items = 5; + const double[] profit = { 40., 50., 100., 95., 30., }; + const double[] weight = { 2., 3.14, 1.98, 5., 3., }; + const double capacity = 10.; + + Env env; + + Model model(env); + + auto x = model.add_vars(Dim<1>(n_items), 0., 1., Binary, "x"); + + model.add_ctr(idol_Sum(j, Range(n_items), weight[j] * x[j]) <= capacity); + + model.set_obj_expr(idol_Sum(j, Range(n_items), -profits[j] * x[j]); + + model.use(Gurobi()); + + model.optimize(); + +If you want to learn more about idol's modeling interface, be sure to visit :ref:`beginner tutorials `. + +If you are more experienced, you may want to have a look at our :ref:`decomposition methods tutorials `. + +Is this a MIP solver? +--------------------- + +The idol library is not a MIP solver in itself. Indeed, it typically needs to call external +solvers (e.g., `GLPK `_ or `Gurobi `_) +as a sub-routine of more complex algorithmic schemes (e.g., column generation). +The idea is to work hand in hand with existing fine-tuned and well-engineered optimization +softwares to enhance their possibilities to solve e.g., larger problems or problems which +cannot directly be modeled as MIPs (e.g., :math:`\Sigma_i^P`-hard problems). + +Each subproblem is then solved by an external and dedicated solver. +Currently, the following external solvers can be interfaced: + +* `Gurobi `_; +* `Mosek `_; +* `GLPK `_. + +Current features +---------------- + +.. warning:: + + Handling quadratic expressions is an experimental feature and extreme care should be taken if used. + +Interfacing external optimization solvers +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The idol library can be used to interface external solvers like `GLPK `_ +or `Gurobi `_ to solve standalone MI(N)LPs. It offers a unified and common +interface to every solver including standard parameters and branch-and-bound callbacks. +Thus, you can write your code once and test it with different solvers! + +Generic Branch-and-Bound algorithms +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Idol allows its user to create custom branch-and-bound scheme very easily where almost everything can be tweaked. + +* *Node agnostic implementation*. The branch-and-bound algorithm can work with any node type as long as the user properly + defines how nodes must be updated. A default node type is already implemented for classical variable branching. This + node type can also be inherited, e.g., to enrich the information carried out from each parent node to its children. +* *Customizable branching rule*. The default branching rules include: most-infeasible rule. +* *Customizable node selection rule*. The default node selection rules include: best-bound, worst-bound, depth-first, breadth-first. +* *Callbacks*. The user can specify its own callback to locally or globally modify a node's problem, submit heuristic solutions, + or influence the execution of the overall algorithm. +* *Branch-and-bound with phases*. Independently on any of the above settings, the B&B algorithm supports sub-trees exploration + to reach valid solutions to the original problem as quick as possible. + +**Features to come/desired features** + +* *Parallelization of the algorithm*. +* *New branching rules*: pseudo-cost, strong-branching and reliability branching. +* *Default cutting planes*. + +Generic Column Generation and Dantzig-Wolfe decomposition +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Idol can be used to build and custom column-generation algorithms with the following features. + +* *Infeasible master problem procedures*. Idol can handle an infeasible master problem by resorting to Farkas pricing or + by adding artificial variables to the original problem (note that if this fails, idol will then switch to pure phase I + so as to exactly prove infeasibility). +* *Automatic pool clean up*. If the master problem contains too many variables, they can be automatically removed. This can be + all controlled by user parameters. +* *Stabilization via dual price smoothing*. The column generation procedure can be stabilized using dual price smoothing + controlled by user inputs. +* *Parallel pricing*. Each pricing problem can be solved in parallel by means of a single parameter. +* *Nested column generation*. A key idea of idol is that every optimizer is seen as a black-box to solve a given optimization model. + As such, a column-generation algorithm can easily be "plugged in" any algorithmic phase. For instance, solving the pricing of + a column-generation algorithm can be done by yet another column-generation algorithm. + +**Features to come/desired features** + +* *Handling identical sub-systems*. +* *Ryan-and-Foster* branching rule. + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 2 + + self + installation/index + tutorials/index + examples/index + api/index + developer_guide/index + +* :ref:`genindex` diff --git a/_sources/installation/global_installation.rst.txt b/_sources/installation/global_installation.rst.txt new file mode 100644 index 00000000..c5b49950 --- /dev/null +++ b/_sources/installation/global_installation.rst.txt @@ -0,0 +1,96 @@ +.. _basics_installation: + +.. role:: bash(code) + :language: bash + +Global installation +=================== + +The installation process is managed by the CMake build system. You will therefore need to have it +installed on your computer (at least version 3.22 is required but it may work with earlier versions). + +.. hint:: + + If you simply want to "try out" idol, we advise you to opt for a :ref:`local installation `. + +Creating the :bash:`install` target +----------------------------------- + +The first step is to create a :bash:`build` directory. +This is where the library will be compiled before being installed (i.e., copied) on your system. + +.. code-block:: bash + + mkdir build + cd build + +Then, you should call CMake in order to create some targets (in particular, the :bash:`idol` and the :bash:`install` target). +To do so, we recommend you to specify some options in order to link with external solvers that you may have +already installed on your computer. + +.. attention:: + + By default, (i.e., if no options are given to CMake) idol will not be linked with any external solver. + See the last section on this page for more details. + +.. code-block:: bash + + cmake .. + +.. admonition:: Example for Gurobi + + Here is an example of possible CMake command which will create the necessary targets for installing idol with Gurobi. + + .. code-block:: bash + + cmake -DUSE_GUROBI=YES .. + + Note that this example assumes that your environment variable :bash:`GUROBI_HOME` has been correctly configured + (see `this official Gurobi page `_). + +Building +-------- + +Now that targets have been created, we can build idol by running the following command. + +.. code-block:: bash + + make idol + +This will compile the idol C++ library and make it ready to be installed (i.e., copied) on your computer. + +Installing +---------- + +If you want to install idol on your computer, run the following command. + +.. code-block:: bash + + sudo make install + +.. hint:: + + Here, you need superuser rights in order to install idol globally. If you want to install idol on a specific folder, + you may also use the :bash:`CMAKE_INSTALL_PREFIX` CMake option to change the destination folder. + + .. code-block:: bash + + cmake -CMAKE_INSTALL_PREFIX=/my/custom/installation/folder .. + make install + +Linking with external solvers +------------------------------ + +To link idol with external solvers, specific options need to be passed to CMake. +A detailed list of such options can be found on :ref:`this page `. + +.. hint:: + + Here is a quick guide on how to pass options to CMake. Say you want + to pass the option :bash:`MY_OPTION` to CMake with the value :bash:`MY_VALUE`. Then, you should run the following + command (inside :bash:`build/`). + + .. code-block:: bash + + cmake -DMY_OPTION=MY_VALUE .. + diff --git a/_sources/installation/index.rst.txt b/_sources/installation/index.rst.txt new file mode 100644 index 00000000..9a5bdc51 --- /dev/null +++ b/_sources/installation/index.rst.txt @@ -0,0 +1,28 @@ +.. _installation: + +Installation guidelines +======================= + +Welcome to idol! You are here on the installation guidelines. + +Installation types +------------------ + +There are two ways of installing idol: + +* :ref:`A global installation ` installs idol globally on your computer (e.g., in `/usr/lib`). +* :ref:`A local installation ` lets CMake automatically download and manage idol's installation on a sub-folder of your + CMake project. + +Table of contents +----------------- + +.. toctree:: + :maxdepth: 1 + :glob: + + global_installation + options + linking + local_installation + mosek-and-socp diff --git a/_sources/installation/linking.rst.txt b/_sources/installation/linking.rst.txt new file mode 100644 index 00000000..d0b5e64d --- /dev/null +++ b/_sources/installation/linking.rst.txt @@ -0,0 +1,48 @@ +.. _linking: + +.. role:: bash(code) + :language: bash + +Linking your C++ project with idol +================================== + +Idol is built with and for CMake (even though it is still possible to link using :bash:`Makefile` or pure :bash:`gcc, clang, ...`). + +If you are using CMake, here is a minimal :bash:`CMakeLists.txt` which creates a new executable target linked with idol. + +.. code-block:: cmake + + cmake_minimum_required(VERSION 3.22) + project(my_project) + + set(CMAKE_CXX_STANDARD 17) + + add_executable(my_target main.cpp) + + find_package(idol REQUIRED) ## Here, we search for the installed library idol + + target_link_library(my_target PUBLIC idol) ## Here, we ask CMake to link with idol + +Note that this will also work when idol is linked with an external solver like Gurobi, Mosek or GLPK. + +The following :bash:`main.cpp` is then a minimal example. + +.. code-block:: cpp + + #include + #include + + int main(int t_argc, const char** t_argv) { + + Env env; + + Model model(env); + + Var x(env, 0., 1., Binary, "x"); + model.add(x); + + // ... + + return 0; + } + diff --git a/_sources/installation/local_installation.rst.txt b/_sources/installation/local_installation.rst.txt new file mode 100644 index 00000000..fcd629ca --- /dev/null +++ b/_sources/installation/local_installation.rst.txt @@ -0,0 +1,87 @@ +.. _installation_local: + +.. role:: bash(code) + :language: bash + +Local installation +================== + +This page is dedicated to local installations of idol. This is the easiest way to get your project working with +idol without installing it globally on your computer. + +.. hint:: + + If you want to install idol globally, please read our :ref:`global installation guide `. + +The idea behind local installations is to let CMake download and manage the installation of idol in a sub-folder of your +project. This is done by using the CMake :bash:`FetchContent_*` directives. + +Using this method, you can also explicitly specify the desired version of idol which you want to use. + +We provide here a minimal :bash:`CMakeLists.txt`. + +.. code-block:: cmake + + cmake_minimum_required(VERSION 3.23) + project(my_project) + + set(CMAKE_CXX_STANDARD 17) + + include(FetchContent) + + # Define your CMake options here + set(USE_GUROBI YES) # For instance, tell CMake to link idol with Gurobi + + # Tell CMake which version of idol you desire + FetchContent_Declare( + idol + GIT_REPOSITORY https://github.com/hlefebvr/idol.git + GIT_TAG origin/main # You may also use a tag, e.g., v0.2.4-alpha + ) + + # Ask CMake to download idol and install it to a sub-folder + FetchContent_MakeAvailable(idol) + + # Normal executable definition + add_executable(my_target main.cpp) + + # Link your CMake target with idol as classically done + target_link_libraries(my_target PUBLIC idol) + +.. hint:: + + As you have seen, some options must be set in CMake in order to tell it to link idol with external solvers. + This is done with the :bash:`set` CMake function. Say you want + to set the option :bash:`MY_OPTION` to the value :bash:`MY_VALUE`. Then, you should add the following + function call. + + .. code-block:: bash + + set(MY_OPTION MY_VALUE) + +.. seealso:: + + A list of all possible options which can be set can be found on the :ref:`global installation guide `. + In particular, you will find options to link with Gurobi, Mosek and GLPK. + +Then, here is a starting :bash:`main.cpp`. + +.. code-block:: cpp + + #include + #include // Note that we do not include + + int main(int t_argc, const char** t_argv) { + + Env env; + + Model model(env); + + Var x(env, 0., 1., Binary, "x"); + model.add(x); + + // ... + + return 0; + } + diff --git a/_sources/installation/mosek-and-socp.rst.txt b/_sources/installation/mosek-and-socp.rst.txt new file mode 100644 index 00000000..a271e9f8 --- /dev/null +++ b/_sources/installation/mosek-and-socp.rst.txt @@ -0,0 +1,56 @@ +.. _mosek_and_socp: + +Using idol with Eigen +===================== + +This page elaborates on some operations made by idol which require usage of the `Eigen `_ +C++ library. + +We first explain how to link idol with Eigen, then discuss several operations which require the use of Eigen. + +.. warning:: + + Calling functionalities which require Eigen without have linked idol with Eigen will result in an Exception being + thrown. + +"Linking" with Eigen +-------------------- + +Eigen is header-only C++ library. In that sense, no installation is required. One only needs to download Eigen's source +code in order to make their header files accessible. + +Then, all you have to do in order to "link" with Eigen is to set the ``USE_EIGEN`` CMake +option to ``YES``. + +.. admonition:: Example + + This example shows you have to create an install target for idol with Mosek and Eigen. + + .. code-block:: + + cmake -DUSE_MOSEK=YES -DUSE_EIGEN=YES .. + + +Interfacing Mosek for solving QPs and SOCPs +------------------------------------------- + +The interface of idol +is based on functional expressions, e.g., like + +.. math:: + + \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^ix_jx_k \le b_i. + +The C++ Mosek interface, instead, is based on conic expressions, e.g., like + +.. math:: + + (x_0, \textbf{Fx}) \in \mathcal Q^n, + +where :math:`\mathcal Q^n` denotes the second-order cone and :math:`F` is some matrix related to :math:`Q^i`. + +In order to compute :math:`F` and thus, to make the conversion between the Mosek interface and +the idol interface, one needs to compute an eigen value decomposition. + +This is automatically done by idol using `Eigen `_. + diff --git a/_sources/installation/options.rst.txt b/_sources/installation/options.rst.txt new file mode 100644 index 00000000..df130753 --- /dev/null +++ b/_sources/installation/options.rst.txt @@ -0,0 +1,125 @@ +.. _cmake_options: + +.. role:: bash(code) + :language: bash + +List of CMake options +===================== + +Linking with external solvers +----------------------------- + +For Gurobi (commercial solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with Gurobi, you will need to pass the :bash:`USE_GUROBI` CMake option with value :bash:`YES`. + +By default, CMake will look for Gurobi inside the folder indicated by the environment variable :bash:`GUROBI_HOME` +(see `this official Gurobi page `_). +Note that it is also possible to pass the CMake option :bash:`GUROBI_DIR=/path/to/gurobi/install/dir` in order to specify +another directory to look for Gurobi. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with Gurobi. + + .. code-block:: bash + + cmake -DUSE_GUROBI=YES -DGUROBI_DIR=/path/to/gurobi/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_GUROBI YES) + set(GUROBI_DIR /path/to/gurobi/install/dir) + + +For Mosek (commercial solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with Mosek, you will need to pass the :bash:`USE_MOSEK` CMake option with value :bash:`YES`. + +By default, CMake will look for Mosek inside the folder indicated by the environment variable :bash:`MOSEK_HOME`. +Note that it is also possible to pass the CMake option :bash:`MOSEK_DIR=/path/to/mosek/install/dir` in order to specify +another directory to look for Mosek. + +Note that :bash:`MOSEK_HOME` (or equivalently :bash:`MOSEK_DIR`) should point to the Mosek installation folder where +folders :bash:`h` and :bash:`bin` can be found. For instance, :bash:`MOSEK_HOME=/home//mosek/10.0/tools/platform/linux64x86`. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with Mosek. + + .. code-block:: bash + + cmake -DUSE_MOSEK=YES -DMOSEK_DIR=/path/to/mosek/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_MOSEK YES) + set(MOSEK_DIR /path/to/mosek/install/dir) + +.. attention:: + + If you intend to use Mosek for solving QPs or SOCPs, please :ref:`read this `. + +For GLPK (open-source solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with GLPK, you will need to pass the :bash:`USE_GLPK` CMake option with value :bash:`YES`. + +By default, CMake will look for GLPK inside the folder indicated by the environment variable :bash:`GLPK_HOME` as well +as in the default installation folders :bash:`/usr/include` and :bash:`/usr/lib`. +Note that it is also possible to pass the CMake option :bash:`GLPK_DIR=/path/to/glpk/install/dir` in order to specify +another directory to look for GLPK. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with GLPK. + + .. code-block:: bash + + cmake -DUSE_GLPK=YES -GLPK_DIR=/path/to/glpk/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_GLPK YES) + set(GLPK_DIR /path/to/glpk/install/dir) + +Building examples +----------------- + +:ref:`Examples :` can be found at the root level of the idol repository, inside the directory ``examples``. + +By default, CMake will not generate targets to build these example. To tell CMake to generate them, you +need to set the CMake option ``BUILD_EXAMPLE`` to ``YES``. + +.. admonition:: Example + + The following will tell CMake to create targets for examples. + + .. code-block:: + + cmake -DBUILD_EXAMPLES=YES .. + + For instance, we can now build the Knapsack Problem example, + + .. code-block:: + + make ex_knapsack_problem + + and run it. + + .. code-block:: + + ./examples/knapsack-problem/ex_knapsack_problem + +Building unit and integration tests +----------------------------------- + +To build tests for idol, please refer to this :ref:`developer page `. \ No newline at end of file diff --git a/_sources/tutorials/decomposition_methods/benders.rst.txt b/_sources/tutorials/decomposition_methods/benders.rst.txt new file mode 100644 index 00000000..e7fbc3c0 --- /dev/null +++ b/_sources/tutorials/decomposition_methods/benders.rst.txt @@ -0,0 +1,153 @@ +.. _decomposition_benders: + +.. role:: cpp(code) + :language: cpp + +Benders Decomposition (with LazyCutCallback) +============================================ + +In this section, we will show how to use the LazyCutCallback callback to implement a simple Benders Decomposition +algorithm. + +.. hint:: + + This tutorial regards the `advanced topic` of Benders Decomposition. + Rudimentary notions in the following subjects are recommended: + + - `Benders Decomposition `_ + - `Linear Programming duality `_ + +Mathematical Model +------------------ + +Original formulation +^^^^^^^^^^^^^^^^^^^^ + +We will base our example on the following model taken from `Blanco, V., (2016), Benders Decomposition, MINLP School: Theory +and Applications `_. + +.. math:: + + \begin{align} + \min_{x,y} \ & 2 x_0 + 3x_1 + 2y \\ + \text{s.t.} \ & x_0 + 2x_1 + y \ge 3, \\ + & 2x_0 - x_1 + 3y \ge 4, \\ + & x,y\ge 0. + \end{align} + +Benders reformulation +^^^^^^^^^^^^^^^^^^^^^ + +We apply a Benders reformulation to this problem by considering :math:`y` as the complicating variable. +The Benders reformulation reads: + +.. math:: + + \begin{align} + \min_{y,z} \ & 2y + z \\ + \text{s.t.} \ & z \ge \lambda_1 ( 3 - y ) + \lambda_2(4 - 3y) \quad \lambda \in \Lambda, \\ + & z \ge 0, + \end{align} + +with :math:`\Lambda` defined as the set of all :math:`\lambda\in\mathbb R^2_+` such that + +.. math:: + + \begin{align} + & \lambda_0 + 2 \lambda_1 \le 2, \\ + & 2\lambda_0 - \lambda_1 \le 3. + \end{align} + +Implementation +-------------- + +We are now ready to implement our decomposition method. We will need to define three different things: + +- the master problem; +- the dual space :math:`\Lambda`; +- the shape of the cuts to be added. + +The master problem +^^^^^^^^^^^^^^^^^^ + +The master problem is created like any optimization model; see our :ref:`Modeling tutorial `. + +.. code:: + + Env env; + + Model master(env); + + auto y = master.add_var(0, Inf, Continuous, "y"); + auto z = master.add_var(0, Inf, Continuous, "z"); + + master.set_obj_expr(2 * y + z); + +The dual space :math:`\Lambda` +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To provide the description of the dual space :math:`\Lambda`, we use another Model object which will contain the variables +and constraints defining :math:`\Lambda`. The objective function is not used and can be left to zero. + +.. code:: + + Model dual_space(env); + + auto lambda = dual_space.add_vars(Dim<1>(2), 0, Inf, Continuous, "lambda"); + + dual_space.add_ctr(lambda[0] + 2 + lambda[1] <= 2); + dual_space.add_ctr(2 * lambda[0] - lambda[1] <= 3); + +The cuts to be added +^^^^^^^^^^^^^^^^^^^^ + +Finally, we need to define the cuts to be added to the master problem for a given dual variable :math:`\lambda`. +The cuts are always expressed in the "master space". What we mean by this is that, here, :math:`y` should be a *variable* +in the constraint while :math:`\lambda` should be a *constant*. + +This is done as follows. + +.. code:: + + auto benders_cut = z >= !lambda[0] * (3 - y) + !lambda[1] * (4 - 3 * y); + +See how the lambda variables are "turned into" constants by prepending them with an "!" symbol. + +Solving the model +----------------- + +In this section, we solve our model using GLPK and the LazyCutCallback from idol. + +This is done as follows. + +.. code:: + + master.use( + GLPK() + .with_callback( + LazyCutCallback(dual_space, benders_cut) + .with_separation_optimizer(GLPK()) + ) + ); + + master.optimize(); + + std::cout << save_primal(master) << std::endl; + +See how we specified also an optimizer for solving the separation problem. Here, we use GLPK. + +.. warning:: + + If you are using Gurobi with the LazyCutCallback, make sure to call the :code:`Gurobi::with_lazy_cuts` method. + This is necessary to turn off some parameters of Gurobi which would otherwise lead to wrong solutions. + + .. code:: + + master.use( + Gurobi() + .with_lazy_cuts(true) + .with_callback( + LazyCutCallback(dual_space, benders_cut) + .with_separation_optimizer(Gurobi()) + ) + ); diff --git a/_sources/tutorials/decomposition_methods/dantzig_wolfe.rst.txt b/_sources/tutorials/decomposition_methods/dantzig_wolfe.rst.txt new file mode 100644 index 00000000..8aa3066f --- /dev/null +++ b/_sources/tutorials/decomposition_methods/dantzig_wolfe.rst.txt @@ -0,0 +1,284 @@ +.. _decomposition_dantzig_wolfe: + +.. role:: cpp(code) + :language: cpp + +Dantzig-Wolfe Decomposition (Automatic) +======================================= + +In this section, we will show how to use the Branch-and-Price solver to solve the *Generalized Assignment Problem* (GAP) +using an external solver to solve each sub-problem. + +.. hint:: + + This tutorial regards the `advanced topic` of Column Generation and Dantzig-Wolfe decomposition. + Rudimentary notions in the following subjects are recommended: + + - `Column Generation and Branch-and-Price algorithms `_ + - `Dantzig-Wolfe decomposition `_ + - `Generalized Assignment Problem `_. + +.. seealso:: + + A `Benchmark on Generalized Assignemnt Problem `_ is + available. + This includes a comparison with `Coluna.jl `_. + +Mathematical models +------------------- + +In this section, we assume that the reader is familiar with GAP. +Let :math:`m` be a given of agents and let :math:`n` be a set of tasks to perform. Let :math:`c_{ij}` be the cost for +assigning task :math:`j` to agent :math:`i`, :math:`w_{ij}` be the resource consumption of task :math:`j` when performed +by agent :math:`i` and let :math:`t_i` be the resource capacity of agent :math:`i`. + +Direct model +^^^^^^^^^^^^ + +The Generalized Assignment Problem (GAP) can be modeled as + +.. math:: + + \min \ & \sum_{i=1}^m\sum_{j=1}^n c_{ij} x_{ij} \\ + \textrm{s.t. } & \sum_{j=1}^n w_{ij} x_{ij} \le t_i & i=1,...,m \\ + & \sum_{i=1}^m x_{ij} = 1 & j = 1,...,n \\ + & x_{ij}\in\{0,1\} & i=1,...,m, j=1,...,n + +Here, variable :math:`x_{ij}` encodes the assignment decision and equals 1 if and only if task :math:`j` is assigned to +agent :math:`i`. + +Dantzig-Wolfe reformulation +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Let us enumerate the list of all feasible assignments, i.e., let + +.. math:: + + \{\bar x^e_{ij} \}_{e\in E} = \{ x \in \{ 0,1 \}^{mn} : \sum_{j=1}^n w_{ij}x_{ij} \le t_i \quad i=1,...,m \}, + +where :math:`E` denotes a list for their indices. The Dantzig-Wolfe reformulation of GAP reads + +.. math:: + + \min \ & \sum_{e\in E} \lambda_e\left( \sum_{i=1}^m\sum_{j=1}^n c_{ij}\bar x_{ij}^e \right) \\ + \textrm{s.t. } & \sum_{e\in E} \lambda_e \left( \sum_{i=1}^m \bar x_{ij}^e \right) = 1 & j=1,...,n \\ + & \sum_{e\in E} \lambda_e = 1 \\ + & \lambda_e \in \{ 0, 1 \} & \forall e\in E + +Though this model contains an exponential number of variables (i.e., columns) it can be solved efficiently using +Column Generation and Branch-and-price. In such case, the pricing problem is a Knapsack Problem. + +Automatic reformulation in idol +------------------------------- + +The simplest way to solve a problem using column generation and idol is through its automatic reformulation feature. +To use this, one simply needs to give the *original space* formulation of the problem (here, the *so-called* direct model) +and to indicate which constraints should be moved to the pricing problem (here, the knapsack constraints). + +Implementing the direct model with idol +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To read an instance for GAP, we first need to include the header file located in :code:`"idol/problems/generalized-assignment-problem/GAP_Instance.h"`. +This will allow us to use idol's instance parser for GAP. +Assuming that the instance file is named :code:`instance.txt`, it can be loaded as follows. + +.. code-block:: cpp + + const auto instance = Problems::GAP::read_instance("instance.txt"); + + const unsigned int n_agents = instance.n_agents(); + const unsigned int n_jobs = instance.n_jobs(); + +We are now ready to model our problem (for more details, refer to :ref:`this tutorial on modeling `) + +.. code-block:: cpp + + // Create optimization environment + Env env; + + // Create model + Model model(env); + + // Create assignment variables (x_ij binaries) + auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, "x"); + + // Create knapsack constraints (i.e., capacity constraints) + for (unsigned int i = 0 ; i < n_agents ; ++i) { + model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i)); + } + + // Create assignment constraints + for (unsigned int j = 0 ; j < n_jobs ; ++j) { + model.add(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j)); + } + + // Set the objective function + model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j]))); + +Giving decomposition instructions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We are now at the crucial step of indicating which constraint should be moved to the pricing problem. In idol, this is done by using +*annotations*. Annotations are additional information associated to an optimization object (e.g., a constraint or a variable). +Note that annotations are global, i.e., they do not relate to a given optimization model. + +Every annotation is formed with two template arguments: an optimization object type and a value type. Here, we want to add +annotations to constraints, thus, the optimization object type must be :code:`Ctr`. The value type can typically be any desired +type. Here, however, the Dantzig-Wolfe decomposition needs an annotation corresponding to an :code:`unsigned int`. Thus, we create +the annotation as follows. + +.. code-block:: cpp + + Annotation decomposition(env, "decomposition", MasterId); + +Here, we pass three arguments to the constructor of :code:`Annotation`. First, we pass the optimization +environment which will store the annotation. Then, a name (mandatory) is given to the annotation, here, "decomposition". +Finally, a default value is given and equals "MasterId". This will tell idol that constraints which have not been annotated +should remain in the master problem. + +Now, observe how the annotation is applied to the capacity constraints. + +.. code:: cpp + + for (unsigned int i = 0 ; i < n_agents ; ++i) { + Ctr capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i)); + capacity.set(decomposition, i); // <-- Annotating the capacity constraint + } + +Here, the first capacity constraint is moved to the first pricing problem (id: 0), +the second constraint to the second pricing problem (id: 1), and so on. + +Note that another decomposition would be materialized as follows. + + +.. code:: cpp + + for (unsigned int i = 0 ; i < n_agents ; ++i) { + Ctr capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i)); + capacity.set(decomposition, 0); // <-- Annotating the capacity constraint + } + +Here, all the knapsack constraints are moved to the same pricing problem (id: 0). + +Decomposing and solving the model +--------------------------------- + +Now that the desired decomposition has been specified, we can specify the desired optimizer to solve our model. +Here, we want to solve our problem using a branch-and-price algorithm, i.e., a branch-and-bound algorithm where each relaxation +in the branch-and-bound tree is solved by a Dantzig-Wolfe decomposition. This is done as follows. + +.. code:: cpp + + model.use( + /* The overall algorithm is a branch-and-bound */ + BranchAndBound() + + /* Each node is solved with a Dantzig-Wolfe decomposition algorithm */ + .with_node_optimizer( + + /* The annotation "decomposition" is used to automatically decompose the problem */ + DantzigWolfeDecomposition(decomposition1) + + /* The master problem is solved using Gurobi */ + .with_master_optimizer(Gurobi::ContinuousRelaxation()) + + /* Each pricing problem is solved by Gurobi as well */ + .with_pricing_optimizer(Gurobi()) + + ) + + /* Variables are selected for branching using the most-infeasible rule */ + .with_branching_rule(MostInfeasible()) + + /* Nodes are selected using the best-bound rule */ + .with_node_selection_rule(BestBound() + + /* The algorithm will run with a time limit of 3600 */ + .with_time_limit(3600) + + ); + +Then, one can simply call the :code:`Model::optimize` method as follows. + +.. code:: cpp + + model.optimize(); + + +That's it! The problem is being solved by column generation, and possibly branching on fractional variables. + + +.. hint:: + + Note that it is possible to obtain logs using the `with_log_level` method on the desired optimizer. + For instance, one may want to have + logs for the branch-and-bound optimizer. Then, one should do as follows. + + .. code:: cpp + + model.use( + BranchAndBound() + + /* ... omitting identical details */ + + .with_log_level(Info, Blue) + ); + +The rest remains unchanged and one can use :code:`Model::optimize` to solve the problem and retrieve the solution +through methods like :code:`Model::get_status` and :code:`Model::get_var_primal`. + +.. admonition:: Example + + Here, we can solve our model using a Dantzig-Wolfe decomposition. + + .. code-block:: + + model.optimize(); + + std::cout << save_primal(model) << std::endl; + + This will produce the following output (e.g.). + + .. code-block:: text + + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [branch-and-bound] + [2023-04-07 13:45:44] [info] [branch-and-bound] + [2023-04-07 13:45:44] [info] [branch-and-bound] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + [2023-04-07 13:45:44] [info] [dantzig-wolfe] + + +----------------------- + | Status: Optimal + | Reason: Proved + | ObjVal: -233.00 + | Values: + | x_1_7 = 1.00 + | x_2_0 = 1.00 + | x_2_1 = 1.00 + | x_1_4 = 1.00 + | x_1_5 = 1.00 + | x_0_6 = 1.00 + | x_0_2 = 1.00 + | x_0_3 = 1.00 + +----------------------- diff --git a/_sources/tutorials/decomposition_methods/index.rst.txt b/_sources/tutorials/decomposition_methods/index.rst.txt new file mode 100644 index 00000000..997bd205 --- /dev/null +++ b/_sources/tutorials/decomposition_methods/index.rst.txt @@ -0,0 +1,11 @@ +.. _decomposition: + +Decomposition methods +===================== + +.. toctree:: + :maxdepth: 1 + :glob: + + dantzig_wolfe + benders diff --git a/_sources/tutorials/getting_started/index.rst.txt b/_sources/tutorials/getting_started/index.rst.txt new file mode 100644 index 00000000..97e5ff89 --- /dev/null +++ b/_sources/tutorials/getting_started/index.rst.txt @@ -0,0 +1,11 @@ +.. _basics: + +Getting started +=============== + +.. toctree:: + :maxdepth: 1 + :glob: + + modeling_optimization_problems + using_an_external_solver diff --git a/_sources/tutorials/getting_started/modeling_optimization_problems.rst.txt b/_sources/tutorials/getting_started/modeling_optimization_problems.rst.txt new file mode 100644 index 00000000..a1b79778 --- /dev/null +++ b/_sources/tutorials/getting_started/modeling_optimization_problems.rst.txt @@ -0,0 +1,218 @@ +.. _modeling_optimization_problems: + +.. role:: cpp(code) + :language: cpp + +Modeling optimization problems +============================== + +On this page, we discuss the very basic ideas of idol's modeling API. +All classes which are used for modeling an optimization problem can be accessed by including :code:`#include `. +Let's get started. + +.. warning:: + + The idol library can be found inside the :code:`idol` namespace, thus, be sure to add :code:`using namespace idol;` + where desired or to explicitly refer to classes using this namespace, e.g., by using :code:`idol::Model` instead of :code:`Model`. + +Env +--- + +Every optimization object (like variables and constraints) are managed by an "optimization environment". Essentially, +it is the environment that controls the death and lives of such objects. It is through the environment that idol +manages the different versions each optimization object may have during the execution of your program. + +Typically, only one environment should be used by your code, though it is possible to instantiate many environment (not advised). + +Environments are objects of the ``Env`` class and can be created as follows. + +.. code-block:: + + Env env; // Creates a new optimization environment. + +Model +----- + +The :cpp:`Model` class is used to represent an optimization model of the following form. + +.. math:: + + \begin{array}{lll} + \min\ & \displaystyle \sum_{j=1}^n c_jx_j + \sum_{j=1}^n\sum_{k=1}^n d_{jk}x_jx_k \\ + \textrm{s.t. } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\ + & l_j \le x_j \le u_j & j=1,...,m \\ + & x_j\in\mathbb Z & j\in J_I + \end{array} + +Here, :math:`x_j` are the variables of this optimization problem while :math:`c_j, d_{jk}, a_{ij}` and :math:`q_{jk}^i` are given +input parameters for this model. Optionally, :math:`J_I\subseteq\{1,...,n\}` is a set of variable indices +whose value must be integral. + +Constructors of :cpp:`Model` can be used to create a new optimization model in idol. The most common takes a single argument +which is the optimization environment to be used. + +.. code-block:: cpp + + int main(int t_argc, const char** t_argv) { + + Env env; + + Model model(env); + + // The model has been created! + + return 0; + } + +Now, we can define optimization variables and constraints. + +Variables +--------- + +Any variable in idol is associated to at least one :cpp:`Model` object. Typically, exactly one. +We can easily create a new variable by using the constructor of the :cpp:`Var` class and add it to a model by calling the :cpp:`Model::add` method. +For instance, the following piece of code +will create a new variable, called "x", which is continuous and non-negative. + +.. code-block:: cpp + + Var x(env, 0., Inf, Continuous, "x"); + + model.add(x); // Variable x is added to the model + +A more straightforward way of creating variables is by directly calling the method ``add_var`` of the ``Model`` class. +For instance, the following piece of code is equivalent to the previous one. + +.. code-block:: cpp + + model.add_var(0, Inf, Continuous, "x"); + +Note that we did not need to repeat the environment since the model's environment is used by default. + +The idol library also offers simple ways for creating multiple variables at once. +For instance, one can call the :cpp:`Var::make_vector` function. This function requires +an extra parameter specifying the dimension of the new variable. For instance, the following code creates variables :math:`y_{ij}` +with :math:`i=1,...,K` and :math:`j=1,...,T`. + +.. code-block:: cpp + + auto y = Var::array(env, Dim<2>(K, T), 0., Inf, Continuous, "y"); + + model.add_array(y); // Variables y_ij are added to the model + + std::cout << y[0][0] << std::endl; // "y_0_0" + +Alternatively, one can use the ``Model::add_vars`` method. + +.. code-block:: cpp + + auto y= model.add_vars(Dim<2>(K, T), 0., Inf, Continuous, "y"); + + std::cout << y[0][0] << std::endl; // "y_0_0" + +Constraints +----------- + +Similarly to variables, constraints are easily created and added to a given ``Model``. + +Constraints can be created by calling the constructor of the :cpp:`Ctr` class and added to a model by means of :cpp:`Model::add`. +See for instance. + +.. code-block:: cpp + + Env env; + Model model(env); + + Var x_0(env, 0., Inf, Continuous, "x_0"); + Var x_1(env, 0., Inf, Continuous, "x_1"); + Ctr constraint(env, x_0 + x_1 >= 1); + + model.add(x_0); + model.add(x_1); + model.add(constraint); + +A more compact of this code is obtained by making use of the ``Model::add_vars`` and ``Model::add_ctr`` methods. + +.. code-block:: cpp + + Env env; + Model model(env); + + auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, "x"); + auto constraint = model.add_ctr(x + y >= 1); + +As you can see, a constraint is created using the pattern :code:`{expression} {sign} {expression}` where + +* :code:`{sign}` is one of :code:`<=`, :code:`>=` and :code:`==`; +* :code:`{expression}` is an instance of :code:`Expr`. + +The :code:`Expr` class is used to represent a mathematical expression in idol. An expression is composed of three parts: + +* :code:`Expr::linear` will give you access to the linear part of the expression (it is an instance of ``LinExpr``); +* :code:`Expr::quadratic` will give you access to the quadratic part of the expression (it is an instance of ``QuadExpr``); +* :code:`Expr::constant` will return the constant (or offset) of the expression (it is an instance of ``Constant``). + +Typically, however, you will not really care about what composes an expression since an :code:`Expr` object can be created +quite naturally. See for instance the following code. + +.. code-block:: cpp + + Expr expr = 1 + 3 * x[0]; + expr += x[1]; + expr += x[0] + 2 * x[0] * x[1]; + + std::cout << expr << std::endl; // "1 + 4 * x[0] + 1 * x[1] + 2 * x[0] * x[1]" + +As mentioned, you can access parts of an expression as follows. + +.. code-block:: cpp + + for (const auto& [var, coefficient] : expr.linear()) { + std::cout << var << " is multiplied by " << coefficient << std::endl; + } + + /* + "x_0 is multiplied by 4" + "x_1 is multiplied by 1" + */ + +.. admonition:: About constants in expressions + + Without diving into too much detail, we should here precise that each constant multiplying a variable in an :cpp:`Expr` + can actually be composite (e.g., a coefficient in the expression may refer to external optimization variables whose + value is considered fixed in the current model). + + Fixing variables in an optimization problem can be achieved thanks to the ``!`` symbol. + + For instance, here is an expression where ``xi_0`` and ``xi_1`` are seen as parameters. + + .. code-block:: + + Expr expr = (1 + 2 * !xi_0) * x + 3 * !xi_1 * y; + + Here, ``1 + 2 * !xi_0`` is an instance of the ``Constant`` object and can be used as follows. + + .. code-block:: + + Constant constant = 1 + 2 * !xi_0; + + std::cout << constant.numerical() << std::endl; // output: 1 + + for (const auto& [param, coeff] : constant) { + std::cout << coeff << " * " << param << std::endl; // output: 2 * !xi_0 + } + +Objective function +------------------ + +The objective function of an optimization model can specified by the ``Model::set_obj_expr`` method. + +Here is an example which sets the objective function to :math:`-x_0 + 2 * x_1`; + +.. code-block:: + + model.set_obj_expr(-x_0 + 2 * x_1); + +In the following tutorial, we will dive into a more practical way to build expressions by considering the simple example +of the combinatorial Knapsack problem. We will also see how to call an external solver like Gurobi or GLPK using idol. +See you there! diff --git a/_sources/tutorials/getting_started/using_an_external_solver.rst.txt b/_sources/tutorials/getting_started/using_an_external_solver.rst.txt new file mode 100644 index 00000000..c2681429 --- /dev/null +++ b/_sources/tutorials/getting_started/using_an_external_solver.rst.txt @@ -0,0 +1,223 @@ +.. _using_an_external_solver: + +.. role:: cpp(code) + :language: cpp + +Using an external solver +======================== + +In this tutorial, we will see how to use an external optimization solver like GLPK or GLPK to solve +a small combinatorial problem. +The considered problem is the Knapsack Problem (see the `Knapsack Problem wikipedia page `_). + +Modeling +-------- + +The first step is to model our problem using idol. Recall the standard model for the knapsack problem: + +.. math:: + + \begin{array}{lll} + \max\ & \displaystyle \sum_{j=1}^n p_jx_j \\ + \textrm{s.t. } & \displaystyle \sum_{j=1}^n w_jx_j \le W \\ + & x_j \in \{ 0, 1 \} & j=1,...,n + \end{array} + +where :math:`n` denotes the number of items and for each item :math:`j\in\{1,...,n\}`, :math:`p_j` denotes its profit while +:math:`w_j` denotes its weight. Finally, we let :math:`W` denote the knapsack capacity. + +We will assume to have the following input data at hand. + +.. code-block:: cpp + + const unsigned int n = 5; // 5 items + const std::vector p = { 40., 50., 100., 95., 30. }; // profits + const std::vector w = { 2., 3.14, 1.98, 5., 3. }; // weights + const double W = 10; // capacity + +Then, using idol's modeling API contained in :cpp:`#include `, we can create our model easily. +We will first present a naive implementation using only the knowledge introduced in the previous tutorial. +Then, we will show a more compact way of implementing it. + +A first approach +^^^^^^^^^^^^^^^^ + +A first approach to model our knapsack problem in idol is as follows. + +.. code-block:: cpp + + // Create environemnt + Env env; + + // Create a new model + Model model(env); + + // Create a vector for storing the x variables + std::vector x; + x.reserve(n); + + // Create x variables as binary with p_j as objective coefficient + for (unsigned int j = 0 ; j < n ; ++j) { + Var x_j(env, 0., 1., Binary, Column(p[j]), "x_" + std::to_string(j)); + model.add(x_j); + x.emplace_back( x_j ); + } + + // Create expression for the knapsack constraint + Expr knapsack_constraint; + for (unsigned int j = 0 ; j < n ; ++j) { + knapsack_constraint += w[j] * x[j]; + } + + // Create the knapsack constraint + Ctr c(knapsack_constraint <= W); + model.add(c); + + // Define objective sense + model.set_obj_sense(Maximize); + +Here, we used the :cpp:`Model::set_obj_sense` method to set the objective sense of our model. By default, all models are +assumed to be minimization problems. + +A more elegant approach +^^^^^^^^^^^^^^^^^^^^^^^ + +Though our first approach works well, its size and readability can greatly be reduced by using the predefined macro :cpp:`idol_Sum` +and calls to methods of the ``Model`` class. + +.. code-block:: cpp + + // Create environemnt + Env env; + + // Create a new model + Model model(env); + + // Create x variables + model.add_vars(Dim<1>(n), 0., 1., Binary, "x"); + + // Create the knapsack constraint + model.add(idol_Sum(j, Range(n), w[j] * x[j] ) <= W); + + // Define objective sense + model.set_obj_sense(Maximize); + model.set_obj_expr(idol_Sum(j, Range(n), p[i] * x[i]); + +Here, we directly add :math:`n` variables with the right types and bounds. + +Then, we use the :cpp:`idol_Sum` macro to create the knapsack constraint. +This macro is used as follows :cpp:`idol_Sum({name}, {iteratable}, {expression})` where :cpp:`{name}` will be the name of an index +taking value in the :cpp:`{iteratable}` (here, :cpp:`Range(n)`) while :cpp:`{expression}` is the piece of expression which will be accumulated. + +.. admonition:: About Range + + In the above example, :cpp:`Range` is used to define an iterable ranging from :math:`0` to :math:`n` (note that it is also possible to range from :math:`l` to :math:`n` for :math:`l < n` + by calling :cpp:`Range(l, n)`). The objective function is created similarly. + +Solving the problem using an external solver +-------------------------------------------- + +The idol library offers different ways for solving optimization problems. +To select the desired approach for a given model, one must call the :cpp:`Model::use` method and specify the +"optimizer" to be used. + +For instance, the following will set the optimizer to GLPK for solving our model. + +.. code-block:: cpp + + model.use(GLPK()); + +.. hint:: + + Here, GLPK is actually an ``OptimizerFactory`` which will eventually create an optimizer to solve our model. + Indeed, the “real” optimizer in this case will be an instance of ``Optimizers::GLPK`` which will be created when necessary. + + If you want to learn more about optimizers and optimizer factories, please refer to :ref:`this page `. + +Now that the optimizer has been configure, we can solve our problem by calling the ``Model::optimize`` method. + +.. code-block:: + + model.optimize(); + +Accessing the solution +---------------------- + +Finally, you may access pieces of information regarding the solution by using one of the following methods: + +* ``get_status`` returns the current solution status (e.g., ``Optimal``, ``Infeasible``, ``Unbounded``, ...). +* ``get_reason`` returns the reason for the solution status (e.g., the solution reports ``Infeasible`` because of + ``TimeLimit``). +* ``get_best_obj`` returns the best objective value found (i.e., the best objective cost among feasible solutions + considered during the execution of the algorithm). +* ``get_best_bound`` returns the best objective value bound (e.g., a dual bound). +* ``get_relative_gap`` returns the relative optimality gap computed as + +.. math:: + + \textrm{relative_gap} = \left| \frac{ \textrm{best_obj} - \textrm{best_bound} }{ 1e^{-10} + \textrm{best_obj} } \right|. + +* ``get_absolute_gap`` returns the absolute optimality gap computed as + +.. math:: + + \textrm{absolute_gap} = | \textrm{best_obj} - \textrm{best_bound} |. + +* ``get_var_primal`` returns the primal value (when status is ``Optimal`` or ``Feasible``) of a given variable. +* ``get_var_ray`` returns the ray value (when status ``Unbounded``) of a given variable. +* ``get_ctr_dual`` returns the dual value (when status is ``Optimal`` or ``Feasible`` for continuous problems) of a given + constraint. +* ``get_ctr_farkas`` returns the Farkas certificate value (when status is ``Infeasible`` for continuous problems) of a given + constraint. + +Additionally, functions ``save_primal``, ``save_ray``, ``save_dual`` and ``save_farkas`` will create objects of the class +``Solution::Primal`` and ``Solution::Dual`` storing the results of corresponding calls to ``get_var_*`` and ``get_ctr_*`` +methods. + +.. admonition:: Example + + This example shows how to solve a model using GLPK and retrieves some piece of information about its solution. + + .. code-block:: + + model.use(GLPK()); + + model.optimize(); + + const SolutionStatus status = model.get_status(); + + if (status == Optimal) { + + std::cout << "Optimal solution found!" << std::endl; + + Solution::Primal primal_values = save_primal(model); + + std::cout << primal_values << std::endl; + + } else { + + std::cout << "An optimal solution could not be found" << std::endl; + + std::cout << "GLPK returned status " << status << std::endl; + + std::cout << "The reason for this status is " << get_reason(model) << std::endl; + + if (status == Feasible) { + + std::cout << "The optimality gap is " << get_relative_gap(model) * 100 << " %" << std::endl; + + } else if (status == Unbounded) { + + std::cout << "An unbounded ray is" << std::endl; + + std::cout << save_ray(model) << std::endl; + + } else if (status == Infeasible) { + + std::cout << "A Farkas certificate is" << std::endl; + + std::cout << save_farkas(model) << std::endl; + + } + + } \ No newline at end of file diff --git a/_sources/tutorials/index.rst.txt b/_sources/tutorials/index.rst.txt new file mode 100644 index 00000000..15150bfd --- /dev/null +++ b/_sources/tutorials/index.rst.txt @@ -0,0 +1,12 @@ +.. _tutorials: + +Tutorials +========= + +.. toctree:: + :maxdepth: 3 + :glob: + + getting_started/index + decomposition_methods/index + robust_optimization/index diff --git a/_sources/tutorials/robust_optimization/dualizing.rst.txt b/_sources/tutorials/robust_optimization/dualizing.rst.txt new file mode 100644 index 00000000..eb270acb --- /dev/null +++ b/_sources/tutorials/robust_optimization/dualizing.rst.txt @@ -0,0 +1,235 @@ +.. _dualizing: + +Dualization +=========== + +Dualization plays a prominent role in robust optimization. In this tutorial we show how one can derive the dual problem +of any convex quadratic problem. This is done both from the theoretical and computational side. In the first section, +the mathematical expression of the dual is derived while we show how it can automatically be obtained by using Idol. + +Dual of a convex quadratic problem +---------------------------------- + +Recall that Idol considers convex problems with quadratic expressions of the following form: + +.. math:: + + \begin{array}{lll} + \textrm{minimize } & \displaystyle \sum_{j=1}^n c_jx_j + \sum_{j=1}^n\sum_{k=1}^n d_{jk}x_jx_k \\ + \textrm{subject to } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\ + & l_j \le x_j \le u_j & j=1,...,m \\ + & x_j\in\mathbb Z & j\in J_I, + \end{array} + +where it is assumed that :math:`C^i\cap[l,u]` are convex sets, with + +.. math:: + + C^i = \{ x\in\mathbb R^n : \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i \}` + +and :math:`i=1,...,m`, and that the objective function :math:`f(x) = \sum_{j=1}^n c_jx_j + \sum_{j=1}^n\sum_{k=1}^n d_{jk}x_jx_k` +is convex over :math:`\mathbb R^n`. The bounds :math:`l_j` and :math:`u_j` (with :math:`j=1,...,n`) belong to the extended real number line. + +We start by re-writing our problem in term of indicator functions. We recall here that the indicator function of a set :math:`C` +is noted :math:`\delta(\bullet|C)` and is defined as + +.. math:: + + \delta(x|C) = \begin{cases} + 0 & \textrm{if } x\in C \\ + +\infty & \textrm{otherwise} + \end{cases}. + +Our (*primal*) problem reads + +.. math:: + + \min_{x\in\mathbb R^n} f(x) + \sum_{i=1}^m\delta(x|C^i) + \delta(x|[l,u]). + +As long as :math:`f` and :math:`C^i\cap [l, u]` are convex, this problem is convex and, assuming constraint qualification holds, the following +equality holds (see `Fenchel duality `_). + +.. math:: + + \begin{multline} + \min_{x\in\mathbb R^n} \sum_{i=1}^m\delta(x|C^i) + \delta(x|[l,u]) - (-f)(x) \\ + = + \max_{\pi\in\mathbb R^n} (-f)_*(\pi) - \left( \sum_{i=1}^m\delta(\bullet|C^i) + \delta(\bullet|[l,u]) \right)^*(\pi) + \end{multline} + +Refering to this `cheatsheet on convex conjugates `_, +one sees that :math:`(-f)_*(\pi) = -f^*(-\pi)`. Moreover, refering to the "Non-separable sum" formula, one obtains the followig problem: + +.. math:: + + \begin{array}{lll} + \textrm{maximize } & -f^*(-\pi) - \sum_{i=1}^m \delta^*(u^i|C^i) - \delta^*(v|[l,u]) \\ + \textrm{subject to } & v + \sum_{i=1}^m u^i = \pi \\ + & \pi\in\mathbb R^n + \end{array} + +Conjugate of the indicator function of bound restrictions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We start by computing :math:`\delta^*(v|[l,u])`. By definition, this equals + +.. math:: + + \delta^*(v|[l,u]) = + \begin{array}[t]{lll} + \max\ & v^\top x \\ + \textrm{s.t. } & x \le u & (\lambda^u \ge 0) \\ + & -x \le -l & (\lambda^l \ge 0) \\ + & x\in \mathbb R^n. + \end{array} + +By standard LP duality, one has + +.. math:: + + \begin{array}{lll} + \min\ & u^\top\lambda^u - l^\top\lambda^l \\ + \textrm{s.t. } & \lambda^u - \lambda^l = v & (x\in\mathbb R^n)\\ + & \lambda^u \ge 0 \\ + & \lambda^l \ge 0. + \end{array} + +We end with some useful remarks: + +- Assume :math:`l_j = -\infty` for some j, then one should remove :math:`\lambda^l_j` from this model; +- Assume :math:`u_j = +\infty` for some j, then one should remove :math:`\lambda^u_j` from this model; + +Conjugate of convex sets defined by quadratic expressions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We may now take interest in :math:`\delta^*(u^i|C^i)`. Now, observe that there must +exist a symmetric matrix :math:`\tilde Q^i` such that + +.. math:: + + \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k - b_i + = + a_{(i)}x + x^\top \tilde Q^ix - b_i + +Since :math:`\tilde Q^i` is a real symmetric matrix, it is diagonalizable by orthogonal matrices. Thus, there exists matrices :math:`P^i` and :math:`D^i` such that +:math:`\tilde Q^i = {P^i}^\top D^iP^i` where :math:`D^i` is diagonal. + +There, idol considers two cases: + +- If :math:`D^i\succeq 0`, then :math:`C^i` is a convex set and the following holds + + .. math:: + + \begin{align} + \delta^*(u^i|C^i) &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & a_{(i)}x + x^\top P^iD^i{P^i}^\top x \le b_i \\ + & x\in\mathbb R^n + \end{array} \\ + &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & || {D^i}^{\frac 12}{P^i}^\top x ||_2^2 \le b_i - a_{(i)} x \\ + & x\in\mathbb R^n + \end{array} + \\ + &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & (\frac 12, b_i - a_{(i)} x, {D^i}^{\frac 12}{P^i}^\top x ) \in \mathcal Q_r^{n+2} \\ + & x\in\mathbb R^n + \end{array} + \end{align} + + where :math:`\mathcal Q_r^n` denotes the :math:`n`-dimensional quadratic rotated cone. + By conic duality (see e.g., `here `_), we obtain + + .. math:: + + \begin{array}{lll} + \min\ & \frac 12\pi_1 + b_i\pi_2 \\ + \textrm{s.t. } & -a_{(i)}^\top\pi_2 + P^i{D^i}^{\frac 12}\lambda = - u^i \\ + & \sum_{j=1}^n \lambda_i^2 \le \pi_1\pi_2 \\ + & \pi_1, \pi_2 \ge 0 + \end{array} + + In the special case where :math:`D^i = 0`, :math:`\pi_1` can be fixed to 0 and one recovers LP duality. + +- Otherwise, Idol expects :math:`\tilde Q^i` to have one negative eigen value, :math:`a = 0` and :math:`b_i = 0`. + We have, + + .. math:: + + \tilde Q^i = PD^iP^\top = d_{kk}p^{(k)}{p^{(k)}}^\top + \sum_{j\neq k} d_{jj}p^{(j)}{p^{(j)}}^\top + + with :math:`d_{kk} < 0` and :math:`d_{jj} \ge 0` (with :math:`j\neq k`). For simplicity, we will assume that :math:`k = 1`. + Then, constraint :math:`x^\top\tilde Q^ix \le 0` can written as + + .. math:: + + \sum_{j=2}^n d_{jj}( {p^{(j)}}^\top x )^2 \le d_{11}( {p^{(1)}}^\top x )^2 + + which can be expressed with a quadratic cone provided that :math:`{p^{(1)}}^\top x \ge 0` over :math:`[l,u]`. We obtain + + .. math:: + + (\sqrt{-d_{11}} {p^{(1)}}^\top x, \sqrt{d_{22}} {p^{(2)}}^\top x, \sqrt{d_{33}} {p^{(3)}}^\top x, ..., \sqrt{d_{nn}} {p^{(n)}}^\top x) \in \mathcal Q^{n} + + where :math:`\mathcal Q^n` denotes the :math:`n`-dimensional quadratic cone. Finally, we obtain the following result. + + .. math:: + + \begin{align} + \delta^*(u^i|C^i) &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & x^\top P^iD^i{P^i}^\top x \le 0 \\ + & x\in\mathbb R^n + \end{array} \\ + &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & (\sqrt{-d_{11}} {p^{(1)}}^\top x, \sqrt{d_{22}} {p^{(2)}}^\top x, \sqrt{d_{33}} {p^{(3)}}^\top x, ..., \sqrt{d_{nn}} {p^{(n)}}^\top x) \in \mathcal Q^{n} \\ + & {p^{(1)}}^\top x \ge 0 \\ + & x\in\mathbb R^n + \end{array} + \\ + &= + \begin{array}[t]{lll} + \min\ & 0 \\ + \textrm{s.t. } & \sqrt{-d_{11}}p^{(1)}(\lambda_1 + \pi) + \sum_{j=2}^n \sqrt{ d_{jj} }p^{(j)}\lambda_j = -u^{i} \\ + & \sum_{j=2}^n \lambda_j^2 \le \lambda_1 \\ + & \pi \ge 0 + \end{array} + \end{align} + +Conjugate of the objective function +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The conjugate function of :math:`f` is well known to equal to + +.. math:: + + f^*(\pi) = + \begin{array}[t]{lll} + \min\ & \frac 14 (\pi - c)^\top \tilde D^{\dagger} (\pi - c) \\ + \textrm{s.t. } & \pi - b \in \textrm{span}(\tilde D) + \end{array} + +where :math:`\tilde D` is the symmetric matrix associated to :math:`f`. + +Final result +^^^^^^^^^^^^ + +For now, we may assume that all :math:`C^i` are convex sets. + +.. math:: + + \begin{array}{lll} + \max\ & \frac 14 (\mu + c)^\top\tilde D^{-1}(\mu + c) + \sum_{i=1}^m(-\frac 12\pi_1^i - b_i\pi_2^i) - u^\top\lambda^u + l^\top\lambda^l \\ + \textrm{s.t. } & \lambda^u - \lambda^l + \sum_{i=1}^m ( a_{(i)}^\top\pi_2^i - P^i{D^i}^{\frac 12}\lambda^i ) = \mu \\ + & \sum_{j=1}^n \lambda_j^i \le \pi_1^i\pi_2^i & i=1,...,m \\ + & \lambda^u, \lambda^l \ge 0 \\ + & \pi_1^i, \pi_2^i \ge 0 & i=1,...,m + \end{array} diff --git a/_sources/tutorials/robust_optimization/index.rst.txt b/_sources/tutorials/robust_optimization/index.rst.txt new file mode 100644 index 00000000..b83c5072 --- /dev/null +++ b/_sources/tutorials/robust_optimization/index.rst.txt @@ -0,0 +1,42 @@ +.. _robust: + +Robust Optimization +=================== + +Single-stage robust optimization +-------------------------------- + +.. math:: + + \begin{align} + \min \ & c^\top x \\ + \textrm{s.t. } & A(\xi)x \ge b & \forall \xi\in\Xi \\ + & x\in X + \end{align} + +Two-stage robust optimization +----------------------------- + +.. math:: + + \begin{align} + \min \ & c^\top x + x_0 \\ + \textrm{s.t. } & \forall \xi\in\Xi, \exists y\in Y, + \begin{cases} + x_0 \ge d^\top y \\ + T(\xi)x + W(\xi) \ge h(\xi) + \end{cases} \\ + & (x_0,X) \in \mathbb R\times X + \end{align} + +.. math:: + + \begin{align} + \min_{x\in X}\left\{ c^\top x + \max_{\xi\in\Xi}\min_{y\in Y(x,\xi)} d^\top y \right\} + \end{align} + +.. toctree:: + :maxdepth: 1 + :glob: + + dualizing diff --git a/_static/_sphinx_javascript_frameworks_compat.js b/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 00000000..81415803 --- /dev/null +++ b/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. 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+ margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/_static/check-solid.svg b/_static/check-solid.svg new file mode 100644 index 00000000..92fad4b5 --- /dev/null +++ b/_static/check-solid.svg @@ -0,0 +1,4 @@ + + + + diff --git a/_static/clipboard.min.js b/_static/clipboard.min.js new file mode 100644 index 00000000..54b3c463 --- /dev/null +++ b/_static/clipboard.min.js @@ -0,0 +1,7 @@ +/*! + * clipboard.js v2.0.8 + * https://clipboardjs.com/ + * + * Licensed MIT © Zeno Rocha + */ +!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1 + + + + diff --git a/_static/copybutton.css b/_static/copybutton.css new file mode 100644 index 00000000..f1916ec7 --- /dev/null +++ b/_static/copybutton.css @@ -0,0 +1,94 @@ +/* Copy buttons */ +button.copybtn { + position: absolute; + display: flex; + top: .3em; + right: .3em; + width: 1.7em; + height: 1.7em; + opacity: 0; + transition: opacity 0.3s, border .3s, background-color .3s; + user-select: none; + padding: 0; + border: none; + outline: none; + border-radius: 0.4em; + /* The colors that GitHub uses */ + border: #1b1f2426 1px solid; + background-color: #f6f8fa; + color: #57606a; +} + +button.copybtn.success { + border-color: #22863a; + color: #22863a; +} + +button.copybtn svg { + stroke: currentColor; + width: 1.5em; + height: 1.5em; + padding: 0.1em; +} + +div.highlight { + position: relative; +} + +/* Show the copybutton */ +.highlight:hover button.copybtn, button.copybtn.success { + opacity: 1; +} + +.highlight button.copybtn:hover { + background-color: rgb(235, 235, 235); +} + +.highlight button.copybtn:active { + background-color: rgb(187, 187, 187); +} + +/** + * A minimal CSS-only tooltip copied from: + * https://codepen.io/mildrenben/pen/rVBrpK + * + * To use, write HTML like the following: + * + *

Short

+ */ + .o-tooltip--left { + position: relative; + } + + .o-tooltip--left:after { + opacity: 0; + visibility: hidden; + position: absolute; + content: attr(data-tooltip); + padding: .2em; + font-size: .8em; + left: -.2em; + background: grey; + color: white; + white-space: nowrap; + z-index: 2; + border-radius: 2px; + transform: translateX(-102%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); +} + +.o-tooltip--left:hover:after { + display: block; + opacity: 1; + visibility: visible; + transform: translateX(-100%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); + transition-delay: .5s; +} + +/* By default the copy button shouldn't show up when printing a page */ +@media print { + button.copybtn { + display: none; + } +} diff --git a/_static/copybutton.js b/_static/copybutton.js new file mode 100644 index 00000000..2ea7ff3e --- /dev/null +++ b/_static/copybutton.js @@ -0,0 +1,248 @@ +// Localization support +const messages = { + 'en': { + 'copy': 'Copy', + 'copy_to_clipboard': 'Copy to clipboard', + 'copy_success': 'Copied!', + 'copy_failure': 'Failed to copy', + }, + 'es' : { + 'copy': 'Copiar', + 'copy_to_clipboard': 'Copiar al portapapeles', + 'copy_success': '¡Copiado!', + 'copy_failure': 'Error al copiar', + }, + 'de' : { + 'copy': 'Kopieren', + 'copy_to_clipboard': 'In die Zwischenablage kopieren', + 'copy_success': 'Kopiert!', + 'copy_failure': 'Fehler beim Kopieren', + }, + 'fr' : { + 'copy': 'Copier', + 'copy_to_clipboard': 'Copier dans le presse-papier', + 'copy_success': 'Copié !', + 'copy_failure': 'Échec de la copie', + }, + 'ru': { + 'copy': 'Скопировать', + 'copy_to_clipboard': 'Скопировать в буфер', + 'copy_success': 'Скопировано!', + 'copy_failure': 'Не удалось скопировать', + }, + 'zh-CN': { + 'copy': '复制', + 'copy_to_clipboard': '复制到剪贴板', + 'copy_success': '复制成功!', + 'copy_failure': '复制失败', + }, + 'it' : { + 'copy': 'Copiare', + 'copy_to_clipboard': 'Copiato negli appunti', + 'copy_success': 'Copiato!', + 'copy_failure': 'Errore durante la copia', + } +} + +let locale = 'en' +if( document.documentElement.lang !== undefined + && messages[document.documentElement.lang] !== undefined ) { + locale = document.documentElement.lang +} + +let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT; +if (doc_url_root == '#') { + doc_url_root = ''; +} + +/** + * SVG files for our copy buttons + */ +let iconCheck = ` + ${messages[locale]['copy_success']} + + +` + +// If the user specified their own SVG use that, otherwise use the default +let iconCopy = ``; +if (!iconCopy) { + iconCopy = ` + ${messages[locale]['copy_to_clipboard']} + + + +` +} + +/** + * Set up copy/paste for code blocks + */ + +const runWhenDOMLoaded = cb => { + if (document.readyState != 'loading') { + cb() + } else if (document.addEventListener) { + document.addEventListener('DOMContentLoaded', cb) + } else { + document.attachEvent('onreadystatechange', function() { + if (document.readyState == 'complete') cb() + }) + } +} + +const codeCellId = index => `codecell${index}` + +// Clears selected text since ClipboardJS will select the text when copying +const clearSelection = () => { + if (window.getSelection) { + window.getSelection().removeAllRanges() + } else if (document.selection) { + document.selection.empty() + } +} + +// Changes tooltip text for a moment, then changes it back +// We want the timeout of our `success` class to be a bit shorter than the +// tooltip and icon change, so that we can hide the icon before changing back. +var timeoutIcon = 2000; +var timeoutSuccessClass = 1500; + +const temporarilyChangeTooltip = (el, oldText, newText) => { + el.setAttribute('data-tooltip', newText) + el.classList.add('success') + // Remove success a little bit sooner than we change the tooltip + // So that we can use CSS to hide the copybutton first + setTimeout(() => el.classList.remove('success'), timeoutSuccessClass) + setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon) +} + +// Changes the copy button icon for two seconds, then changes it back +const temporarilyChangeIcon = (el) => { + el.innerHTML = iconCheck; + setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon) +} + +const addCopyButtonToCodeCells = () => { + // If ClipboardJS hasn't loaded, wait a bit and try again. This + // happens because we load ClipboardJS asynchronously. + if (window.ClipboardJS === undefined) { + setTimeout(addCopyButtonToCodeCells, 250) + return + } + + // Add copybuttons to all of our code cells + const COPYBUTTON_SELECTOR = 'div.highlight pre'; + const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR) + codeCells.forEach((codeCell, index) => { + const id = codeCellId(index) + codeCell.setAttribute('id', id) + + const clipboardButton = id => + `` + codeCell.insertAdjacentHTML('afterend', clipboardButton(id)) + }) + +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} + + +var copyTargetText = (trigger) => { + var target = document.querySelector(trigger.attributes['data-clipboard-target'].value); + + // get filtered text + let exclude = '.linenos'; + + let text = filterText(target, exclude); + return formatCopyText(text, '', false, true, true, true, '', '') +} + + // Initialize with a callback so we can modify the text before copy + const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText}) + + // Update UI with error/success messages + clipboard.on('success', event => { + clearSelection() + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success']) + temporarilyChangeIcon(event.trigger) + }) + + clipboard.on('error', event => { + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure']) + }) +} + +runWhenDOMLoaded(addCopyButtonToCodeCells) \ No newline at end of file diff --git a/_static/copybutton_funcs.js b/_static/copybutton_funcs.js new file mode 100644 index 00000000..dbe1aaad --- /dev/null +++ b/_static/copybutton_funcs.js @@ -0,0 +1,73 @@ +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +export function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} diff --git a/_static/css/badge_only.css b/_static/css/badge_only.css new file mode 100644 index 00000000..c718cee4 --- /dev/null +++ b/_static/css/badge_only.css @@ -0,0 +1 @@ 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+ +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + `Search finished, found ${resultCount} page(s) matching the search query.` + ); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + /** + * execute search (requires search index to be loaded) + */ + query: (query) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // lookup as object + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); + + // now sort the results by score (in opposite order of appearance, since the + // display function below uses pop() to retrieve items) and then + // alphabetically + results.sort((a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; + }); + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + results = results.reverse(); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], score: Scorer.partialTitle }); + }); + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [word]); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords) => { + const text = Search.htmlToText(htmlText); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/_static/sphinx_highlight.js b/_static/sphinx_highlight.js new file mode 100644 index 00000000..8a96c69a --- /dev/null +++ b/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/api/index.html b/api/index.html new file mode 100644 index 00000000..b5a92301 --- /dev/null +++ b/api/index.html @@ -0,0 +1,165 @@ + + + + + + + API — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Annotation.html b/api/modeling/Annotation.html new file mode 100644 index 00000000..e6c871b1 --- /dev/null +++ b/api/modeling/Annotation.html @@ -0,0 +1,205 @@ + + + + + + + Annotation — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Annotation

+
+
+template<class ObjectT, class ValueT = unsigned int>
class Annotation : public idol::impl::Annotation
+
+

Public Functions

+
+
+inline Annotation(Env &t_env, std::string t_name)
+
+ +
+
+template<class ...ArgsT>
inline Annotation(Env &t_env, std::string t_name, ArgsT&&... t_args)
+
+ +
+
+inline virtual bool is_var_annotation() const override
+
+ +
+
+inline virtual bool is_ctr_annotation() const override
+
+ +
+
+inline const ValueT &default_value() const
+
+ +
+
+inline unsigned int id() const
+
+ +
+
+inline const std::string &name() const
+
+ +
+
+inline bool has_default() const
+
+ +
+
+void free()
+
+ +
+
+

Public Static Functions

+
+
+template<class ...ArgsT>
static inline Annotation<ObjectT, ValueT> make_with_default_value(Env &t_env, std::string t_name, ArgsT&&... t_args)
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Column.html b/api/modeling/Column.html new file mode 100644 index 00000000..a0a3a243 --- /dev/null +++ b/api/modeling/Column.html @@ -0,0 +1,287 @@ + + + + + + + Column — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Column

+
+
+class Column : public idol::impl::Column
+

Column modeling object.

+

This class is used to represent an optimization model’s column. It is made of an objective coefficient and a set of Ctr-Constant pairs representing the Constant coefficient of the column in each row Ctr. Such pairs are called components.

+
+

Public Functions

+
+
+Column() = default
+
+ +
+
+inline Column(Constant &&t_obj)
+
+ +
+
+inline Column(const Constant &t_obj)
+
+ +
+
+Column(const Column &t_src) = default
+
+ +
+
+Column(Column &&t_src) noexcept = default
+
+ +
+
+Column &operator=(const Column &t_src) = default
+
+ +
+
+Column &operator=(Column &&t_src) noexcept = default
+
+ +
+
+Column fix(const Solution::Primal &t_primals) const
+
+ +
+
+inline Constant &obj()
+
+ +
+
+inline const Constant &obj() const
+
+ +
+
+inline ::idol::LinExpr<Var> &obj_quadratic()
+
+ +
+
+inline const ::idol::LinExpr<Var> &obj_quadratic() const
+
+ +
+
+inline LinExpr<Ctr> &linear()
+
+ +
+
+inline const LinExpr<Ctr> &linear() const
+
+ +
+
+inline QuadExpr<Ctr, Var> &quadratic()
+
+ +
+
+inline const QuadExpr<Ctr, Var> &quadratic() const
+
+ +
+
+inline void set_linear(LinExpr<Ctr> &&t_lin_expr)
+
+ +
+
+inline void set_linear(const LinExpr<Ctr> &t_lin_expr)
+
+ +
+
+inline void set_quadratic(QuadExpr<Ctr, Var> &&t_quad_expr)
+
+ +
+
+inline void set_quadratic(const QuadExpr<Ctr, Var> &t_quad_expr)
+
+ +
+
+inline void set_obj(Constant &&t_obj)
+
+ +
+
+inline void set_obj(const Constant &t_obj)
+
+ +
+
+inline Column &operator+=(const Column &t_rhs)
+
+ +
+
+inline Column &operator-=(const Column &t_rhs)
+
+ +
+
+inline Column &operator*=(double t_rhs)
+
+ +
+
+

Public Static Attributes

+
+
+static const Column EmptyColumn
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Constant.html b/api/modeling/Constant.html new file mode 100644 index 00000000..2c7bbdfe --- /dev/null +++ b/api/modeling/Constant.html @@ -0,0 +1,397 @@ + + + + + + + Constant — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Constant

+
+
+class Constant
+

Constant term modeling object.

+

This class is used to build constant terms which will appear in models.

+

Typically, they represent a real number. However, they can also be an affine combination of Param. This can be useful for defining specific decomposition schemes such as Dantzig-Wolfe reformulations where decision variables from a model A are seen as constant terms in a model B.

+

It is composed of a numerical term and a set of Param-numerical pairs representing the following mathematical expression.

+

\( double_0 + \sum_{j=1}^n double_j \times Param_j \)

+

Constant terms can be created by calling the appropriate constructor or by using overloaded operators such as + and *. For instance, 2 * xi where xi is a Param will yield a Constant.

+
+

Public Functions

+
+
+Constant() = default
+

Create a new constant term equal to zero.

+
+ +
+
+Constant(const Param &t_param, double t_value = 1.)
+

Creates a new constant term representing t_value * t_param.

+
+
Parameters:
+
    +

  • t_param – The parameter.

    • +

  • t_value – The factor for the parameter.

    • +
+
+
+
+ +
+
+Constant(const Param &t_param_1, const Param &t_param_2, double t_value = 1.)
+
+ +
+
+Constant(double t_constant)
+

Creates a new constant term equal to the constant given as argument.

+
+
Parameters:
+

t_constant – The constant.

+
+
+
+ +
+
+Constant(const Constant&) = default
+
+ +
+
+Constant(Constant&&) noexcept = default
+
+ +
+
+Constant &operator=(const Constant&) = default
+
+ +
+
+Constant &operator=(Constant&&) noexcept = default
+
+ +
+
+void set(const Param &t_param, double t_value)
+

Sets the factor for a given parameter in the constant term.

+

If t_factor is zero, the entry for t_param is removed (i.e., not stored).

+
+
Parameters:
+
    +

  • t_param – The parameter.

    • +

  • t_value – The factor associated to the parameter.

    • +
+
+
+
+ +
+
+void set(const Param &t_param_1, const Param &t_param_2, double t_value)
+

Sets the factor for a given pair of parameters in the constant term.

+

If t_factor is zero, the entry for t_param is removed (i.e., not stored).

+
+
Parameters:
+
    +

  • t_param_1 – The parameter 1.

    • +

  • t_param_2 – The parameter 3.

    • +

  • t_value – The factor associated to the pair of parameters.

    • +
+
+
+
+ +
+
+double get(const Param &t_param) const
+

Returns the factor associated to the parameter given as argument.

+

If no factor is found, zero is returned.

+
+
Parameters:
+

t_param – The queried parameter.

+
+
+
+ +
+
+double get(const Param &t_param_1, const Param &t_param_2) const
+
+ +
+
+inline void set_numerical(double t_constant)
+

Sets the numerical term equal to the constant given as parameter.

+
+
Parameters:
+

t_constant – The numerical term.

+
+
+
+ +
+
+inline double numerical() const
+

Returns the numerical term of the constant, false otherwise.

+
+ +
+
+bool is_zero() const
+

Returns true if the constant is equal to zero (i.e., if its numerical term is zero and no Param-double pair can be found)

+
+ +
+
+inline unsigned int size() const
+

Returns the number of Param-double pairs stored inside the Constant.

+
+ +
+
+bool is_numerical() const
+

Returns true if the Constant does not contain any Param-double pair.

+
+ +
+
+inline auto linear()
+
+ +
+
+inline auto linear() const
+
+ +
+
+inline auto quadratic()
+
+ +
+
+inline auto quadratic() const
+
+ +
+
+Constant &operator*=(double t_factor)
+

Multiplies the Constant by t_factor (i.e., every Param-double pairs and the numerical term are multiplied).

+
+
Parameters:
+

t_factor – The factor for multiplication.

+
+
+
+ +
+
+Constant &operator+=(double t_term)
+

Adds up a numerical term to the current numerical term.

+
+
Parameters:
+

t_term – The numerical term to add.

+
+
+
+ +
+
+Constant &operator+=(const Param &t_term)
+

Adds a parameter to the constant (equivalent to adding Constant(t_param, 1)).

+

Resulting zero entries are removed.

+
+
Parameters:
+

t_term – The parameter to add.

+
+
+
+ +
+
+Constant &operator+=(const Constant &t_term)
+

Adds up another constant term (i.e., both the numerical terms and every Param-double pairs are added up).

+

Resulting zero-entries are removed.

+
+
Parameters:
+

t_term –

+
+
+
+ +
+
+Constant &operator-=(const Constant &t_term)
+
+ +
+
+Constant &operator-=(double t_term)
+
+ +
+
+Constant &operator-=(Param t_term)
+
+ +
+
+double fix(const Solution::Primal &t_primals) const
+
+ +
+
+double fix(const Solution::Dual &t_duals) const
+
+ +
+
+

Public Static Attributes

+
+
+static Constant Zero
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Ctr.html b/api/modeling/Ctr.html new file mode 100644 index 00000000..4d8debb6 --- /dev/null +++ b/api/modeling/Ctr.html @@ -0,0 +1,223 @@ + + + + + + + Ctr — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Ctr

+
+
+class Ctr : public idol::Object<CtrVersion, Ctr>
+
+

Public Functions

+
+
+Ctr(Env &t_env, TempCtr &&t_temp_ctr, std::string t_name = "")
+
+ +
+
+Ctr(Env &t_env, const TempCtr &t_temp_ctr, std::string t_name = "")
+
+ +
+
+Ctr(Env &t_env, CtrType t_type, Constant &&t_constant, std::string t_name = "")
+
+ +
+
+Ctr(Env &t_env, CtrType t_type, const Constant &t_constant, std::string t_name = "")
+
+ +
+
+inline const std::string &name() const
+
+ +
+
+inline unsigned int id() const
+
+ +
+
+inline bool operator==(const Object<CtrVersion, Ctr> &t_rhs) const
+
+ +
+
+inline bool operator!=(const Object<CtrVersion, Ctr> &t_rhs) const
+
+ +
+
+inline bool is_in(const Model &t_model) const
+
+ +
+
+inline const ValueT &get(const Annotation<Ctr, ValueT> &t_annotation) const
+
+ +
+
+inline void set(const Annotation<Ctr, ValueT> &t_annotation, ArgsT&&... t_args) const
+
+ +
+
+

Public Static Functions

+
+
+template<unsigned int N = 1, unsigned int I = 0>
static inline Vector<Ctr, N - I> make_vector(Env &t_env, const Dim<N> &t_dim, CtrType t_type, const Constant &t_constant, const std::string &t_name = "")
+
+ +
+
+

Friends

+
+
+friend class impl::Env
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Env.html b/api/modeling/Env.html new file mode 100644 index 00000000..d1947322 --- /dev/null +++ b/api/modeling/Env.html @@ -0,0 +1,166 @@ + + + + + + + Env — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Env

+
+
+class Env : public idol::impl::Env
+

This class manages an “optimization environment”. It is used to actually store the versions of each variables and constraints which may arise in optimization problems.

+
+

Public Functions

+
+
+template<class T>
inline const auto &operator[](const T &t_object) const
+
+ +
+
+

Friends

+
+
+friend class impl::Annotation
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Expr.html b/api/modeling/Expr.html new file mode 100644 index 00000000..7185ea39 --- /dev/null +++ b/api/modeling/Expr.html @@ -0,0 +1,287 @@ + + + + + + + Expr — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Expr

+
+
+template<class Key1 = idol::Var, class Key2 = Key1>
class Expr : public idol::impl::Expr<idol::Var, idol::Var>
+
+

Public Functions

+
+
+Expr() = default
+
+ +
+
+inline Expr(double t_num)
+
+ +
+
+inline Expr(const Param &t_param)
+
+ +
+
+inline Expr(Constant &&t_expr)
+
+ +
+
+inline Expr(const Constant &t_expr)
+
+ +
+
+inline Expr(const Key1 &t_var)
+
+ +
+
+inline Expr(LinExpr<Key1> &&t_expr)
+
+ +
+
+inline Expr(const LinExpr<Key1> &t_expr)
+
+ +
+
+inline Expr(QuadExpr<Key1> &&t_expr)
+
+ +
+
+inline Expr(const QuadExpr<Key1> &t_expr)
+
+ +
+
+inline Expr(LinExpr<Key1> &&t_lin_expr, QuadExpr<Key1, Key2> &&t_quad_expr, Constant &&t_constant)
+
+ +
+
+inline Expr(const LinExpr<Key1> &t_lin_expr, const QuadExpr<Key1, Key2> &t_quad_expr, const Constant &t_constant)
+
+ +
+
+Expr(const Expr &t_src) = default
+
+ +
+
+Expr(Expr&&) noexcept = default
+
+ +
+
+Expr &operator=(const Expr &t_rhs) = default
+
+ +
+
+Expr &operator=(Expr&&) noexcept = default
+
+ +
+
+Expr<idol::Var, idol::Var> &operator+=(const Expr<idol::Var, idol::Var> &t_rhs)
+
+ +
+
+Expr<idol::Var, idol::Var> &operator-=(const Expr<idol::Var, idol::Var> &t_rhs)
+
+ +
+
+Expr<idol::Var, idol::Var> &operator*=(double t_rhs)
+
+ +
+
+inline LinExpr<idol::Var> &linear()
+
+ +
+
+inline const LinExpr<idol::Var> &linear() const
+
+ +
+
+inline QuadExpr<idol::Var, idol::Var> &quadratic()
+
+ +
+
+inline const QuadExpr<idol::Var, idol::Var> &quadratic() const
+
+ +
+
+inline Constant &constant()
+
+ +
+
+inline const Constant &constant() const
+
+ +
+
+inline bool is_zero() const
+
+ +
+
+inline void clear()
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/LinExpr.html b/api/modeling/LinExpr.html new file mode 100644 index 00000000..f1d7227b --- /dev/null +++ b/api/modeling/LinExpr.html @@ -0,0 +1,358 @@ + + + + + + + LinExpr — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

LinExpr

+

This class is used to represent linear expressions in the modeling interface of idol.

+

It consists in a set of linear terms which represent products of keys (typically, variables) and scalars.

+
+

Example

+

In this example, we create a linear expression representing the following linear expression.

+
+\[3 x_0 + 2 x_1\]
+
auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x");
+
+LinExpr lin_expr = 3 * x[0] + 2 * x[1];
+
+
+
+
+
+template<class Key = idol::Var>
class LinExpr : public idol::AbstractExpr<idol::Var, LinTerm<idol::Var>>
+
+
Template Parameters:
+

Key – the class representing keys

+
+
+
+

Public Functions

+
+
+LinExpr() = default
+
+ +
+
+LinExpr(const Key &t_key)
+
+ +
+
+LinExpr(Constant &&t_factor, const Key &t_key)
+
+ +
+
+LinExpr(const Constant &t_factor, const Key &t_key)
+
+ +
+
+void set(const Key &t_key, const Constant &t_coefficient)
+

Sets the value of a key’s coefficient

+

The constant is copied.

+

Example: 

LinExpr lin_expr;
+lin_expr.set(x[0], -1);
+
+
+

+
+
Parameters:
+
    +

  • t_key – the key

    • +

  • t_coefficient – the key’s coefficient

    • +
+
+
+
+ +
+
+virtual void set(const Key &t_key, Constant &&t_coefficient) override
+

Sets the value of a key’s coefficient

+

The constant is moved.

+

Example: 

LinExpr lin_expr;
+lin_expr.set(x[0], -1);
+
+
+

+
+
Parameters:
+
    +

  • t_key – the key

    • +

  • t_coefficient – the key’s coefficient

    • +
+
+
+
+ +
+
+virtual const Constant &get(const Key &t_key) const override
+

Returns a key’s coefficient

+

Example: 

LinExpr lin_expr = 2 * x[0] + 3 * x[1];
+
+std::cout << lin_expr.get(x[0]) << std::endl; // output: 2
+
+
+

+
+
Parameters:
+

t_key – the key

+
+
Returns:
+

the key’s coefficient

+
+
+
+ +
+
+virtual void remove(const Key &t_key) override
+

Sets the coefficient of a key to zero

+

This is equivalent to calling LinExpr<Key>::set with a zero coefficient.

+
+
Parameters:
+

t_key – the key

+
+
+
+ +
+
+AbstractExpr<Key, IteratorOutputT, Hash, EqualTo> &operator+=(const AbstractExpr<Key, IteratorOutputT, Hash, EqualTo> &t_rhs)
+

Adds each term of t_rhs to the expression.

+

Zero entries are removed from the resulting expression.

+
+
Parameters:
+

t_rhs – the expression whose terms are to be added up.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+AbstractExpr<Key, IteratorOutputT, Hash, EqualTo> &operator-=(const AbstractExpr<Key, IteratorOutputT, Hash, EqualTo> &t_rhs)
+

Subtracts each term of t_rhs to the expression.

+

Zero entries are removed from the resulting expression.

+
+
Parameters:
+

t_rhs – The object whose terms are to be subtracted.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+AbstractExpr<Key, IteratorOutputT, Hash, EqualTo> &operator*=(double t_factor)
+

Multiplies every term of the expression by t_factor.

+

If t_factor equals zero with tolerance Tolerance::Sparsity, then the expression is emptied.

+
+
Parameters:
+

t_factor – The multiplying factor.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+inline unsigned int size() const
+

Returns the size of the expression (i.e., number of non-zero entries which are currently stored).

+
+
Returns:
+

the size of the expression

+
+
+
+ +
+
+inline bool empty() const
+

Returns true if and only if the size is zero.

+
+
Returns:
+

true if and only if the size is zero

+
+
+
+ +
+
+inline const_iterator begin() const
+

Returns an iterator pointing to the first term of the expression.

+
+
Returns:
+

an iterator pointing to the first term of the expression

+
+
+
+ +
+
+inline const_iterator end() const
+

Returns an iterator pointing to the end of the expression.

+
+
Returns:
+

an iterator pointing to the end the expression

+
+
+
+ +
+
+inline void clear()
+

Removes all entries from the expression.

+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Model.html b/api/modeling/Model.html new file mode 100644 index 00000000..dc108252 --- /dev/null +++ b/api/modeling/Model.html @@ -0,0 +1,1702 @@ + + + + + + + Model — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Model

+

The Model class is probably the most central of idol. It is used to represent a mathematical optimization problem of the +following general form.

+
+\[\begin{split}\begin{array}{lll} + \textrm{minimize } & \displaystyle \sum_{j=1}^n a_{0j}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^0x_jx_k + b_0\\ + \textrm{subject to } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\ + & l_j \le x_j \le u_j & j=1,...,m \\ + & x_j\in\mathbb Z & j\in J_I, +\end{array}\end{split}\]
+

Here, \(x_1, ..., x_n\) are the decision variables with bounds \([l_1,u_1],...,[l_n,u_n]\) (possibly, +\(l_j = -\infty\) or \(u_j = +\infty\)). Note that some variables have integrality requirements (i.e., those whose +indices are in \(J_I\)). Other entities are input parameters of the problem and must typically have real values +(e.g., \(c_j, a_{ij}, q_{jk}^i\) and \(b_i\in\mathbb R\)). Alternatively, optimization problems can also be maximization +problems.

+
+

Example:

+

Here is a short example which builds and solves the following optimization problem.

+
+\[\begin{split}\begin{array}{ll} + \textrm{minimize } & -x_0 - 1.5 x_1 + 3 \\ + \textrm{subject to } & x_0 + 2 x_1 \le 1.5 \\ + & 0 \le x_0 \le 1 \\ + & 0 \le x_1 \le 1 +\end{array}\end{split}\]
+
Env env;
+
+Model model(env);
+
+auto x = model.add_vars(Dim<1>(2), 0, 1, Continuous, "x");
+
+auto c = model.add_ctr(x[0] + 2 * x[1] <= 1.5);
+
+model.set_obj_expr(-x[0] - 1.5 * x[1] + 3);
+
+model.use(Gurobi());
+
+model.optimize();
+
+std::cout << "Best obj = " << model.get_best_obj() << std::endl;
+
+
+
+
+
+class Model : public idol::Matrix
+

This class is used to represent a mathematical optimization model.

+
+

Public Functions

+
+
+explicit Model(Env &t_env)
+

Creates a new model for a mathematical optimization problem.

+

Example: 

Env env;
+Model model(env);
+
+
+

+
+
Parameters:
+

t_env – the optimization environment which will store the model

+
+
+
+ +
+
+Model(Env &t_env, ObjectiveSense t_sense)
+
+ +
+
+Model(const Model&) = delete
+
+ +
+
+Model(Model&&) noexcept
+
+ +
+
+Model &operator=(const Model&) = delete
+
+ +
+
+Model &operator=(Model&&) noexcept = delete
+
+ +
+
+~Model() override
+
+ +
+
+Var add_var(double t_lb, double t_ub, VarType t_type, std::string t_name = "")
+

Creates a new decision variable in the model and returns it.

+

Example: 

model.add_var(0, 1, Binary, "x");
+
+
+

+
+
Parameters:
+
    +

  • t_lb – the lower bound in the model

    • +

  • t_ub – the upper bound in the model

    • +

  • t_type – the type in the model

    • +

  • t_name – the name of the variable

    • +
+
+
Returns:
+

the created variable

+
+
+
+ +
+
+Var add_var(double t_lb, double t_ub, VarType t_type, Column t_column, std::string t_name = "")
+

Creates a new decision variable in the model and returns it.

+

Example: 

model.add_var(0, 1, Binary, Column(-2), "x"); // Adds an objective coefficient of -2
+
+
+

+

Attention: every constraint involved in t_column must already be part of the model.

+
+
Parameters:
+
    +

  • t_lb – the lower bound in the model

    • +

  • t_ub – the upper bound in the model

    • +

  • t_type – the type in the model

    • +

  • t_column – the column in the model

    • +

  • t_name – the name of the variable

    • +
+
+
Returns:
+

the created variable

+
+
+
+ +
+
+template<unsigned int N>
Vector<Var, N> add_vars(Dim<N> t_dim, double t_lb, double t_ub, VarType t_type, const std::string &t_name = "")
+

Creates multiple decision variables in the model and returns them.

+

Example: 

auto x = model.add_vars(Dim<2>(n, m), 0, 1, Binary, "x");
+
+for (unsigned int i = 0 ; i < n ; ++i) {
+     for (unsigned int j = 0 ; j < m ; ++j) {
+         std::cout << x[i][j].name() << std::endl;
+     }
+}
+
+
+

+
+
Template Parameters:
+

N – the number of dimensions for the indices (e.g., N = 2 will create variables with 2 indices, \( x_{ij} \))

+
+
Parameters:
+
    +

  • t_dim – the dimensions for the indices

    • +

  • t_lb – the lower bound for the variables in the model

    • +

  • t_ub – the upper bound for the variables in the model

    • +

  • t_type – the type for the variables in the model

    • +

  • t_name – the base name for the variables (variables are then named by a combination of this name and indices)

    • +
+
+
Returns:
+

the create variables

+
+
+
+ +
+
+void add(const Var &t_var)
+

Adds an existing variable to the model.

+

Example: 

Env env;
+
+Model model1(env);
+auto x = model1.add_var(0, Inf, Continuous, "x");
+
+Model model2(env);
+model2.add(x);
+
+
+

+

Note that the default version of the variable is added to the model (i.e., the variable is added identical to its first version as defined at creation time).

+
+
Parameters:
+

t_var – the variable to add

+
+
+
+ +
+
+void add(const Var &t_var, TempVar t_temp_var)
+

Adds an existing variable to the model with different attributes than the default version (i.e., the variable is added to the model and has the attributes defined in t_temp_var).

+

Example: 

Env env;
+
+Model model1(env);
+auto x = model1.add_var(0, Inf, Continuous, Column(-2), "x"); // x has an objective cost of -2 in model1
+
+Model model2(env);
+model2.add(x, TempVar(0, Inf, Continuous, Column(0))); // x has an objective cost of 0 in model2
+
+
+

+

Attention: every constraint involved in t_temp_var must already be part of the model.

+
+
Parameters:
+
    +

  • t_var – the variable to add

    • +

  • t_temp_var – the attributes of the variable in the model

    • +
+
+
+
+ +
+
+bool has(const Var &t_var) const
+

Returns true if and only if the variable is part of the model

+

Example: 

auto x = model.add_var(-Inf, Inf, Continuous, "x");
+
+std::cout << model.has(x) << std::endl; // output: 1
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

true if and only if the variable is part of the model

+
+
+
+ +
+
+void remove(const Var &t_var)
+

Removes a variable from the model.

+

Example: 

auto x = model.add_var(0, 1, Binary, "x");
+
+std::cout << model.has(x) << std::endl; // output: 1
+
+model.remove(x);
+
+std::cout << model.has(x) << std::endl; // output: 0
+
+
+

+

This also removes every reference to the variable in the objective and within the constraints.

+
+
Parameters:
+

t_var –

+
+
+
+ +
+
+inline ConstIteratorForward<std::vector<Var>> vars() const
+

Returns an object able to construct iterators over the set of variables of the model.

+

Example:

+

for (const Var& var : model.vars()) {
+     std::cout << var.name() << std::endl;
+}
+
+
+

+
+
Returns:
+

an object able to construct iterators over the set of variables of the model.

+
+
+
+ +
+
+Ctr add_ctr(TempCtr t_temp_ctr, std::string t_name = "")
+

Creates a new constraint in the model and returns it.

+

Example: 

auto constraint = model.add_ctr(x[0] + 2 * x[1] <= 1.5, "constraint");
+
+
+

+

Attention: every variable involved in t_temp_ctr must already be part of the model.

+
+
Parameters:
+
    +

  • t_temp_ctr – the constraint attributes in the model

    • +

  • t_name – the name of the constraint

    • +
+
+
Returns:
+

+
+
+
+ +
+
+Ctr add_ctr(Row &&t_row, CtrType t_type, std::string t_name = "")
+

Creates a new constraint in the model and returns it.

+

Example: 

auto constraint = model.add_ctr(Row(x[0] + 2 * x[1], 1.5), LessOrEqual);
+
+
+

+
+
Parameters:
+
    +

  • t_row – the row of the constraint in the model

    • +

  • t_type – the type of the constraint in the model

    • +

  • t_name – the name of the constraint

    • +
+
+
Returns:
+

the created constraint

+
+
+
+ +
+
+template<unsigned int N>
Vector<Ctr, N> add_ctrs(Dim<N> t_dim, CtrType t_type, const Constant &t_constant, const std::string &t_name = "")
+

Creates multiple constraints in the model and returns them.

+

Example: 

auto constraints = model.add_ctrs(Dim<2>(m, n), EqualTo, 1, "constraint");
+
+for (unsigned int i = 0 ; i < n ; ++i) {
+     for (unsigned int j = 0 ; j < m ; ++j) {
+         std::cout << constraints[i][j].name() << std::endl;
+     }
+}
+
+
+

+
+
Template Parameters:
+

N – the number of dimensions for the indices

+
+
Parameters:
+
    +

  • t_dim – the dimensions for the indices

    • +

  • t_type – the type of the constraints in the model

    • +

  • t_constant – the right hand-side of the constraints in the model

    • +

  • t_name – the base name for the constraints (constraints are then named by a combination of this name and indices)

    • +
+
+
Returns:
+

the created constraints

+
+
+
+ +
+
+void add(const Ctr &t_ctr)
+

Adds an existing variable to the model.

+

Example: 

Env env;
+
+Model model1(env);
+auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x");
+auto constraint = model1.add_ctr(x[0] + 2 * x[1] <= 1.5);
+
+Model model2(env)
+model2.add(x[0]);
+model2.add(x[1]);
+model2.add(constraint);
+
+
+

+

Note that the default version of the constraint is added to the model (i.e., the constraint is added identical to its first version as defined at creation time).

+

Attention: every variable involved in the default version must already be part of the model.

+
+
Parameters:
+

t_ctr –

+
+
+
+ +
+
+void add(const Ctr &t_ctr, TempCtr t_temp_ctr)
+

Adds an existing constraint to the model with different attributes than the default version (i.e., the constraint is added to the model and has the attributes defined in t_temp_ctr).

+

Example: 

Env env;
+
+Model model1(env);
+auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x");
+auto constraint = model1.add_ctr(x[0] + 2 * x[1] <= 1.5);
+
+Model model2(env)
+model2.add(x[0]);
+model2.add(x[1]);
+model2.add(constraint, x[0] - x[1] >= 0);
+
+
+

+

Attention: every variable involved in t_temp_var must already be part of the model.

+
+
Parameters:
+
    +

  • t_ctr – the constraint to add

    • +

  • t_temp_ctr – the attributes for the constraint in the model

    • +
+
+
+
+ +
+
+bool has(const Ctr &t_ctr) const
+

Returns true if and only if the constraint is part of the model.

+

Example: 

auto c = model.add_ctr(x[0] + 1.5 * x[1] <= 2);
+
+std::cout << model.has(c) << std::endl; // output: 1
+
+
+

+
+
Parameters:
+

t_ctr – the constraint

+
+
Returns:
+

true if and only if the constraint is part of the model

+
+
+
+ +
+
+void remove(const Ctr &t_ctr)
+

Removes a constraint from the model.

+

Example: 

auto c = model.add_ctr(x[0] + 1.5 * x[1] <= 2);
+
+std::cout << model.has(c) << std::endl; // output: 1
+
+model.remove(c);
+
+std::cout << model.has(c) << std::endl; // output: 0
+
+
+

+
+
Parameters:
+

t_ctr –

+
+
+
+ +
+
+inline ConstIteratorForward<std::vector<Ctr>> ctrs() const
+

Returns an object able to construct iterators over the set of constraints of the model.

+

Example: 

for (const Ctr& ctr : model.ctrs()) {
+     std::cout << ctr.name() << std::endl;
+}
+
+
+

+
+
Returns:
+

an object able to construct iterators over the set of constraints of the model.

+
+
+
+ +
+
+inline unsigned int id() const
+

Returns the unique id (within a given environment) of the model.

+

Example:

+

std::cout << model.id() << std::endl;
+
+
+

+
+
Returns:
+

+
+
+
+ +
+
+Model *clone() const
+

Creates a new identical model.

+

Example: 

Model* copy = model.clone();
+// ...
+delete copy;
+
+
+

+
+
Returns:
+

a pointer to the new copy

+
+
+
+ +
+
+inline Env &env() const
+

Returns the optimization environment of the model

+

Example:

+

Env& env = model.env();
+Var x(env, 0, 1, Binary, "x");
+
+
+

+
+
Returns:
+

the optimization environment

+
+
+
+ +
+
+void use(const OptimizerFactory &t_optimizer_factory)
+

Sets the optimizer for the model.

+

The optimizer is directly created using t_optimizer_factory. If an optimizer was already created, it is replaced by the new one.

+

Example: 

model.use(Gurobi());
+
+
+

+
+
Parameters:
+

t_optimizer_factory –

+
+
+
+ +
+
+bool has_optimizer() const
+

Returns true if and only if the model currently has an optimizer.

+

Example: 

model.use(Gurobi());
+
+std::cout << model.has_optimizer() << std::endl; // output: 1
+
+
+

+
+
Returns:
+

true if and only if the model currently has an optimizer.

+
+
+
+ +
+
+void unuse()
+

Removes an existing optimizer.

+

The model is therefore left without any optimizer.

+

Example: 

model.use(Gurobi());
+
+std::cout << model.has_optimizer() << std::endl; // output: 1
+
+model.unuse();
+
+std::cout << model.has_optimizer() << std::endl; // output: 0
+
+
+

+
+ +
+
+template<class T, unsigned int N>
void add_vector(const Vector<T, N> &t_vector)
+

Adds a vector of optimization objects to the model (i.e., variables or constraints).

+

Example: 

std::vector<std::vector<Var>> x = Var::make_vector(Dim<2>(n, m), 0, 1, Binary, "x");
+
+model.add_vector<Var, 2>(x);
+
+
+

+
+
Template Parameters:
+
    +

  • T – the type of optimization objects to add

    • +

  • N – the number of dimensions

    • +
+
+
Parameters:
+

t_vector – the vector of objects

+
+
+
+ +
+
+inline Optimizer &optimizer()
+

Returns a reference to the model’s optimizer.

+

Example: 

std::cout << model.optimizer().as<Optimizers::BranchAndBound>().n_solved_nodes() << std::endl;
+
+
+

+
+
Returns:
+

a reference to the model’s optimizer

+
+
+
+ +
+
+inline const Optimizer &optimizer() const
+

Returns a const reference to the model’s optimizer.

+

Example: 

std::cout << model.optimizer().as<Optimizers::BranchAndBound>().n_solved_nodes() << std::endl;
+
+
+

+
+
Returns:
+

a const reference to the model’s optimizer

+
+
+
+ +
+
+void optimize()
+

Solves the model using the model’s optimizer

+

Example: 

model.use(Gurobi());
+
+model.optimize();
+
+
+ Attention: an optimizer must have been set beforehand.

+
+ +
+
+void write(const std::string &t_name)
+

Asks the model’s optimizer to write the model (or any useful piece of information) to a file.

+

Example: 

model.use(Gurobi());
+
+model.write("model.lp");
+
+
+

+

Attention: an optimizer must have been set beforehand.

+
+
Parameters:
+

t_name – the destination file

+
+
+
+ +
+
+void update()
+

Asks the model’s optimizer to update his current version of the model.

+

Note that you typically do not need to call this method since updates are automatically done. While some optimizers perform “lazy updates” and actually update their representation of the model only when necessary (e.g., before solving or writing to file), even in this case, updates are automatically done so that the user should not need to use this method.

+

Example: 

model.add(x);
+
+model.update();
+
+
+

+

Attention: an optimizer must have been set beforehand.

+
+ +
+
+ObjectiveSense get_obj_sense() const
+

Returns the objective sense of the model (Minimize or Maximize).

+

Example: 

ObjectiveSense sense = model.get_obj_sense();
+
+if (sense == Minimize) {
+     std::cout << "This is a minimization problem" << std::endl;
+}
+
+
+

+
+
Returns:
+

the objective sense of the model

+
+
+
+ +
+
+const Expr<Var, Var> &get_obj_expr() const
+

Returns the objective function of the model.

+

Example: 

const Expr& objective = model.get_obj_expr();
+
+std::cout << "The objective function is " << objective << std::endl;
+
+
+

+
+
Returns:
+

the objective function of the model

+
+
+
+ +
+
+const LinExpr<Ctr> &get_rhs_expr() const
+

Returns the right hand-side of the model.

+

Example: 

const LinExpr<Ctr> rhs = model.get_rhs_expr();
+
+std::cout << "The model RHS is " << rhs << std::endl;
+
+
+

+
+
Returns:
+

the right hand-side of the model

+
+
+
+ +
+
+const Constant &get_mat_coeff(const Ctr &t_ctr, const Var &t_var) const
+

Returns a specific coefficient in the model’s matrix.

+

Example: 

const Constant& coeff = model.get_mat_coeff(c1, x[0]);
+std::cout << "The coefficient of x_0 in constraint c1 is " << coeff << std::endl;
+
+
+

+
+
Parameters:
+
    +

  • t_ctr – the constraint corresponding to the row

    • +

  • t_var – the column corresponding to the column

    • +
+
+
Returns:
+

the matrix coefficient

+
+
+
+ +
+
+SolutionStatus get_status() const
+

Returns the current status of the optimizer.

+

Example: 

model.optimize();
+
+if (model.get_status() == Optimal) {
+     std::cout << "Optimal solution found!" << std::endl;
+}
+
+
+

+

Attention: an optimizer must have been set beforehand.

+
+
Returns:
+

+
+
+
+ +
+
+SolutionReason get_reason() const
+

Returns the reason for the current status of the optimizer.

+

Example: 

model.optimize();
+
+if (get_status() == Fail) {
+     std::cout << "The optimizer failed because of " << get_reason() << std::endl; // e.g. output: Numeric
+}
+
+
+

+

Attention: an optimizer must have been set beforehand.

+
+
Returns:
+

+
+
+
+ +
+
+double get_best_obj() const
+

Returns the best objective value currently known by the optimizer (i.e., feasible solution objective value)

+

Example: 

model.optimize();
+
+if (model.get_status() == Optimal) {
+    std::cout << "Optimum = " << model.get_best_obj() << std::endl;
+}
+
+
+

+

Attention: an optimizer must have been set beforehand.

+
+
Returns:
+

the best objective value currently known by the optimizer

+
+
+
+ +
+
+double get_best_bound() const
+

Returns the best bound currently known by the optimizer (e.g., dual bound).

+

Example: 

model.optimize();
+
+if (get_status() == Feasible) {
+     const double best_obj = model.get_best_obj();
+     const double best_bound = model.get_best_bound();
+     std::cout << "Gap: " << relative_gap(best_bound, best_obj) * 100 << " % << std::endl;
+}
+
+
+

+
+
Returns:
+

the best bound currently known by the optimizer

+
+
+
+ +
+
+void set_obj_sense(ObjectiveSense t_value)
+

Sets the objective sense of the model.

+

Example: 

model.set_obj_sense(Maximize);
+
+
+

+
+
Parameters:
+

t_value – the new objective sense

+
+
+
+ +
+
+void set_obj_expr(const Expr<Var, Var> &t_objective)
+

Sets the objective expression of the model.

+

The expression is copied.

+

Example: 

Expr objective = - x[0] - 2 * x[2];
+model.set_obj_expr(objective);
+
+
+

+

Attention: every variable involved in t_objective must already be part of the model.

+
+
Parameters:
+

t_objective –

+
+
+
+ +
+
+void set_obj_expr(Expr<Var, Var> &&t_objective)
+

Sets the objective expression of the model.

+

The expression is moved.

+

Example: 

model.set_obj_expr(- x[0] - 2 * x[2]);
+
+
+

+

Attention: every variable involved in t_objective must already be part of the model.

+
+
Parameters:
+

t_objective –

+
+
+
+ +
+
+void set_rhs_expr(const LinExpr<Ctr> &t_rhs)
+

Sets the right hand-side of the model

+

The expression is copied.

+

Example: 

Lin<Ctr> rhs = 2 * c1 + 3 * c2;
+
+model.set_rhs_expr(rhs); // RHS is then 2 for constraint c1, 2 for constraint c2, 0 for others
+
+
+

+

Attention: every constraint involved in t_rhs must already be part of the model.

+
+
Parameters:
+

t_rhs – the right hand-side

+
+
+
+ +
+
+void set_rhs_expr(LinExpr<Ctr> &&t_rhs)
+

Sets the right hand-side of the model

+

The expression is moved.

+

Example: 

Lin<Ctr> rhs = 2 * c1 + 3 * c2;
+
+model.set_rhs_expr(std::move(rhs)); // RHS is then 2 for constraint c1, 2 for constraint c2, 0 for others
+
+
+

+

Attention: every constraint involved in t_rhs must already be part of the model.

+
+
Parameters:
+

t_rhs – the right hand-side

+
+
+
+ +
+
+void set_obj_const(const Constant &t_constant)
+

Sets the objective constant.

+

The constant is copied.

+

Example: 

Constant constant = 10;
+model.set_obj_const(constant);
+
+
+

+
+
Parameters:
+

t_constant – the constant

+
+
+
+ +
+
+void set_obj_const(Constant &&t_constant)
+

Sets the objective constant.

+

The constant is moved.

+

Example: 

model.set_obj_const(10);
+
+
+

+
+
Parameters:
+

t_constant – the constant

+
+
+
+ +
+
+void set_mat_coeff(const Ctr &t_ctr, const Var &t_var, const Constant &t_coeff)
+

Sets a specific matrix coefficient.

+

The coefficient is copied.

+

Example: 

Constant coeff = 3;
+model.set_mat_coeff(c1, x[0], coeff); // The coefficient of x_0 in constraint c1 is 3
+
+
+

+
+
Parameters:
+
    +

  • t_ctr – the constraint corresponding to the row

    • +

  • t_var – the variable corresponding to the column

    • +

  • t_coeff – the coefficient

    • +
+
+
+
+ +
+
+void set_mat_coeff(const Ctr &t_ctr, const Var &t_var, Constant &&t_coeff)
+

Sets a specific matrix coefficient.

+

The coefficient is moved.

+

Example: 

model.set_mat_coeff(c1, x[0], 3); // The coefficient of x_0 in constraint c1 is 3
+
+
+

+
+
Parameters:
+
    +

  • t_ctr – the constraint corresponding to the row

    • +

  • t_var – the variable corresponding to the column

    • +

  • t_coeff – the coefficient

    • +
+
+
+
+ +
+
+Ctr get_ctr_by_index(unsigned int t_index) const
+
+ +
+
+Var get_var_by_index(unsigned int t_index) const
+
+ +
+
+unsigned int get_ctr_index(const Ctr &t_ctr) const
+

Returns the current index of the constraint in the model.

+

Example: 

unsigned int index = model.get_ctr_index(c1);
+
+std::cout << "The current index of c1 is " << index << std::endl;
+
+
+

+

Note that the index of the constraint may change over time (in particular, when objects are removed from the model)

+
+
Parameters:
+

t_ctr – the constraint

+
+
Returns:
+

the constraint’s index

+
+
+
+ +
+
+CtrType get_ctr_type(const Ctr &t_ctr) const
+

Returns the type of the constraint in the model

+

Example: 

CtrType type = model.get_ctr_type(c1);
+
+if (type == LessOrEqual) {
+     std::cout << "c1 is a <= constraint" << std::endl;
+}
+
+
+

+
+
Parameters:
+

t_ctr – the constraint

+
+
Returns:
+

the type of the constraint

+
+
+
+ +
+
+const Row &get_ctr_row(const Ctr &t_ctr) const
+

Returns the row of the constraint in the model.

+

Example: 

const Row& row = model.get_ctr_row(c1);
+
+std::cout << "The linear part of c1 is " << row.linear() << std::endl;
+std::cout << "The quadratic part of c1 is " << row.quadratic() << std::endl;
+std::cout << "The RHS of c1 is " << row.rhs() << std::endl;
+
+
+

+
+
Parameters:
+

t_ctr – the constraint

+
+
Returns:
+

the constraint’s row

+
+
+
+ +
+
+double get_ctr_dual(const Ctr &t_ctr) const
+

Returns the dual value of a constraint

+

Example: 

model.optimize();
+
+const double dual = model.get_ctr_dual(c1);
+
+
+

+
+
Parameters:
+

t_ctr – the constraint

+
+
Returns:
+

the constraint’s dual value

+
+
+
+ +
+
+double get_ctr_farkas(const Ctr &t_ctr) const
+

Returns the Farkas certificate of the constraint

+

Example: 

model.optimize();
+
+if (model.get_status() == Infeasible) {
+     std::cout << "The Farkas certificate for c1 is " << model.get_ctr_farkas(c1) << std::endl;
+}
+
+
+

+
+
Parameters:
+

t_ctr – the constraint

+
+
Returns:
+

the farkas certificate for the constraint

+
+
+
+ +
+
+void set_ctr_rhs(const Ctr &t_ctr, const Constant &t_rhs)
+

Sets a constraint’s right hand-side

+

The constant is copied.

+

Example: 

Constant rhs = 10;
+model.set_ctr_rhs(rhs);
+
+
+

+
+
Parameters:
+
    +

  • t_ctr – the constraint

    • +

  • t_rhs – the right hand-side

    • +
+
+
+
+ +
+
+void set_ctr_rhs(const Ctr &t_ctr, Constant &&t_rhs)
+

Sets a constraint’s right hand-side

+

The constant is moved.

+

Example: 

model.set_ctr_rhs(10);
+
+
+

+
+
Parameters:
+
    +

  • t_ctr – the constraint

    • +

  • t_rhs – the constraint’s right hand-side

    • +
+
+
+
+ +
+
+void set_ctr_type(const Ctr &t_ctr, CtrType t_type)
+

Sets a constraint’s type.

+

Example: 

model.set_ctr_type(LessOrEqual);
+
+
+

+
+
Parameters:
+
    +

  • t_ctr – the constraint

    • +

  • t_type – the constraint’s type

    • +
+
+
+
+ +
+
+void set_ctr_row(const Ctr &t_ctr, const Row &t_row)
+

Sets a constraint’s row.

+

The row is copied.

+

Example: 

Row row(x[0] + 2 * x[1], 1.5);
+model.set_ctr_row(row);
+
+
+

+

Attention: every variable involved in t_row must already be part of the model.

+
+
Parameters:
+
    +

  • t_ctr – the constraint

    • +

  • t_row – the constraint’s row

    • +
+
+
+
+ +
+
+void set_ctr_row(const Ctr &t_ctr, Row &&t_row)
+

Sets a constraint’s row.

+

The row is moved.

+

Example: 

Row row(x[0] + 2 * x[1], 1.5);
+model.set_ctr_row(std::move(row));
+
+
+

+

Attention: every variable involved in t_row must already be part of the model.

+
+
Parameters:
+
    +

  • t_ctr – the constraint

    • +

  • t_row – the constraint’s row

    • +
+
+
+
+ +
+
+unsigned int get_var_index(const Var &t_var) const
+

Returns the current index of the variable in the model.

+

Example: 

unsigned int index = model.get_ctr_index(x[0]);
+
+std::cout << "The current index of x_0 is " << index << std::endl;
+
+
+

+

Note that the index of the variable may change over time (in particular, when objects are removed from the model)

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the variable’s index

+
+
+
+ +
+
+VarType get_var_type(const Var &t_var) const
+

Returns the variable’s type in the model

+

Example: 

VarType type = model.get_var_type(x[0]);
+
+if (type == Continuous) {
+     std::cout << "x_0 is a continuous variable" << std::endl;
+}
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the variable’s type

+
+
+
+ +
+
+double get_var_lb(const Var &t_var) const
+

Returns the lower bound of a variable in the model

+

Example: 

const double lb = model.get_var_lb(x[0]);
+
+std::cout << "x_0 >= " << lb << " is part of the model" << std::endl;
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the variable’s lower bound

+
+
+
+ +
+
+double get_var_ub(const Var &t_var) const
+

Returns the upper bound of a variable in the model

+

Example: 

const double ub = model.get_var_ub(x[0]);
+
+std::cout << "x_0 <= " << ub << " is part of the model" << std::endl;
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the variable’s upper bound

+
+
+
+ +
+
+double get_var_primal(const Var &t_var) const
+

Returns the primal value of a variable in the model

+

Example: 

model.optimize();
+
+if (model.get_status() == Optimal) {
+     std::cout << "Primal value of x_0 is " << model.get_var_primal(x[0]) << std::endl;
+}
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the primal value

+
+
+
+ +
+
+double get_var_ray(const Var &t_var) const
+

When the model is unbounded, returns the ray value of a variable of the model

+

Example: 

model.optimize();
+
+if (model.get_status() == Unbounded) {
+     std::cout << "Ray value of x_0 is " << model.get_var_ray(x[0]) << std::endl;
+}
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the ray value

+
+
+
+ +
+
+const Column &get_var_column(const Var &t_var) const
+

Returns the column of a variable in the model.

+

Example: 

const Column& column = model.get_var_column(t_var);
+
+std::cout << "The objective coefficient of x_0 is " << column.obj() << std::endl;
+
+
+

+
+
Parameters:
+

t_var – the variable

+
+
Returns:
+

the variable’s column

+
+
+
+ +
+
+void set_var_type(const Var &t_var, VarType t_type)
+

Sets a variable’s type in the model.

+

Example: 

model.set_var_type(x[0], Binary); // x_0 is now binary
+
+
+

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_type – the variable’s type

    • +
+
+
+
+ +
+
+void set_var_lb(const Var &t_var, double t_lb)
+

Sets a variable’s lower bound in the model

+

Example: 

model.set_var_lb(x[0], 1); // Set the restriction x_0 >= 1
+
+
+

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_lb – the variable’s lower bound

    • +
+
+
+
+ +
+
+void set_var_ub(const Var &t_var, double t_ub)
+

Sets a variable’s upper bound in the model

+

Example: 

model.set_var_ub(x[0], 0); // Set the restriction x_0 <= 1
+
+
+

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_lb – the variable’s upper bound

    • +
+
+
+
+ +
+
+void set_var_obj(const Var &t_var, const Constant &t_obj)
+

Sets a variable’s objective coefficient in the model.

+

The constant is copied.

+

Example: 

Constant obj = 10;
+model.set_var_obj(x[0], obj);
+
+
+

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_obj – the variable’s objective coefficient

    • +
+
+
+
+ +
+
+void set_var_obj(const Var &t_var, Constant &&t_obj)
+

Sets a variable’s objective coefficient in the model.

+

The constant is moved.

+

Example: 

model.set_var_obj(x[0], 10);
+
+
+

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_obj – the variable’s objective coefficient

    • +
+
+
+
+ +
+
+void set_var_column(const Var &t_var, const Column &t_column)
+

Sets a variable’s column in the model.

+

The column is copied.

+

Example: 

Column column(10);
+model.set_var_column(x[0], column);
+
+
+

+

Attention: every constraint involved in t_column must already be part of the model.

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_column – the variable’s column

    • +
+
+
+
+ +
+
+void set_var_column(const Var &t_var, Column &&t_column)
+

Sets a variable’s column in the model.

+

The column is moved.

+

Example: 

Column column(10);
+model.set_var_column(x[0], std::move(column));
+
+
+

+

Attention: every constraint involved in t_column must already be part of the model.

+
+
Parameters:
+
    +

  • t_var – the variable

    • +

  • t_column – the variable’s column

    • +
+
+
+
+ +
+
+unsigned int get_n_solutions() const
+

Returns the number of available primal solutions.

+

Some optimizers can find several optimal or sub-optimal solutions (e.g., in branch-and-bound algorithms with solution pools). This function can be used to query the number of available solutions. The solution is selected with Model::set_solution_index and retrieved via get_var_primal and get_best_obj.

+

Example: 

model.optimize();
+
+std::cout << n_solutions << " solution(s) have been found" << std::endl;
+
+
+

+
+
Returns:
+

the number of available solution primal solutions

+
+
+
+ +
+
+unsigned int get_solution_index() const
+

Returns the current solution index.

+

Some optimizers can find several optimal or sub-optimal solutions (e.g., in branch-and-bound algorithms with solution pools). This function return the current solution index which is being returned by the model.

+

Example: 

model.optimize();
+
+std::cout << model.get_solution_index() << std::endl; // output: 0
+
+
+

+
+
Returns:
+

+
+
+
+ +
+
+void set_solution_index(unsigned int t_index)
+

Sets the index of the solution returned by get_var_primal, get_status and get_reason.

+

Some optimizers can find several optimal or sub-optimal solutions (e.g., in branch-and-bound algorithms with solution pools). This method can be used to change the solution index which is being returned by the model.

+

Example: 

model.optimize();
+
+const unsigned int n_solutions = model.get_n_solutions();
+
+std::cout << n_solutions << " solution(s) have been found" << std::endl;
+
+for (unsigned int i = 0 ; i < n_solutions ; ++i) {
+     model.set_solution_index(i);
+     std::cout << save_primal(model) << std::endl;
+}
+
+
+

+
+
Returns:
+

the number of available solution primal solutions

+
+
+
+ +
+
+template<unsigned int N>
idol::Vector<idol::Var, N> add_vars(Dim<N> t_dim, double t_lb, double t_ub, VarType t_type, const std::string &t_name)
+
+ +
+
+template<unsigned int N>
idol::Vector<idol::Ctr, N> add_ctrs(Dim<N> t_dim, CtrType t_type, const Constant &t_constant, const std::string &t_name)
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Param.html b/api/modeling/Param.html new file mode 100644 index 00000000..f79d341a --- /dev/null +++ b/api/modeling/Param.html @@ -0,0 +1,208 @@ + + + + + + + Param — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Param

+
+
+class Param
+

Parameter modeling object.

+

This class is used to model attributes for optimization models. More precisely, it represents a variable from a model A which is considered constant in another model B.

+

Parameters are created using the Model::add_parameter method, rather than by using standard constructors.

+

A model cannot have a parameter referring to one of its own variables.

+
+

Public Functions

+
+
+inline explicit Param(const Var &t_var)
+
+ +
+
+inline explicit Param(const Ctr &t_ctr)
+
+ +
+
+Param(const Param &t_param) = default
+
+ +
+
+Param(Param &&t_param) noexcept = default
+
+ +
+
+Param &operator=(const Param &t_param) = default
+
+ +
+
+Param &operator=(Param &&t_param) noexcept = default
+
+ +
+
+template<class T>
inline bool is() const
+
+ +
+
+template<class T>
inline T as() const
+
+ +
+
+inline unsigned int id() const
+

Returns the id of the parameter.

+
+ +
+
+inline const std::string &name() const
+

Returns the name of the parameter.

+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/QuadExpr.html b/api/modeling/QuadExpr.html new file mode 100644 index 00000000..f9b15f2c --- /dev/null +++ b/api/modeling/QuadExpr.html @@ -0,0 +1,207 @@ + + + + + + + QuadExpr — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

QuadExpr

+
+
+template<class Key1 = idol::Var, class Key2 = Key1, class Hash = std::conditional_t<std::is_same_v<Key1, Key2>, idol::impl::symmetric_pair_hash, std::hash<std::pair<Key1, Key2>>>, class EqualTo = std::conditional_t<std::is_same_v<Key1, Key2>, idol::impl::symmetric_pair_equal_to, std::equal_to<std::pair<Key1, Key2>>>>
class QuadExpr : public AbstractExpr<std::pair<idol::Var, idol::Var>, QuadTerm<idol::Var, idol::Var>, std::conditional_t<std::is_same_v<idol::Var, idol::Var>, idol::impl::symmetric_pair_hash, std::hash<std::pair<idol::Var, idol::Var>>>, std::conditional_t<std::is_same_v<idol::Var, idol::Var>, idol::impl::symmetric_pair_equal_to, std::equal_to<std::pair<idol::Var, idol::Var>>>>
+
+

Public Functions

+
+
+QuadExpr() = default
+
+ +
+
+QuadExpr(const Key1 &t_a, const Key2 &t_b)
+
+ +
+
+QuadExpr(Constant &&t_factor, const Key1 &t_a, const Key2 &t_b)
+
+ +
+
+QuadExpr(const Constant &t_factor, const Key1 &t_a, const Key2 &t_b)
+
+ +
+
+QuadExpr(const QuadExpr&) = default
+
+ +
+
+QuadExpr(QuadExpr&&) noexcept = default
+
+ +
+
+QuadExpr &operator=(const QuadExpr&) = default
+
+ +
+
+QuadExpr &operator=(QuadExpr&&) noexcept = default
+
+ +
+
+virtual ~QuadExpr() = default
+
+ +
+
+void set(const Key1 &t_a, const Key2 &t_b, Constant t_coefficient)
+
+ +
+
+const Constant &get(const Key1 &t_a, const Key2 &t_b) const
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Row.html b/api/modeling/Row.html new file mode 100644 index 00000000..87770b48 --- /dev/null +++ b/api/modeling/Row.html @@ -0,0 +1,293 @@ + + + + + + + Row — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Row

+
+
+class Row : public idol::impl::Row
+

Row modeling object.

+

This class is used to represent an optimization model’s row. It is made of a right handside and a set of Var-Constant pairs representing the Constant coefficient of the row in each column Var. Such pairs are called left handside terms.

+

The whole left handside is stored as an Expr while the whole right handside is stored as a Constant.

+
+

Public Functions

+
+
+Row() = default
+
+ +
+
+inline Row(Expr<Var, Var> &&t_lhs, Expr<Var, Var> &&t_rhs)
+
+ +
+
+inline Row(Expr<Var, Var> &&t_lhs, const Expr<Var, Var> &t_rhs)
+
+ +
+
+inline Row(const Expr<Var, Var> &t_lhs, Expr<Var, Var> &&t_rhs)
+
+ +
+
+inline Row(const Expr<Var, Var> &t_lhs, const Expr<Var, Var> &t_rhs)
+
+ +
+
+Row(const Row &t_src) = default
+
+ +
+
+Row(Row &&t_src) noexcept = default
+
+ +
+
+Row &operator=(const Row &t_src) = default
+
+ +
+
+Row &operator=(Row &&t_src) noexcept = default
+
+ +
+
+Row fix(const Solution::Primal &t_primals) const
+
+ +
+
+Row fix(const Solution::Dual &t_duals) const
+
+ +
+
+inline Constant &rhs()
+
+ +
+
+inline const Constant &rhs() const
+
+ +
+
+inline LinExpr<Var> &linear()
+
+ +
+
+inline const LinExpr<Var> &linear() const
+
+ +
+
+inline QuadExpr<Var, Var> &quadratic()
+
+ +
+
+inline const QuadExpr<Var, Var> &quadratic() const
+
+ +
+
+inline void set_linear(LinExpr<Var> &&t_lin_expr)
+
+ +
+
+inline void set_linear(const LinExpr<Var> &t_lin_expr)
+
+ +
+
+inline void set_quadratic(QuadExpr<Var, Var> &&t_quad_expr)
+
+ +
+
+inline void set_quadratic(const QuadExpr<Var, Var> &t_quad_expr)
+
+ +
+
+inline void set_rhs(Constant &&t_rhs)
+
+ +
+
+inline void set_rhs(const Constant &t_rhs)
+
+ +
+
+inline Row &operator+=(const Row &t_rhs)
+
+ +
+
+inline Row &operator-=(const Row &t_rhs)
+
+ +
+
+inline Row &operator*=(double t_rhs)
+
+ +
+
+

Public Static Attributes

+
+
+static const Row EmptyRow
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/SolutionDual.html b/api/modeling/SolutionDual.html new file mode 100644 index 00000000..dd63ccb5 --- /dev/null +++ b/api/modeling/SolutionDual.html @@ -0,0 +1,311 @@ + + + + + + + Solution::Dual — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Solution::Dual

+
+
+class Dual : public idol::AbstractSolution<Ctr, Dual>
+
+

Public Types

+
+
+using const_iterator = typename Map<Ctr, double>::const_iterator
+
+ +
+
+

Public Functions

+
+
+inline void set_status(SolutionStatus t_status)
+

Sets the solution status.

+
+
Parameters:
+

t_status – The desired solution status.

+
+
+
+ +
+
+inline SolutionStatus status() const
+

Returns the stored solution status.

+
+ +
+
+inline void set_reason(SolutionReason t_reason)
+
+ +
+
+inline SolutionReason reason() const
+
+ +
+
+inline void set_objective_value(double t_value)
+

Sets the stored objective value.

+
+
Parameters:
+

t_value – The desired objective value.

+
+
+
+ +
+
+inline double objective_value() const
+

Returns the stored objective value.

+
+ +
+
+inline bool has_objective_value() const
+
+ +
+
+inline void reset_objective_value()
+
+ +
+
+void set(const Ctr &t_key, double t_value)
+

Sets the value associated to the key given as argument.

+
+
Parameters:
+
    +

  • t_key – The key for which the entry should be set.

    • +

  • t_value – The desired value associated to the key.

    • +
+
+
+
+ +
+
+double get(const Ctr &t_key) const
+

Returns the value associated to the key given as argument.

+

If no value is stored, zero is returned.

+
+
Parameters:
+

t_key – The queried key.

+
+
+
+ +
+
+inline const_iterator begin() const
+
+ +
+
+inline const_iterator end() const
+
+ +
+
+inline const_iterator cbegin() const
+
+ +
+
+inline const_iterator cend() const
+
+ +
+
+double norm(double t_p = 2.) const
+

Returns the \( l_p \)-norm of the solution.

+

Note that Inf is a possible value for t_p, in which case, the infinite norm is computed.

+
+
Parameters:
+

t_p – The \( p \) parameter for the \( l_p \)-norm.

+
+
+
+ +
+
+Dual &merge_without_conflict(Dual t_rhs)
+

Merges the solution with another solution, explicitly expecting that no conflict will arise (i.e., expecting that no entry from the solution is also present in the other solution). If a conflict is detected, an Exception is thrown.

+
+
Parameters:
+

t_rhs – The solution to merge.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+Dual &normalize(double t_p = 2.)
+

Normalizes the solution (i.e., divides by the norm every entry) with a given \( l_p \)-norm.

+
+
Parameters:
+

t_p – The parameter \( p \) for the norm.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+Dual &operator+=(const Dual &t_rhs)
+
+ +
+
+Dual &operator*=(double t_factor)
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/SolutionPrimal.html b/api/modeling/SolutionPrimal.html new file mode 100644 index 00000000..a112f874 --- /dev/null +++ b/api/modeling/SolutionPrimal.html @@ -0,0 +1,311 @@ + + + + + + + Solution::Primal — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Solution::Primal

+
+
+class Primal : public idol::AbstractSolution<Var, Primal>
+
+

Public Types

+
+
+using const_iterator = typename Map<Var, double>::const_iterator
+
+ +
+
+

Public Functions

+
+
+inline void set_status(SolutionStatus t_status)
+

Sets the solution status.

+
+
Parameters:
+

t_status – The desired solution status.

+
+
+
+ +
+
+inline SolutionStatus status() const
+

Returns the stored solution status.

+
+ +
+
+inline void set_reason(SolutionReason t_reason)
+
+ +
+
+inline SolutionReason reason() const
+
+ +
+
+inline void set_objective_value(double t_value)
+

Sets the stored objective value.

+
+
Parameters:
+

t_value – The desired objective value.

+
+
+
+ +
+
+inline double objective_value() const
+

Returns the stored objective value.

+
+ +
+
+inline bool has_objective_value() const
+
+ +
+
+inline void reset_objective_value()
+
+ +
+
+void set(const Var &t_key, double t_value)
+

Sets the value associated to the key given as argument.

+
+
Parameters:
+
    +

  • t_key – The key for which the entry should be set.

    • +

  • t_value – The desired value associated to the key.

    • +
+
+
+
+ +
+
+double get(const Var &t_key) const
+

Returns the value associated to the key given as argument.

+

If no value is stored, zero is returned.

+
+
Parameters:
+

t_key – The queried key.

+
+
+
+ +
+
+inline const_iterator begin() const
+
+ +
+
+inline const_iterator end() const
+
+ +
+
+inline const_iterator cbegin() const
+
+ +
+
+inline const_iterator cend() const
+
+ +
+
+double norm(double t_p = 2.) const
+

Returns the \( l_p \)-norm of the solution.

+

Note that Inf is a possible value for t_p, in which case, the infinite norm is computed.

+
+
Parameters:
+

t_p – The \( p \) parameter for the \( l_p \)-norm.

+
+
+
+ +
+
+Primal &merge_without_conflict(Primal t_rhs)
+

Merges the solution with another solution, explicitly expecting that no conflict will arise (i.e., expecting that no entry from the solution is also present in the other solution). If a conflict is detected, an Exception is thrown.

+
+
Parameters:
+

t_rhs – The solution to merge.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+Primal &normalize(double t_p = 2.)
+

Normalizes the solution (i.e., divides by the norm every entry) with a given \( l_p \)-norm.

+
+
Parameters:
+

t_p – The parameter \( p \) for the norm.

+
+
Returns:
+

The object itself.

+
+
+
+ +
+
+Primal &operator+=(const Primal &t_rhs)
+
+ +
+
+Primal &operator*=(double t_factor)
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/TempCtr.html b/api/modeling/TempCtr.html new file mode 100644 index 00000000..71e4adea --- /dev/null +++ b/api/modeling/TempCtr.html @@ -0,0 +1,238 @@ + + + + + + + TempCtr — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

TempCtr

+
+
+class TempCtr
+

Temporary constraint object.

+

This class represents a constraint which has not been built yet by a Model. It contains all the arguments needed to create a real constraint as instantiated by the Ctr class. It is made of a row (i.e., a Row) and a type (i.e., a CtrType).

+

Typically, one creates a TempCtr by using the overloaded <=, >= and == operators between variable expressions (i.e., Expr) and constant terms (i.e., Constant).

+

Example 1: 

...
+model.add_ctr(x + y <= 1.);
+
+
+ Example 2 (equivalent to Example 1): 
...
+model.add_ctr(TempCtr(Row(x + y, 1.), LessOrEqual));
+
+
+

+

Subclassed by idol::CtrVersion

+
+

Public Functions

+
+
+TempCtr() = default
+
+ +
+
+inline TempCtr(Row &&t_row, CtrType t_type)
+

Creates a new temporary constraint.

+
+
Parameters:
+
    +

  • t_row – The desired row.

    • +

  • t_type – The desired constraint type.

    • +
+
+
+
+ +
+
+TempCtr(const TempCtr&) = default
+
+ +
+
+TempCtr(TempCtr&&) noexcept = default
+
+ +
+
+TempCtr &operator=(const TempCtr&) = default
+
+ +
+
+TempCtr &operator=(TempCtr&&) noexcept = default
+
+ +
+
+inline const Row &row() const
+

Returns the row for the constraint (see Row).

+
+ +
+
+inline Row &row()
+

Returns the row for the constraint (see Row).

+
+ +
+
+inline CtrType type() const
+

Returns the constraint type.

+
+ +
+
+inline void set_type(CtrType t_type)
+
+ +
+
+bool is_violated(const Solution::Primal &t_solution) const
+

Returns true if the temporary constraint is violated by the given solution, false otherwise.

+
+
Parameters:
+

t_solution – The solution to check.

+
+
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/TempVar.html b/api/modeling/TempVar.html new file mode 100644 index 00000000..4b75c4c3 --- /dev/null +++ b/api/modeling/TempVar.html @@ -0,0 +1,247 @@ + + + + + + + TempVar — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

TempVar

+
+
+class TempVar
+

Temporary variable object.

+

This class represents a variable which has not been built yet by a Model. It contains all the arguments needed to create a real variable as instantiated by the Var class. It is made of a lower and an upper bound, a type (see VarType), and a column (see Column).

+

Example 1: 

model.add_var(0., 1., Binary, 2.);
+// is the same as
+model.add_var(TempVar(0., 1., Binary, 2.));
+
+
+

+

Subclassed by idol::VarVersion

+
+

Public Functions

+
+
+TempVar() = default
+
+ +
+
+inline TempVar(double t_lb, double t_ub, VarType t_type, Column &&t_column)
+

Creates a new temporary variable.

+
+
Parameters:
+
    +

  • t_lb – The desired lower bound.

    • +

  • t_ub – The desired upper bound.

    • +

  • t_type – The desired variable type.

    • +

  • t_column – The desired column.

    • +
+
+
+
+ +
+
+TempVar(TempVar&&) = default
+
+ +
+
+TempVar(const TempVar&) = default
+
+ +
+
+TempVar &operator=(TempVar&&) = default
+
+ +
+
+TempVar &operator=(const TempVar&) = default
+
+ +
+
+inline const Column &column() const
+

Returns the column associated to the temporary variable (see Column).

+
+ +
+
+inline Column &column()
+

Returns the column associated to the temporary variable (see Column).

+
+ +
+
+inline double lb() const
+

Returns the lower bound associated to the temporary variable.

+
+ +
+
+inline void set_lb(double t_lb)
+
+ +
+
+inline double ub() const
+

Returns the upper bound associated to the temporary variable.

+
+ +
+
+inline void set_ub(double t_ub)
+
+ +
+
+inline VarType type() const
+

Returns the type associated to the temporary variable.

+
+ +
+
+inline void set_type(VarType t_type)
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/Var.html b/api/modeling/Var.html new file mode 100644 index 00000000..e56555bf --- /dev/null +++ b/api/modeling/Var.html @@ -0,0 +1,218 @@ + + + + + + + Var — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Var

+
+
+class Var : public idol::Object<VarVersion, Var>
+
+

Public Functions

+
+
+Var(Env &t_env, double t_lb, double t_ub, VarType t_type, std::string t_name = "")
+
+ +
+
+Var(Env &t_env, double t_lb, double t_ub, VarType t_type, Column &&t_column, std::string t_name = "")
+
+ +
+
+Var(Env &t_env, double t_lb, double t_ub, VarType t_type, const Column &t_column, std::string t_name = "")
+
+ +
+
+inline const std::string &name() const
+
+ +
+
+inline unsigned int id() const
+
+ +
+
+inline bool operator==(const Object<VarVersion, Var> &t_rhs) const
+
+ +
+
+inline bool operator!=(const Object<VarVersion, Var> &t_rhs) const
+
+ +
+
+inline bool is_in(const Model &t_model) const
+
+ +
+
+inline const ValueT &get(const Annotation<Var, ValueT> &t_annotation) const
+
+ +
+
+inline void set(const Annotation<Var, ValueT> &t_annotation, ArgsT&&... t_args) const
+
+ +
+
+

Public Static Functions

+
+
+template<unsigned int N = 1, unsigned int I = 0>
static inline Vector<Var, N - I> make_vector(Env &t_env, const Dim<N> &t_dim, double t_lb, double t_ub, VarType t_type, const std::string &t_name = "")
+
+ +
+
+

Friends

+
+
+friend class impl::Env
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/modeling/index.html b/api/modeling/index.html new file mode 100644 index 00000000..e85fa713 --- /dev/null +++ b/api/modeling/index.html @@ -0,0 +1,163 @@ + + + + + + + Modeling — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/BranchAndBound.html b/api/optimizers/branch-and-bound/BranchAndBound.html new file mode 100644 index 00000000..d9468d97 --- /dev/null +++ b/api/optimizers/branch-and-bound/BranchAndBound.html @@ -0,0 +1,687 @@ + + + + + + + BranchAndBound — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

BranchAndBound

+

This class is an optimizer factory which creates a new branch-and-bound algorithm. +It can be used to create customized branch-and-bound algorithms with a large degree of freedom.

+
+

See also

+

If you are not familiar with optimizers and optimizer factories, please refer to this page.

+
+
+

Example

+

Here, we create a simple branch-and-bound algorithm where branching is done on integer variables which are being +relaxed. Each node is solved by the external solver GLPK. Nodes are selected according to the “best-bound” +rule while variables are selected according to the “most-infeasible” branching rule.

+

The created algorithm also incorporates sub-tree exploration of maximum depth 2.

+
model.use(
+    BranchAndBound()
+        .with_node_optimizer( GLPK::ContinuousRelaxation() )
+        .with_branching_rule( MostInfeasible() )
+        .with_node_selection_rule( BestBound() )
+        .with_subtree_depth(2)
+);
+
+
+
+
+
+template<class NodeT = idol::NodeInfo>
class BranchAndBound : public idol::OptimizerFactoryWithDefaultParameters<BranchAndBound<idol::NodeInfo>>
+
+
Template Parameters:
+

NodeT – the class used to store nodes information. It is strongly advised to inherit from NodeInfo in order to create your own node type.

+
+
+
+

Public Types

+
+
+template<class ReturnT, class T>
using only_if_has_Strategy = typename std::pair<typename T::template Strategy<NodeT>, ReturnT>::second_type
+

This type is used to exploit SFINAE in order to identify classes having a sub-class named Strategy<NodeT>. This is used to make calls like .with_node_selection_rule(DepthFirst()); which will actually call .with_node_selection_rule(DepthFirst::Strategy<NodeT>()).

+
+ +
+
+

Public Functions

+
+
+BranchAndBound() = default
+

Creates a new branch-and-bound algorithm.

+

Example: 

model.use( BranchAndBound() );
+
+
+

+
+ +
+
+BranchAndBound<NodeT> &with_node_optimizer(const OptimizerFactory &t_node_optimizer)
+

Sets the optimizer for solving each of the branch-and-bound tree nodes

+

Example: 

auto algorithm = BranchAndBound()
+                     .with_node_optimizer(GLPK::ContinuousRelaxation());
+
+
+

+
+
Parameters:
+

t_node_optimizer – the optimizer factory the node problems

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_branching_rule(const BranchingRuleFactory<NodeT> &t_branching_rule)
+

Sets the branching rule used to create child nodes

+

Example: 

auto algorithm = BranchAndBound<NodeInfo>()
+                     .with_branching_rule(MostInfeasible::Strategy<NodeInfo>());
+
+
+

+
+
Parameters:
+

t_branching_rule – the branching rule

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+template<class BranchingRuleFactoryT>
only_if_has_Strategy<BranchAndBound<NodeT>&, BranchingRuleFactoryT> with_branching_rule(const BranchingRuleFactoryT &t_branching_rule)
+

Sets the branching rule used to create child nodes.

+

Here, the function is called only when BranchingRuleFactoryT has a nested template class named Strategy<NodeT>. In such a case, the branching rule is created by calling BranchingRuleFactoryT::Strategy<NodeT>(t_branching_rule). This is used to avoid the user repeating the node type NodeT being used.

+

Example: 

auto algorithm = BranchAndBound<NodeInfo>()
+                     .with_branching_rule(MostInfeasible());
+
+
+

+
+
Template Parameters:
+

BranchingRuleFactoryT – the class containing a nested template class named Strategy

+
+
Parameters:
+

t_branching_rule – the branching rule

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_node_selection_rule(const NodeSelectionRuleFactory<NodeT> &t_node_selection)
+

Sets the node selection rule to explore the branch and bound tree.

+

auto algorithm = BranchAndBound<NodeInfo>()
+                     .with_node_selection(BestBound::Strategy<NodeInfo>());
+
+
+

+
+
Parameters:
+

t_node_selection – the node selection rule

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+template<class NodeSelectionRuleFactoryT>
only_if_has_Strategy<BranchAndBound<NodeT>&, NodeSelectionRuleFactoryT> with_node_selection_rule(const NodeSelectionRuleFactoryT &t_node_selection_rule)
+

Sets the node selection rule to explore the branch and bound tree.

+

Here, the function is called only when NodeSelectionRuleFactoryT has a nested template class named Strategy<NodeT>. In such a case, the node selection rule is created by calling NodeSelectionRuleFactoryT::Strategy<NodeT>(t_node_selection_rule). This is used to avoid the user repeating the node type NodeT being used.

+

Example: 

auto algorithm = BranchAndBound<NodeInfo>()
+                     .with_node_selection_rule(BestBound());
+
+
+

+
+
Template Parameters:
+

NodeSelectionRuleFactoryT – the class containing a nested template class named Strategy

+
+
Parameters:
+

t_node_selection_rule – the node selection rule

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound(BranchAndBound&&) noexcept = delete
+
+ +
+
+BranchAndBound &operator=(const BranchAndBound&) = delete
+
+ +
+
+BranchAndBound &operator=(BranchAndBound&&) noexcept = delete
+
+ +
+
+virtual Optimizer *operator()(const Model &t_model) const override
+

Creates and returns a new optimizer to solve the model given as parameter.

+
+
Parameters:
+

t_model – The model which the optimizer will solve

+
+
Returns:
+

A new optimizer for the model

+
+
+
+ +
+
+virtual OptimizerFactory *clone() const override
+

Creates and return a copy of the optimizer factory. This is used for polymorphism.

+
+
Returns:
+

A copied object of the current object (i.e., *this)

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_subtree_depth(unsigned int t_depth)
+

Sets the depth for sub-tree exploration.

+

When a node is selected for branching, each of its children is explored. This exploration takes the form of a sub-tree exploration. When this parameter is set to 0, only the root node of this sub-tree is solved. Thus every child node are solved and the branch-and-bound algorithm is continued.

+

For strictly greater values of this parameter, the sub-tree is explored with a maximum depth equal to the value of this parameter.

+

For example, with a value of 1, each child node is solved along with its child nodes.

+

Example: 

auto algorithm = BranchAndBound()
+                     .with_subtree_depth(1);
+
+
+

+
+
Parameters:
+

t_depth – the maximum sub-tree exploration depth

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_log_frequency(unsigned int t_log_frequency)
+

Sets the log frequency of the optimizer, i.e., nodes are logged every t_log_frequency nodes.

+

Note that this in only relevant when the log level is at least set to Info.

+

Example: 

auto algorithm = BranchAndBound()
+                     .with_log_level(Info, Blue)
+                     .with_log_frequency(1); // log every explored node
+
+
+

+
+
Parameters:
+

t_log_frequency – the frequency for logging

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_callback(const BranchAndBoundCallbackFactory<NodeT> &t_callback)
+

Adds a callback which will be called by the optimizer.

+

Note that this method can be called multiple times so that multiple callbacks can be added.

+

auto algorithm = BranchAndBound()
+                     .with_callback(IntegerMasterHeuristic());
+
+
+

+
+
Parameters:
+

t_callback – the callback factory

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_callback(const CallbackFactory &t_callback)
+

Adds a (solver independent) callback which will be called by the optimizer.

+

Note that this method can be called multiple times so that multiple callbacks can be added.

+

Here, the Callback is automatically converted into a BranchAndBoundCallback<NodeT>.

+

auto algorithm = BranchAndBound()
+                     .with_callback(UserCutCallback(separation_model, my_cut));
+
+
+

+
+
Parameters:
+

t_callback – the callback factory

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<NodeT> &with_cutting_planes(const CuttingPlaneGenerator &t_cutting_place_generator)
+
+ +
+
+template<class NodeSelectionRuleFactoryT>
idol::BranchAndBound<NodeT>::template only_if_has_Strategy<idol::BranchAndBound<NodeT>&, NodeSelectionRuleFactoryT> with_node_selection_rule(const NodeSelectionRuleFactoryT &t_node_selection_rule)
+
+ +
+
+template<class BranchingRuleFactoryT>
idol::BranchAndBound<NodeT>::template only_if_has_Strategy<idol::BranchAndBound<NodeT>&, BranchingRuleFactoryT> with_branching_rule(const BranchingRuleFactoryT &t_branching_rule)
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_log_level(LogLevel t_log_level, Color t_log_color = Color::Default)
+

Sets the log level and color for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_log_level(Info, Green);
+
+
+

+
+
Parameters:
+
    +

  • t_log_level – the log level

    • +

  • t_log_color – the output color

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_time_limit(double t_time_limit)
+

Sets the time limit for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
+
+

+
+
Parameters:
+

t_time_limit – the time limit (in seconds)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_thread_limit(unsigned int t_max_n_threads)
+

Sets the maximum number of threads which the optimizer can use

+

Example: 

auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
+
+

+
+
Parameters:
+

t_max_n_threads – the number of threads which can be used

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_iteration_count_limit(unsigned int t_iteration_count_limit)
+

Sets the maximum number of iterations which the optimizer go through

+

Example: 

auto algorithm = GLPK()
+                     .with_iteration_count_limit(200);
+
+
+

+
+
Parameters:
+

t_iteration_count_limit – the maximum number of iterations

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_best_bound_stop(double t_best_bound_stop)
+

Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
+
+

+
+
Parameters:
+

t_best_bound_stop – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_best_obj_stop(double t_user_best_obj)
+

Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
+
+

+
+
Parameters:
+

t_user_best_obj – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_relative_gap_tolerance(double t_relative_gap_tolerance)
+

Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
+
+

+
+
Parameters:
+

t_relative_gap_tolerance – the relative gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
+

Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
+
+

+
+
Parameters:
+

t_absolute_gap_tolerance – the absolute gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_presolve(bool t_value)
+

Sets the get_param_presolve activation for the optimizer.

+

Example: 

auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
+
+

+
+
Parameters:
+

t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &with_infeasible_or_unbounded_info(bool t_value)
+

Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

+

Example: 

auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
+
+

+
+
Parameters:
+

t_value – the activation level

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &conditional(bool t_conditional_value, const std::function<void(BranchAndBound<idol::NodeInfo>&)> &t_if)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+BranchAndBound<idol::NodeInfo> &conditional(bool t_conditional_value, const std::function<void(BranchAndBound<idol::NodeInfo>&)> &t_if, const std::function<void(BranchAndBound<idol::NodeInfo>&)> &t_else)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +

  • t_else – lambda function to execute in case t_conditional_value is false

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/BranchAndBoundCallback.html b/api/optimizers/branch-and-bound/BranchAndBoundCallback.html new file mode 100644 index 00000000..c49a8b5e --- /dev/null +++ b/api/optimizers/branch-and-bound/BranchAndBoundCallback.html @@ -0,0 +1,309 @@ + + + + + + + BranchAndBoundCallback — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

BranchAndBoundCallback

+

This class can be used to create callbacks to run on idol’s branch-and-bound implementation.

+
+

Warning

+

BranchAndBoundCallback-s is an advanced feature.

+

Please, make sure that what you are trying do cannot be done with +a solver-independent callback first, or with pre-existing callbacks, e.g., +UserCutCallback or LazyCutCallback.

+

The advantage of using a BranchAndBoundCallback instead of a standard +solver-independent Callback lies in the possibility to access specific information regarding +the execution of the branch-and-bound algorithm. For instance, accessing a node’s information, or the current +relaxation model being solved.

+
+
+

Example

+

Here is an example of callback which prints out the event triggering it and, when the event corresponds to NodeLoaded, +prints the node’s model to be solved.

+
class MyCallback : public BranchAndBoundCallbackFactory<NodeInfo> {
+public:
+    class Strategy : public BranchAndBoundCallback<NodeInfo> {
+    protected:
+        void operator()(CallbackEvent t_event) override {
+
+            std::cout << "MyCallback is called for " << t_event << std::endl;
+
+            if (t_event != NodeLoaded) {
+                return;
+            }
+
+            std::cout << "The problem being solve at node " << node().id() << std::endl;
+            std::cout << relaxation() << std::endl;
+
+        }
+    };
+
+    BranchAndBoundCallback<NodeInfo> *operator()() override {
+        return new Strategy();
+    }
+
+    [[nodiscard]] BranchAndBoundCallbackFactory<NodeInfo> *clone() const override {
+        return new MyCallback(*this);
+    }
+};
+
+
+

Then, this callback can be used as follows.

+
model.use(
+    BranchAndBound()
+        .with_node_optimizer(GLPK::ContinuousRelaxation())
+        .with_branching_rule(MostInfeasible())
+        .with_node_selection_rule(DepthFirst())
+        .with_callback(MyCallback());
+);
+
+
+
+
+

Hint

+

By default, most of the objects returned by BranchAndBoundCallback methods are const. If you wish to access non-const +versions (e.g., if you want to perform non-standard updates to the relaxed model or want to change the node’s current +information manually), you should use the advanced interface obtained by calling BranchAndBoundCallback::advanced_interface.

+
+
+
+template<class NodeInfoT>
class BranchAndBoundCallback
+

Subclassed by idol::CallbackAsBranchAndBoundCallback< NodeInfoT >::Strategy

+
+

Public Functions

+
+
+virtual ~BranchAndBoundCallback() = default
+
+ +
+
+

Protected Functions

+
+
+virtual void operator()(CallbackEvent t_event) = 0
+

This method is left for the user to write and consists in the main execution block of the callback.

+
+ +
+
+void add_user_cut(const TempCtr &t_cut)
+

Adds a user cut to the relaxation

+
+
Parameters:
+

t_cut – the cut to be added

+
+
+
+ +
+
+void add_lazy_cut(const TempCtr &t_cut)
+

Adds a lazy cut to the relaxation

+
+
Parameters:
+

t_cut – the cut to be added

+
+
+
+ +
+
+const Node<NodeInfoT> &node() const
+

Returns the node which is currently explored

+
+
Returns:
+

the node which is currently explored

+
+
+
+ +
+
+const Model &relaxation() const
+

Returns the current node’s model being solved

+
+
Returns:
+

the current node’s model being solved

+
+
+
+ +
+
+const Model &original_model() const
+

Returns the original model from which the branch-and-bound algorithm started (i.e., the original non-relaxed model)

+
+
Returns:
+

the original model

+
+
+
+ +
+
+void submit_heuristic_solution(NodeInfoT *t_info)
+

Submits a new solution to the branch-and-bound tree algorithm.

+

The solution is checked for validity according to the branch-and-bound tree branching rule and is set as incumbent if and only if it is valid and improves the current best objective.

+
+
Parameters:
+

t_info – a node information storing the solution

+
+
+
+ +
+
+void submit_bound(double t_bound)
+

Submits a new proven bound.

+

The given bound is set as best bound if and only if it improves the current best bound.

+
+
Parameters:
+

t_bound – a proven bound

+
+
+
+ +
+
+const Timer &time() const
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.html b/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.html new file mode 100644 index 00000000..d82f2bf4 --- /dev/null +++ b/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.html @@ -0,0 +1,191 @@ + + + + + + + MostInfeasible — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+ +
+
+ +
+

MostInfeasible

+
+
+class MostInfeasible
+
+

Public Functions

+
+
+MostInfeasible() = default
+
+ +
+
+template<class IteratorT>
inline MostInfeasible(IteratorT t_begin, IteratorT t_end)
+
+ +
+
+
+template<class NodeT>
class Strategy : public idol::BranchingRuleFactory<NodeT>
+
+

Public Functions

+
+
+Strategy() = default
+
+ +
+
+inline explicit Strategy(const MostInfeasible &t_parent)
+
+ +
+
+inline virtual BranchingRules::MostInfeasible<NodeT> *operator()(const Model &t_model) const override
+
+ +
+
+inline virtual Strategy *clone() const override
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/branching-rules/index.html b/api/optimizers/branch-and-bound/branching-rules/index.html new file mode 100644 index 00000000..7cb8ec54 --- /dev/null +++ b/api/optimizers/branch-and-bound/branching-rules/index.html @@ -0,0 +1,152 @@ + + + + + + + Branching rules — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Branching rules

+
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/index.html b/api/optimizers/branch-and-bound/index.html new file mode 100644 index 00000000..4eb99cd3 --- /dev/null +++ b/api/optimizers/branch-and-bound/index.html @@ -0,0 +1,163 @@ + + + + + + + Branch-And-Bound algorithms — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/node-selection-rules/BestBound.html b/api/optimizers/branch-and-bound/node-selection-rules/BestBound.html new file mode 100644 index 00000000..1d0f80c9 --- /dev/null +++ b/api/optimizers/branch-and-bound/node-selection-rules/BestBound.html @@ -0,0 +1,176 @@ + + + + + + + BestBound — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+ +
+
+ +
+

BestBound

+
+
+class BestBound
+
+
+template<class NodeT>
class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
+
+

Public Functions

+
+
+inline explicit Strategy(const BestBound &t_parent)
+
+ +
+
+inline virtual NodeSelectionRules::BestBound<NodeT> *operator()() const override
+
+ +
+
+inline virtual Strategy *clone() const override
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.html b/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.html new file mode 100644 index 00000000..ecc2ad07 --- /dev/null +++ b/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.html @@ -0,0 +1,176 @@ + + + + + + + BreadthFirst — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+ +
+
+ +
+

BreadthFirst

+
+
+class BreadthFirst
+
+
+template<class NodeT>
class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
+
+

Public Functions

+
+
+inline explicit Strategy(const BreadthFirst &t_parent)
+
+ +
+
+inline virtual NodeSelectionRules::BreadthFirst<NodeT> *operator()() const override
+
+ +
+
+inline virtual Strategy *clone() const override
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.html b/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.html new file mode 100644 index 00000000..e1e2c017 --- /dev/null +++ b/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.html @@ -0,0 +1,176 @@ + + + + + + + DepthFirst — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+ +
+
+ +
+

DepthFirst

+
+
+class DepthFirst
+
+
+template<class NodeT>
class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
+
+

Public Functions

+
+
+inline explicit Strategy(const DepthFirst &t_parent)
+
+ +
+
+inline virtual NodeSelectionRules::DepthFirst<NodeT> *operator()() const override
+
+ +
+
+inline virtual Strategy *clone() const override
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.html b/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.html new file mode 100644 index 00000000..ac23f7ce --- /dev/null +++ b/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.html @@ -0,0 +1,176 @@ + + + + + + + WorstBound — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+ +
+
+ +
+

WorstBound

+
+
+class WorstBound
+
+
+template<class NodeT>
class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
+
+

Public Functions

+
+
+inline explicit Strategy(const WorstBound &t_parent)
+
+ +
+
+inline virtual NodeSelectionRules::WorstBound<NodeT> *operator()() const override
+
+ +
+
+inline virtual Strategy *clone() const override
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/branch-and-bound/node-selection-rules/index.html b/api/optimizers/branch-and-bound/node-selection-rules/index.html new file mode 100644 index 00000000..4810b974 --- /dev/null +++ b/api/optimizers/branch-and-bound/node-selection-rules/index.html @@ -0,0 +1,167 @@ + + + + + + + Node selection rules — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Node selection rules

+
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/callbacks/Callback.html b/api/optimizers/callbacks/Callback.html new file mode 100644 index 00000000..bdfe4d3e --- /dev/null +++ b/api/optimizers/callbacks/Callback.html @@ -0,0 +1,290 @@ + + + + + + + Callback — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Callback

+

Callbacks are user-defined functions which are invoked during the execution of branch-and-bound algorithms at certain +key steps of the procedure. These key points are called events in idol. +Callback functions can be used to monitor the algorithm’s progress, control its behavior, or perform additional processing.

+
+

UserCutCallback and LazyCutCallback

+

A common use of callbacks is to implement custom cut generation procedures at each node of the branch-and-bound tree. Note that +idol offers out-of-the-box callback routines for cut separation. Namely, UserCutCallback +and LazyCutCallback. Yet, it is totally possible to define your own cut generation procedure +by using the Callback::add_user_cut and Callback::add_lazy_cut methods inside your callback.

+

In a nutshell, UserCutCallback (or, similarly, Callback::add_user_cut) are intended for +cuts which have a potential to improve the quality of the relaxation but whose presence in the model is not necessary for the +branch-and-bound to converge to an optimal solution. UserCutCallback callbacks are called when +a non-valid solution has been found.

+

LazyCutCallback (or, similarly, Callback::add_lazy_cut), +instead, are intended to generate constraints which should be part of the model but which were omitted in the model for some reason. +A typical reason for omitting constraints in a model’s definition is the large number of such constraints. +LazyCutCallback callbacks are called when a valid solution has been found.

+
+
+

Creating your own callback

+

If you want to create your own callback, you should first create a new class which inherits the Callback class and +overrides the operator()(CallbackEvent) method.

+

Note that callbacks cannot be given “as-is” to an optimizer but must be passed through a CallbackFactory. A callback +factory is a class whose role is to create a new callback object whenever it is needed. Every callback factories must be +a child (or little child) of the CallbackFactory class.

+
+

Example

+

We now give an example of callback which prints out every valid solution found.

+
class MyCallback : public CallbackFactory {
+public:
+
+    class Strategy { // Real callback implementation
+    protected:
+        void operator()(CallbackEvent t_event) {
+
+               if (t_event != IncumbentSolution) {
+                    return;
+               }
+
+               std::cout << primal_solution() << std::endl;
+        }
+    }
+
+    Callback* operator()() { // Creates a new callback object
+        return new Strategy();
+    }
+
+    CallbackFactory* clone() const { // Creates a copy of the callback factory
+        return new MyCallback(*this);
+    }
+
+}
+
+
+

Later, it is then possible to use this callback in compliant optimizers like Gurobi or BranchAndBound.

+
model.use(
+    Gurobi().with_callback(MyCallback();
+);
+
+model.optimize();
+
+
+
+
+

Hint

+

Note that there also exists more advanced callbacks which are specific to idol’s branch-and-bound implementation. +For these advanced feature, see BranchAndBoundCallback.

+
+
+
+class Callback
+

Subclassed by idol::impl::CutSeparation

+
+

Public Functions

+
+
+virtual ~Callback() = default
+
+ +
+
+

Protected Functions

+
+
+virtual void add_user_cut(const TempCtr &t_cut)
+

Adds a user cut to the relaxation

+
+
Parameters:
+

t_cut – the cut to be added

+
+
+
+ +
+
+virtual void add_lazy_cut(const TempCtr &t_cut)
+

Adds a lazy cut to the relaxation

+
+
Parameters:
+

t_cut – the cut to be added

+
+
+
+ +
+
+virtual Solution::Primal primal_solution() const
+

Returns the solution of the node which is currently being explored (when available)

+
+
Returns:
+

the solution of the current node

+
+
+
+ +
+
+const Timer &time() const
+

Returns the current time

+
+
Returns:
+

the optimizer’s time

+
+
+
+ +
+
+virtual void operator()(CallbackEvent t_event) = 0
+

This method is left for the user to write and consists in the main execution block of the callback.

+
+
Parameters:
+

t_event – the event which triggered the call

+
+
+
+ +
+
+

Friends

+
+
+friend class ::idol::CallbackI
+
+ +
+
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/callbacks/CallbackEvent.html b/api/optimizers/callbacks/CallbackEvent.html new file mode 100644 index 00000000..a8347b5b --- /dev/null +++ b/api/optimizers/callbacks/CallbackEvent.html @@ -0,0 +1,178 @@ + + + + + + + Events — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Events

+
+
+enum idol::CallbackEvent
+

CallbackEvent is an enumerated type used to indicate events during a branch-and-bound tree execution.

+

It is typically used inside of a Callback to influence or modify the behaviour of the algorithm at execution time.

+

Values:

+
+
+enumerator AlgorithmStarts
+
+ +
+
+enumerator AlgorithmStops
+

Occurs when the algorithm starts

+
+ +
+
+enumerator NodeLoaded
+

Occurs when the algorithm stops Occurs when a node is about to be solved

+
+ +
+
+enumerator IncumbentSolution
+

Occurs when an incumbent solution has been found

+
+ +
+
+enumerator InvalidSolution
+

Occurs when a solution of the relaxation is not valid (e.g., not integer)

+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/callbacks/LazyCutCallback.html b/api/optimizers/callbacks/LazyCutCallback.html new file mode 100644 index 00000000..a8dacad3 --- /dev/null +++ b/api/optimizers/callbacks/LazyCutCallback.html @@ -0,0 +1,226 @@ + + + + + + + LazyCutCallback — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

LazyCutCallback

+

Lazy cuts are essentially constraints which are part of an optimization model but which have been omitted in the current +definition of the model. Lazy cuts typically arise in models with a large number of constraints. Instead of enumerating +then all, it may be judicious to omit some of them to get a smaller optimization model. Then, the returned solution is +checked for feasibility against the whole set of constraints. If a violated constraint is identified, we add the +constraint to the model and resolve. If not, then all the constraints are satisfied and the solution is optimal for the +original model in which all constraints materializes.

+

The LazyCutCallback can be used to implement lazy cut constraint generation on the fly, during the optimization process.

+

Consider the following optimization problem:

+
+\[\begin{split}\begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X, \\ + & \xi^\top x \le \xi_0 \quad (\xi_0,\xi) \in \Xi, +\end{align}\end{split}\]
+

in which assume that \(|\Xi|\) is large (potentially infinite). The idea is to start by solving the following +relaxed master problem in which constraints associated to \((\xi_0,\xi)\) have been omitted.

+
+\[\begin{split}\begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X. +\end{align}\end{split}\]
+

If we assume that this problem is feasible and bounded, we can denote by \(x^*\) a solution of this problem. Then, +we search for a violated constraint “\(\xi^\top x \le \xi_0\)” for some \((\xi_0,\xi)\in\Xi\). Observe that +a constraint is violated if, and only if, the following holds:

+
+\[\left(\exists(\xi_0,\xi)\in\Xi, \ \xi^\top x^* > \xi_0\right) +\Leftrightarrow +\left(\max_{(\xi_0,\xi)\in\Xi} \xi_0 - \xi^\top x^* < 0\right).\]
+

Thus, the LazyCutCallback automatically solve the optimization problem on the right handside and checks for its value. +A new constraint is added if, and only if,

+
+\[\max_{\xi\in\Xi} \xi_0 - \xi^\top x^* < -\varepsilon,\]
+

with \(\varepsilon\) a given tolerance (by default, Tolerance::Feasibility).

+
+

Hint

+

You may also be interested by a tutorial showing how you can implement a simple Benders Decomposition using lazy +cuts. See Benders Decomposition tutorial.

+
+
+
+class LazyCutCallback : public idol::CallbackFactory
+
+

Public Functions

+
+
+inline LazyCutCallback(const Model &t_model, TempCtr t_cut)
+
+ +
+
+inline virtual Callback *operator()() override
+
+ +
+
+inline virtual CallbackFactory *clone() const override
+
+ +
+
+inline LazyCutCallback &with_separation_optimizer(const OptimizerFactory &t_optimizer_factory)
+
+ +
+
+inline LazyCutCallback &with_log_level(LogLevel t_level, Color t_color)
+
+ +
+
+
+class Strategy : public idol::impl::CutSeparation
+
+

Public Functions

+
+
+inline explicit Strategy(Model *t_separation_problem, TempCtr t_cut, LogLevel t_level, Color t_color)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/callbacks/UserCutCallback.html b/api/optimizers/callbacks/UserCutCallback.html new file mode 100644 index 00000000..d40ffab2 --- /dev/null +++ b/api/optimizers/callbacks/UserCutCallback.html @@ -0,0 +1,182 @@ + + + + + + + UserCutCallback — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

UserCutCallback

+
+
+class UserCutCallback : public idol::CallbackFactory
+
+

Public Functions

+
+
+inline UserCutCallback(const Model &t_model, TempCtr t_cut)
+
+ +
+
+inline virtual Callback *operator()() override
+
+ +
+
+inline virtual CallbackFactory *clone() const override
+
+ +
+
+inline UserCutCallback &with_separation_optimizer(const OptimizerFactory &t_optimizer_factory)
+
+ +
+
+
+class Strategy : public idol::impl::CutSeparation
+
+

Public Functions

+
+
+inline explicit Strategy(Model *t_separation_problem, TempCtr t_cut, LogLevel t_log_level, Color t_log_color)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/callbacks/index.html b/api/optimizers/callbacks/index.html new file mode 100644 index 00000000..a0f13832 --- /dev/null +++ b/api/optimizers/callbacks/index.html @@ -0,0 +1,203 @@ + + + + + + + Callbacks — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Callbacks

+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/column-generation/ColumnGeneration.html b/api/optimizers/column-generation/ColumnGeneration.html new file mode 100644 index 00000000..d65c849f --- /dev/null +++ b/api/optimizers/column-generation/ColumnGeneration.html @@ -0,0 +1,564 @@ + + + + + + + ColumnGeneration — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

ColumnGeneration

+
+

Danger

+

Currently, the master problem must have a “convexity constraint” for the algorithm to converge. +Problems without this property will lead to undefined behavior.

+

We strongly advise you to use DantzigWolfeDecomposition instead.

+
+
+
+class ColumnGeneration : public idol::impl::OptimizerFactoryWithColumnGenerationParameters<ColumnGeneration>
+
+

Public Functions

+
+
+explicit ColumnGeneration(unsigned int t_n_subproblems)
+
+ +
+
+virtual Optimizer *operator()(const Model &t_model) const override
+

Creates and returns a new optimizer to solve the model given as parameter.

+
+
Parameters:
+

t_model – The model which the optimizer will solve

+
+
Returns:
+

A new optimizer for the model

+
+
+
+ +
+
+virtual ColumnGeneration *clone() const override
+

Creates and return a copy of the optimizer factory. This is used for polymorphism.

+
+
Returns:
+

A copied object of the current object (i.e., *this)

+
+
+
+ +
+
+ColumnGeneration &reserve_for_subproblems(unsigned int t_n_subproblems)
+
+ +
+
+inline unsigned int n_subproblems() const
+
+ +
+
+ColumnGeneration &with_master_optimizer(const OptimizerFactory &t_master_optimizer)
+
+ +
+
+ColumnGeneration &with_subproblem(const Model &t_model, Column t_column)
+
+ +
+
+ColumnGeneration &with_parallel_pricing_limit(unsigned int t_limit)
+

Configures the maximum number of pricing problems which can be solved in parallel

+
+
Parameters:
+

t_limit – the desired limit

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ColumnGeneration &with_column_pool_clean_up(unsigned int t_threshold, double t_ratio)
+

Configures the column pool clean up

+

When the number of columns in the column pool is larger than the given threshold, columns are removed from the pool (and possibly from the master problem) from the oldest columns to the newest. Only t_threshold * t_ratio are kept.

+
+
Parameters:
+
    +

  • t_threshold – the desired threshold

    • +

  • t_ratio – the clean up ratio

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ColumnGeneration &with_farkas_pricing(bool t_value)
+

Configures the activation of Farkas pricing.

+

If set to true, a Farkas certificate is asked to the master problem solver so as to generate new columns to improve feasibility or to show infeasibility of the problem.

+

By default, it is turned off.

+
+
Parameters:
+

t_value – true if Farkas pricing is desired, false otherwise

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ColumnGeneration &with_artificial_variables_cost(double t_artificial_variable_cost)
+

Configures the cost for the artificial variables added when the master problem is infeasible and Farkas pricing is turned off.

+

When the master problem is infeasible, artificial variables are added to the master problem with an objective cost of t_artificial_variable_cost. In case this approach fails to generate columns making the master problem feasible (e.g., the costs are too small), the algorithm switches to pure phase I where the constraint violations are optimized.

+

If t_artificial_variable_cost is less or equal than zero, pure phase I is directly applied.

+
+
Parameters:
+

t_artificial_variable_cost – the desired cost for the artificial variables.

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ColumnGeneration &with_dual_price_smoothing_stabilization(double t_smoothing_factor)
+

Configures the stabilization factor of the dual price smoothing stabilization. This value should be in [0,1). Note that when this parameter is zero, no stabilization is performed.

+
+
Parameters:
+

t_smoothing_factor – the desired stabilization factor

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ColumnGeneration &with_log_frequency(unsigned int t_log_frequency)
+

Configures the frequency for logging. Logging information is displayed every t_log_frequency iterations.

+
+
Parameters:
+

t_log_frequency – the desired log frequency

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ColumnGeneration &with_max_columns_per_pricing(unsigned int t_n_columns)
+

Configures the maximum number of columns which are added for each pricing operation.

+
+
Parameters:
+

t_n_columns – the maximum nuber of added columns

+
+
Returns:
+

the optimizer itself

+
+
+
+ +
+
+ColumnGeneration &with_non_optimal_pricing_phase(double t_time_limit, double t_relative_gap)
+
+ +
+
+CRTP &with_log_level(LogLevel t_log_level, Color t_log_color = Color::Default)
+

Sets the log level and color for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_log_level(Info, Green);
+
+
+

+
+
Parameters:
+
    +

  • t_log_level – the log level

    • +

  • t_log_color – the output color

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_time_limit(double t_time_limit)
+

Sets the time limit for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
+
+

+
+
Parameters:
+

t_time_limit – the time limit (in seconds)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_thread_limit(unsigned int t_max_n_threads)
+

Sets the maximum number of threads which the optimizer can use

+

Example: 

auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
+
+

+
+
Parameters:
+

t_max_n_threads – the number of threads which can be used

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_iteration_count_limit(unsigned int t_iteration_count_limit)
+

Sets the maximum number of iterations which the optimizer go through

+

Example: 

auto algorithm = GLPK()
+                     .with_iteration_count_limit(200);
+
+
+

+
+
Parameters:
+

t_iteration_count_limit – the maximum number of iterations

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_best_bound_stop(double t_best_bound_stop)
+

Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
+
+

+
+
Parameters:
+

t_best_bound_stop – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_best_obj_stop(double t_user_best_obj)
+

Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
+
+

+
+
Parameters:
+

t_user_best_obj – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_relative_gap_tolerance(double t_relative_gap_tolerance)
+

Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
+
+

+
+
Parameters:
+

t_relative_gap_tolerance – the relative gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
+

Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
+
+

+
+
Parameters:
+

t_absolute_gap_tolerance – the absolute gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_presolve(bool t_value)
+

Sets the get_param_presolve activation for the optimizer.

+

Example: 

auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
+
+

+
+
Parameters:
+

t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_infeasible_or_unbounded_info(bool t_value)
+

Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

+

Example: 

auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
+
+

+
+
Parameters:
+

t_value – the activation level

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &conditional(bool t_conditional_value, const std::function<void(CRTP&)> &t_if)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &conditional(bool t_conditional_value, const std::function<void(CRTP&)> &t_if, const std::function<void(CRTP&)> &t_else)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +

  • t_else – lambda function to execute in case t_conditional_value is false

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/column-generation/DantzigWolfeDecomposition.html b/api/optimizers/column-generation/DantzigWolfeDecomposition.html new file mode 100644 index 00000000..71e840a7 --- /dev/null +++ b/api/optimizers/column-generation/DantzigWolfeDecomposition.html @@ -0,0 +1,591 @@ + + + + + + + DantzigWolfeDecomposition — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

DantzigWolfeDecomposition

+
+

Hint

+

This page documents on the DantzigWolfeDecomposition optimizer factory. Note that there is also a +Dantzig-Wolfe decomposition tutorial which shows how to solve a +Generalized Assignment Problem by using a branch-and-price algorithm.

+
+
+
+class DantzigWolfeDecomposition : public idol::impl::OptimizerFactoryWithColumnGenerationParameters<DantzigWolfeDecomposition>
+
+

Public Functions

+
+
+explicit DantzigWolfeDecomposition(const Annotation<Ctr, unsigned int> &t_decomposition)
+
+ +
+
+DantzigWolfeDecomposition &with_master_optimizer(const OptimizerFactory &t_master_optimizer)
+

Configures the optimizer factory for the master problem

+
+
Parameters:
+

t_master_optimizer – the desired optimizer factory for the master problem

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_pricing_optimizer(const OptimizerFactory &t_pricing_optimizer)
+

Configures the optimizer factory for the pricing problems

+
+
Parameters:
+

t_pricing_optimizer – the desired optimizer factory for the pricing problems

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_branching_on_master(bool t_value)
+

When set to true, branching is applied to the master problem. Otherwise, branching decisions are applied to the pricing problems.

+
+
Parameters:
+

t_value – the desired value

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_aggregation_type(CtrType t_type)
+
+ +
+
+virtual Optimizer *operator()(const Model &t_original_formulation) const override
+

Creates and returns a new optimizer to solve the model given as parameter.

+
+
Parameters:
+

t_model – The model which the optimizer will solve

+
+
Returns:
+

A new optimizer for the model

+
+
+
+ +
+
+virtual DantzigWolfeDecomposition *clone() const override
+

Creates and return a copy of the optimizer factory. This is used for polymorphism.

+
+
Returns:
+

A copied object of the current object (i.e., *this)

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_parallel_pricing_limit(unsigned int t_limit)
+

Configures the maximum number of pricing problems which can be solved in parallel

+
+
Parameters:
+

t_limit – the desired limit

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_column_pool_clean_up(unsigned int t_threshold, double t_ratio)
+

Configures the column pool clean up

+

When the number of columns in the column pool is larger than the given threshold, columns are removed from the pool (and possibly from the master problem) from the oldest columns to the newest. Only t_threshold * t_ratio are kept.

+
+
Parameters:
+
    +

  • t_threshold – the desired threshold

    • +

  • t_ratio – the clean up ratio

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_farkas_pricing(bool t_value)
+

Configures the activation of Farkas pricing.

+

If set to true, a Farkas certificate is asked to the master problem solver so as to generate new columns to improve feasibility or to show infeasibility of the problem.

+

By default, it is turned off.

+
+
Parameters:
+

t_value – true if Farkas pricing is desired, false otherwise

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_artificial_variables_cost(double t_artificial_variable_cost)
+

Configures the cost for the artificial variables added when the master problem is infeasible and Farkas pricing is turned off.

+

When the master problem is infeasible, artificial variables are added to the master problem with an objective cost of t_artificial_variable_cost. In case this approach fails to generate columns making the master problem feasible (e.g., the costs are too small), the algorithm switches to pure phase I where the constraint violations are optimized.

+

If t_artificial_variable_cost is less or equal than zero, pure phase I is directly applied.

+
+
Parameters:
+

t_artificial_variable_cost – the desired cost for the artificial variables.

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_dual_price_smoothing_stabilization(double t_smoothing_factor)
+

Configures the stabilization factor of the dual price smoothing stabilization. This value should be in [0,1). Note that when this parameter is zero, no stabilization is performed.

+
+
Parameters:
+

t_smoothing_factor – the desired stabilization factor

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_log_frequency(unsigned int t_log_frequency)
+

Configures the frequency for logging. Logging information is displayed every t_log_frequency iterations.

+
+
Parameters:
+

t_log_frequency – the desired log frequency

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_max_columns_per_pricing(unsigned int t_n_columns)
+

Configures the maximum number of columns which are added for each pricing operation.

+
+
Parameters:
+

t_n_columns – the maximum nuber of added columns

+
+
Returns:
+

the optimizer itself

+
+
+
+ +
+
+DantzigWolfeDecomposition &with_non_optimal_pricing_phase(double t_time_limit, double t_relative_gap)
+
+ +
+
+CRTP &with_log_level(LogLevel t_log_level, Color t_log_color = Color::Default)
+

Sets the log level and color for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_log_level(Info, Green);
+
+
+

+
+
Parameters:
+
    +

  • t_log_level – the log level

    • +

  • t_log_color – the output color

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_time_limit(double t_time_limit)
+

Sets the time limit for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
+
+

+
+
Parameters:
+

t_time_limit – the time limit (in seconds)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_thread_limit(unsigned int t_max_n_threads)
+

Sets the maximum number of threads which the optimizer can use

+

Example: 

auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
+
+

+
+
Parameters:
+

t_max_n_threads – the number of threads which can be used

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_iteration_count_limit(unsigned int t_iteration_count_limit)
+

Sets the maximum number of iterations which the optimizer go through

+

Example: 

auto algorithm = GLPK()
+                     .with_iteration_count_limit(200);
+
+
+

+
+
Parameters:
+

t_iteration_count_limit – the maximum number of iterations

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_best_bound_stop(double t_best_bound_stop)
+

Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
+
+

+
+
Parameters:
+

t_best_bound_stop – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_best_obj_stop(double t_user_best_obj)
+

Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
+
+

+
+
Parameters:
+

t_user_best_obj – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_relative_gap_tolerance(double t_relative_gap_tolerance)
+

Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
+
+

+
+
Parameters:
+

t_relative_gap_tolerance – the relative gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
+

Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
+
+

+
+
Parameters:
+

t_absolute_gap_tolerance – the absolute gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_presolve(bool t_value)
+

Sets the get_param_presolve activation for the optimizer.

+

Example: 

auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
+
+

+
+
Parameters:
+

t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &with_infeasible_or_unbounded_info(bool t_value)
+

Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

+

Example: 

auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
+
+

+
+
Parameters:
+

t_value – the activation level

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &conditional(bool t_conditional_value, const std::function<void(CRTP&)> &t_if)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+CRTP &conditional(bool t_conditional_value, const std::function<void(CRTP&)> &t_if, const std::function<void(CRTP&)> &t_else)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +

  • t_else – lambda function to execute in case t_conditional_value is false

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/column-generation/index.html b/api/optimizers/column-generation/index.html new file mode 100644 index 00000000..1ff7c773 --- /dev/null +++ b/api/optimizers/column-generation/index.html @@ -0,0 +1,211 @@ + + + + + + + Column-Generation algorithms — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Column-Generation algorithms

+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/glpk/GLPK.html b/api/optimizers/glpk/GLPK.html new file mode 100644 index 00000000..26dc6a9c --- /dev/null +++ b/api/optimizers/glpk/GLPK.html @@ -0,0 +1,449 @@ + + + + + + + GLPK — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

GLPK

+
+
+class GLPK : public idol::OptimizerFactoryWithDefaultParameters<GLPK>
+
+

Public Functions

+
+
+GLPK() = default
+
+ +
+
+GLPK(GLPK&&) noexcept = default
+
+ +
+
+GLPK &operator=(const GLPK&) = delete
+
+ +
+
+GLPK &operator=(GLPK&&) noexcept = delete
+
+ +
+
+virtual Optimizer *operator()(const Model &t_model) const override
+

Creates and returns a new optimizer to solve the model given as parameter.

+
+
Parameters:
+

t_model – The model which the optimizer will solve

+
+
Returns:
+

A new optimizer for the model

+
+
+
+ +
+
+virtual GLPK *clone() const override
+

Creates and return a copy of the optimizer factory. This is used for polymorphism.

+
+
Returns:
+

A copied object of the current object (i.e., *this)

+
+
+
+ +
+
+GLPK &with_log_level(LogLevel t_log_level, Color t_log_color = Color::Default)
+

Sets the log level and color for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_log_level(Info, Green);
+
+
+

+
+
Parameters:
+
    +

  • t_log_level – the log level

    • +

  • t_log_color – the output color

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_time_limit(double t_time_limit)
+

Sets the time limit for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
+
+

+
+
Parameters:
+

t_time_limit – the time limit (in seconds)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_thread_limit(unsigned int t_max_n_threads)
+

Sets the maximum number of threads which the optimizer can use

+

Example: 

auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
+
+

+
+
Parameters:
+

t_max_n_threads – the number of threads which can be used

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_iteration_count_limit(unsigned int t_iteration_count_limit)
+

Sets the maximum number of iterations which the optimizer go through

+

Example: 

auto algorithm = GLPK()
+                     .with_iteration_count_limit(200);
+
+
+

+
+
Parameters:
+

t_iteration_count_limit – the maximum number of iterations

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_best_bound_stop(double t_best_bound_stop)
+

Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
+
+

+
+
Parameters:
+

t_best_bound_stop – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_best_obj_stop(double t_user_best_obj)
+

Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
+
+

+
+
Parameters:
+

t_user_best_obj – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_relative_gap_tolerance(double t_relative_gap_tolerance)
+

Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
+
+

+
+
Parameters:
+

t_relative_gap_tolerance – the relative gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
+

Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
+
+

+
+
Parameters:
+

t_absolute_gap_tolerance – the absolute gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_presolve(bool t_value)
+

Sets the get_param_presolve activation for the optimizer.

+

Example: 

auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
+
+

+
+
Parameters:
+

t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &with_infeasible_or_unbounded_info(bool t_value)
+

Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

+

Example: 

auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
+
+

+
+
Parameters:
+

t_value – the activation level

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &conditional(bool t_conditional_value, const std::function<void(GLPK&)> &t_if)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+GLPK &conditional(bool t_conditional_value, const std::function<void(GLPK&)> &t_if, const std::function<void(GLPK&)> &t_else)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +

  • t_else – lambda function to execute in case t_conditional_value is false

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+

Public Static Functions

+
+
+static GLPK ContinuousRelaxation()
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/glpk/index.html b/api/optimizers/glpk/index.html new file mode 100644 index 00000000..9df14bbe --- /dev/null +++ b/api/optimizers/glpk/index.html @@ -0,0 +1,148 @@ + + + + + + + GLPK interface — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

GLPK interface

+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/gurobi/Gurobi.html b/api/optimizers/gurobi/Gurobi.html new file mode 100644 index 00000000..9625f490 --- /dev/null +++ b/api/optimizers/gurobi/Gurobi.html @@ -0,0 +1,479 @@ + + + + + + + Gurobi — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Gurobi

+
+
+class Gurobi : public idol::OptimizerFactoryWithDefaultParameters<Gurobi>
+
+

Public Functions

+
+
+Gurobi() = default
+
+ +
+
+Gurobi(Gurobi&&) noexcept = default
+
+ +
+
+Gurobi &operator=(const Gurobi&) = delete
+
+ +
+
+Gurobi &operator=(Gurobi&&) noexcept = default
+
+ +
+
+virtual Optimizer *operator()(const Model &t_model) const override
+

Creates and returns a new optimizer to solve the model given as parameter.

+
+
Parameters:
+

t_model – The model which the optimizer will solve

+
+
Returns:
+

A new optimizer for the model

+
+
+
+ +
+
+Gurobi &with_callback(const CallbackFactory &t_cb)
+
+ +
+
+Gurobi &with_lazy_cut(bool t_value)
+
+ +
+
+Gurobi &with_max_n_solution_in_pool(unsigned int t_value)
+
+ +
+
+Gurobi &with_continuous_relaxation_only(bool t_value)
+
+ +
+
+Gurobi &with_external_param(GRB_IntParam t_param, int t_value)
+
+ +
+
+Gurobi &with_external_param(GRB_DoubleParam t_param, double t_value)
+
+ +
+
+virtual Gurobi *clone() const override
+

Creates and return a copy of the optimizer factory. This is used for polymorphism.

+
+
Returns:
+

A copied object of the current object (i.e., *this)

+
+
+
+ +
+
+Gurobi &with_log_level(LogLevel t_log_level, Color t_log_color = Color::Default)
+

Sets the log level and color for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_log_level(Info, Green);
+
+
+

+
+
Parameters:
+
    +

  • t_log_level – the log level

    • +

  • t_log_color – the output color

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_time_limit(double t_time_limit)
+

Sets the time limit for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
+
+

+
+
Parameters:
+

t_time_limit – the time limit (in seconds)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_thread_limit(unsigned int t_max_n_threads)
+

Sets the maximum number of threads which the optimizer can use

+

Example: 

auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
+
+

+
+
Parameters:
+

t_max_n_threads – the number of threads which can be used

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_iteration_count_limit(unsigned int t_iteration_count_limit)
+

Sets the maximum number of iterations which the optimizer go through

+

Example: 

auto algorithm = GLPK()
+                     .with_iteration_count_limit(200);
+
+
+

+
+
Parameters:
+

t_iteration_count_limit – the maximum number of iterations

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_best_bound_stop(double t_best_bound_stop)
+

Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
+
+

+
+
Parameters:
+

t_best_bound_stop – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_best_obj_stop(double t_user_best_obj)
+

Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
+
+

+
+
Parameters:
+

t_user_best_obj – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
+

Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
+
+

+
+
Parameters:
+

t_relative_gap_tolerance – the relative gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
+

Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
+
+

+
+
Parameters:
+

t_absolute_gap_tolerance – the absolute gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_presolve(bool t_value)
+

Sets the get_param_presolve activation for the optimizer.

+

Example: 

auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
+
+

+
+
Parameters:
+

t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &with_infeasible_or_unbounded_info(bool t_value)
+

Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

+

Example: 

auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
+
+

+
+
Parameters:
+

t_value – the activation level

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &conditional(bool t_conditional_value, const std::function<void(Gurobi&)> &t_if)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Gurobi &conditional(bool t_conditional_value, const std::function<void(Gurobi&)> &t_if, const std::function<void(Gurobi&)> &t_else)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +

  • t_else – lambda function to execute in case t_conditional_value is false

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+

Public Static Functions

+
+
+static Gurobi ContinuousRelaxation()
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/gurobi/index.html b/api/optimizers/gurobi/index.html new file mode 100644 index 00000000..7c0008b4 --- /dev/null +++ b/api/optimizers/gurobi/index.html @@ -0,0 +1,148 @@ + + + + + + + Gurobi interface — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Gurobi interface

+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/index.html b/api/optimizers/index.html new file mode 100644 index 00000000..3de6570c --- /dev/null +++ b/api/optimizers/index.html @@ -0,0 +1,397 @@ + + + + + + + Optimizers — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Optimizers

+
+

Introduction

+

Optimizers denote the algorithms which are being used by idol to solve a given Model. +They are set by using the Model::use method, as done in the following example.

+
Env env;
+
+Model my_model(env);
+
+my_model.use( Gurobi() ); // setting the optimizer of my_model to Gurobi()
+
+
+

Here, Gurobi is actually an OptimizerFactory which will eventually create an optimizer to solve our model. Indeed, +the “real” optimizer in this case will be an instance of Optimizers::Gurobi which will be created when necessary.

+

This mechanism is what allows idol to create complex algorithms by combining optimizers together. Here is a second example +which creates a nested branch-and-price algorithm.

+
auto nested_branch_and_price =
+
+    /* The overall algorithm is a branch-and-bound */
+    BranchAndBound()
+
+        /* Each node is solved with a Dantzig-Wolfe decomposition algorithm */
+        .with_node_solver(
+
+            /* The annotation "decomposition1" is used to automatically decompose the problem */
+            DantzigWolfeDecomposition(decomposition1)
+
+                /* The master problem is solved using Gurobi */
+                .with_master_optimizer(Gurobi::ContinuousRelaxation())
+
+                /* Each pricing problem is solved by a (nested) branch-and-bound algorithm */
+                .with_pricing_solver(
+
+                    BranchAndBound()
+
+                        /* Each node is solved by a dantzig-wolfe decomposition algorithm */
+                        .with_nodes_solver(
+
+                            /* The annotation "decomposition2" is used to decompose the sub-problem again */
+                            DantzigWolfeDecomposition(decomposition2)
+
+                                /* The master problem is solved using Mosek */
+                                .with_master_optimizer(Mosek::ContinuousRelaxation())
+
+                                /* The sub-problem is solved by a (nested) branch-and-bound algorithm [we could have used, e.g., Gurobi instead] */
+                                .with_pricing_optimizer(
+
+                                    BranchAndBound()
+
+                                        /* Each node is solved by GLPK */
+                                        .with_node_solver(GLPK::ContinuousRelaxation())
+
+                                        /* Variables are selected for branching using the most-infeasible rule */
+                                        .with_branching_rule(MostInfeasible())
+
+                                        /* Nodes are selected using the worst-bound rule */
+                                        .with_node_selection_rule(WorstBound())
+
+                                )
+
+                                /* Branching constraints are applied to the pricing problem */
+                                .with_branching_on_master(false)
+                        )
+                        /* Variables are selected for branching using the most-infeasible rule */
+                        .with_branching_rule(MostInfeasible())
+
+                        /* Nodes are selected using the depth-first rule */
+                        .with_node_selection_rule(DepthFirst())
+                )
+
+                /* Column generation is stabilized by dual-price smoothing */
+                .with_dual_price_smoothing_stabilization(.3)
+
+                /* Infeasible master problem are dealt with using Farkas pricing */
+                .with_farkas_pricing()
+
+                /* Branching constraints are applied to the master problem */
+                .with_branching_on_master()
+        )
+        /* Variables are selected for branching using the most-infeasible rule */
+        .with_branching_rule(MostInfeasible())
+
+        /* Nodes are selected using the best-bound rule */
+        .with_node_selection_rule(BestBound()
+
+        /* Only informational logs will be printed (in blue) */
+        .with_log_level(Info, Blue)
+
+        /* The algorithm will run with a time limit of 3600 */
+        .with_time_limit(3600)
+    )
+
+my_model.use(nested_branch_and_price);
+
+
+

Once an optimizer, or rather, an optimizer factory, has been given, the Model::optimize method can be called to actually +solve the model.

+
my_model.optimize();
+
+
+
+
+

Optimizer factories

+

Typically, a user mostly works with optimizer factories rather than with optimizers. Optimizer factories are like +“building plans” for creating actual optimizers. They usually can be recognized by their with_* functions allowing +the user to customize this plan. For instance, the BranchAndBound optimizer factory has a method with_node_optimizer +allowing the user to pass yet another optimizer factory which will be used to create optimizers for the branch-and-bound +nodes.

+
+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/mosek/Mosek.html b/api/optimizers/mosek/Mosek.html new file mode 100644 index 00000000..fecb99b0 --- /dev/null +++ b/api/optimizers/mosek/Mosek.html @@ -0,0 +1,469 @@ + + + + + + + Mosek — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Mosek

+
+
+class Mosek : public idol::OptimizerFactoryWithDefaultParameters<Mosek>
+
+

Public Functions

+
+
+Mosek() = default
+
+ +
+
+Mosek(Mosek&&) noexcept = default
+
+ +
+
+Mosek &operator=(const Mosek&) = delete
+
+ +
+
+Mosek &operator=(Mosek&&) noexcept = delete
+
+ +
+
+virtual Optimizer *operator()(const Model &t_model) const override
+

Creates and returns a new optimizer to solve the model given as parameter.

+
+
Parameters:
+

t_model – The model which the optimizer will solve

+
+
Returns:
+

A new optimizer for the model

+
+
+
+ +
+
+virtual Mosek *clone() const override
+

Creates and return a copy of the optimizer factory. This is used for polymorphism.

+
+
Returns:
+

A copied object of the current object (i.e., *this)

+
+
+
+ +
+
+Mosek &with_continuous_relaxation_only(bool t_value)
+
+ +
+
+Mosek &with_external_parameter(const std::string &t_param, double t_value)
+
+ +
+
+Mosek &with_external_parameter(const std::string &t_param, int t_value)
+
+ +
+
+Mosek &with_external_parameter(const std::string &t_param, std::string t_value)
+
+ +
+
+Mosek &with_log_level(LogLevel t_log_level, Color t_log_color = Color::Default)
+

Sets the log level and color for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_log_level(Info, Green);
+
+
+

+
+
Parameters:
+
    +

  • t_log_level – the log level

    • +

  • t_log_color – the output color

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_time_limit(double t_time_limit)
+

Sets the time limit for the optimizer

+

Example: 

auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
+
+

+
+
Parameters:
+

t_time_limit – the time limit (in seconds)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_thread_limit(unsigned int t_max_n_threads)
+

Sets the maximum number of threads which the optimizer can use

+

Example: 

auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
+
+

+
+
Parameters:
+

t_max_n_threads – the number of threads which can be used

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_iteration_count_limit(unsigned int t_iteration_count_limit)
+

Sets the maximum number of iterations which the optimizer go through

+

Example: 

auto algorithm = GLPK()
+                     .with_iteration_count_limit(200);
+
+
+

+
+
Parameters:
+

t_iteration_count_limit – the maximum number of iterations

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_best_bound_stop(double t_best_bound_stop)
+

Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
+
+

+
+
Parameters:
+

t_best_bound_stop – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_best_obj_stop(double t_user_best_obj)
+

Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

+

Example: 

const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
+
+

+
+
Parameters:
+

t_user_best_obj – the threshold

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_relative_gap_tolerance(double t_relative_gap_tolerance)
+

Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
+
+

+
+
Parameters:
+

t_relative_gap_tolerance – the relative gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
+

Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

+

Example: 

auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
+
+

+
+
Parameters:
+

t_absolute_gap_tolerance – the absolute gap tolerance

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_presolve(bool t_value)
+

Sets the get_param_presolve activation for the optimizer.

+

Example: 

auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
+
+

+
+
Parameters:
+

t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &with_infeasible_or_unbounded_info(bool t_value)
+

Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

+

Example: 

auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
+
+

+
+
Parameters:
+

t_value – the activation level

+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &conditional(bool t_conditional_value, const std::function<void(Mosek&)> &t_if)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+Mosek &conditional(bool t_conditional_value, const std::function<void(Mosek&)> &t_if, const std::function<void(Mosek&)> &t_else)
+

Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

+

Example: 

for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
+
+

+
+
Parameters:
+
    +

  • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

    • +

  • t_if – lambda function to execute in case t_conditional_value is true

    • +

  • t_else – lambda function to execute in case t_conditional_value is false

    • +
+
+
Returns:
+

the optimizer factory itself

+
+
+
+ +
+
+

Public Static Functions

+
+
+static Mosek ContinuousRelaxation()
+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/optimizers/mosek/index.html b/api/optimizers/mosek/index.html new file mode 100644 index 00000000..2cf7204b --- /dev/null +++ b/api/optimizers/mosek/index.html @@ -0,0 +1,148 @@ + + + + + + + Mosek interface — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Mosek interface

+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/problems/ProblemsFLP.html b/api/problems/ProblemsFLP.html new file mode 100644 index 00000000..47ff26ff --- /dev/null +++ b/api/problems/ProblemsFLP.html @@ -0,0 +1,225 @@ + + + + + + + Facility Location Problem (FLP) — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Facility Location Problem (FLP)

+
+
+namespace FLP
+
+

Functions

+
+
+Instance read_instance_2021_Cheng_et_al(const std::string &t_filename)
+

Reads an instance from Chun Cheng, Yossiri Adulyasak, Louis-Martin Rousseau, Robust facility location under demand uncertainty and facility disruptions, Omega, Volume 103, 2021, 102429, ISSN 0305-0483, https://doi.org/10.1016/j.omega.2021.102429.

+
+
Parameters:
+

t_filename – the filename

+
+
+
+ +
+
+Instance read_instance_1991_Cornuejols_et_al(const std::string &t_filename)
+
+ +
+
+Instance generate_instance_1991_Cornuejols_et_al(unsigned int t_n_facilities, unsigned int t_n_customers, double t_ratio_capacity_over_demand)
+
+ +
+
+
+class Instance
+
+

Public Functions

+
+
+explicit Instance(unsigned int t_n_facilities, unsigned int t_n_customers)
+
+ +
+
+inline unsigned int n_facilities() const
+
+ +
+
+inline unsigned int n_customers() const
+
+ +
+
+inline virtual double fixed_cost(unsigned int t_i) const
+
+ +
+
+inline virtual double capacity(unsigned int t_i) const
+
+ +
+
+inline virtual double demand(unsigned int t_j) const
+
+ +
+
+inline virtual double per_unit_transportation_cost(unsigned int t_i, unsigned int t_j) const
+
+ +
+
+inline void set_fixed_cost(unsigned int t_i, double t_value)
+
+ +
+
+inline void set_capacity(unsigned int t_i, double t_value)
+
+ +
+
+inline void set_demand(unsigned int t_j, double t_value)
+
+ +
+
+inline void set_per_unit_transportation_cost(unsigned int t_i, unsigned int t_j, double t_value)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/problems/ProblemsGAP.html b/api/problems/ProblemsGAP.html new file mode 100644 index 00000000..9afec2a9 --- /dev/null +++ b/api/problems/ProblemsGAP.html @@ -0,0 +1,232 @@ + + + + + + + Generalized Assignment Problem (GAP) — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Generalized Assignment Problem (GAP)

+
+
+namespace GAP
+
+

Functions

+
+
+Instance read_instance(const std::string &t_filename)
+
+ +
+
+Instance generate_instance_Chu_and_Beasley_1997_C(unsigned int t_n_machines, unsigned int t_n_jobs)
+
+ +
+
+
+class Instance
+
+#include <GAP_Instance.h>
+

See also https://en.wikipedia.org/wiki/Generalized_assignment_problem.

+
+

Public Functions

+
+
+Instance(unsigned int t_n_agents, unsigned int t_n_jobs)
+
+ +
+
+Instance(const Instance&) = default
+
+ +
+
+Instance(Instance&&) noexcept = default
+
+ +
+
+Instance &operator=(const Instance&) = default
+
+ +
+
+Instance &operator=(Instance&&) noexcept = default
+
+ +
+
+~Instance() = default
+
+ +
+
+inline unsigned int n_agents() const
+
+ +
+
+inline unsigned int n_jobs() const
+
+ +
+
+inline double cost(unsigned int t_agent, unsigned int t_job) const
+
+ +
+
+inline double resource_consumption(unsigned int t_agent, unsigned int t_job) const
+
+ +
+
+inline double capacity(unsigned int t_agent) const
+
+ +
+
+inline void set_cost(unsigned int t_agent, unsigned int t_job, double t_value)
+
+ +
+
+inline void set_resource_consumption(unsigned int t_agent, unsigned int t_job, double t_value)
+
+ +
+
+inline void set_capacity(unsigned int t_agent, double t_value)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/problems/ProblemsKP.html b/api/problems/ProblemsKP.html new file mode 100644 index 00000000..2d135058 --- /dev/null +++ b/api/problems/ProblemsKP.html @@ -0,0 +1,224 @@ + + + + + + + Knapsack Problem (KP) — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Knapsack Problem (KP)

+
+
+namespace KP
+
+

Functions

+
+
+Instance read_instance(const std::string &t_filename)
+
+ +
+
+Instance read_instance_kplib(const std::string &t_filename)
+
+ +
+
+
+class Instance
+
+

Public Functions

+
+
+explicit Instance(unsigned int t_n_items)
+
+ +
+
+Instance(const Instance&) = default
+
+ +
+
+Instance(Instance&&) noexcept = default
+
+ +
+
+Instance &operator=(const Instance&) = default
+
+ +
+
+Instance &operator=(Instance&&) noexcept = default
+
+ +
+
+~Instance() = default
+
+ +
+
+inline unsigned int n_items() const
+
+ +
+
+inline double profit(unsigned int t_item) const
+
+ +
+
+inline double weight(unsigned int t_item) const
+
+ +
+
+inline double capacity() const
+
+ +
+
+inline void set_profit(unsigned int t_item, double t_value)
+
+ +
+
+inline void set_weight(unsigned int t_item, double t_value)
+
+ +
+
+inline void set_capacity(double t_value)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/problems/ProblemsMKP.html b/api/problems/ProblemsMKP.html new file mode 100644 index 00000000..d1a89424 --- /dev/null +++ b/api/problems/ProblemsMKP.html @@ -0,0 +1,227 @@ + + + + + + + Multiple Knapsack Problem (MKP) — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Multiple Knapsack Problem (MKP)

+
+
+namespace MKP
+
+

Functions

+
+
+Instance read_instance(const std::string &t_filename)
+
+ +
+
+
+class Instance
+
+#include <MKP_Instance.h>
+

See also https://en.wikipedia.org/wiki/Generalized_assignment_problem.

+
+

Public Functions

+
+
+Instance(unsigned int t_n_knapsacks, unsigned int t_n_items)
+
+ +
+
+Instance(const Instance&) = default
+
+ +
+
+Instance(Instance&&) noexcept = default
+
+ +
+
+Instance &operator=(const Instance&) = default
+
+ +
+
+Instance &operator=(Instance&&) noexcept = default
+
+ +
+
+~Instance() = default
+
+ +
+
+inline unsigned int n_knapsacks() const
+
+ +
+
+inline unsigned int n_items() const
+
+ +
+
+inline double p(unsigned int t_item) const
+
+ +
+
+inline double w(unsigned int t_item) const
+
+ +
+
+inline double t(unsigned int t_knapsack) const
+
+ +
+
+inline void set_p(unsigned int t_item, double t_value)
+
+ +
+
+inline void set_w(unsigned int t_item, double t_value)
+
+ +
+
+inline void set_t(unsigned int t_knapsack, double t_value)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/problems/ProblemsSRP.html b/api/problems/ProblemsSRP.html new file mode 100644 index 00000000..5b8d0102 --- /dev/null +++ b/api/problems/ProblemsSRP.html @@ -0,0 +1,297 @@ + + + + + + + Staff Rostering Problem (SRP) — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Staff Rostering Problem (SRP)

+
+
+namespace SRP
+
+

Functions

+
+
+Instance generate_random_instance_Zhao_et_al_2012(unsigned int t_n_regular_staff, unsigned int t_n_part_time_staff, unsigned int t_n_time_periods)
+
+ +
+
+Instance read_instance_from_file(const std::string &t_path_to_file)
+
+ +
+
+std::ostream &operator<<(std::ostream &t_os, const Instance &t_instance)
+
+ +
+
+
+class Instance
+
+

Public Functions

+
+
+Instance(unsigned int t_n_regular_staff, unsigned int t_n_part_time_staff, unsigned int t_n_time_periods)
+
+ +
+
+inline unsigned int n_regular_staff() const
+
+ +
+
+inline unsigned int n_part_time_staff() const
+
+ +
+
+inline unsigned int n_time_periods() const
+
+ +
+
+inline unsigned int shift_duration() const
+
+ +
+
+inline double regular_staff_fixed_wage_cost(unsigned int t_staff_index, unsigned int t_time_index) const
+
+ +
+
+inline double regular_staff_minimum_number_of_shifts(unsigned int t_staff_index) const
+
+ +
+
+inline double regular_staff_maximum_number_of_shifts(unsigned int t_staff_index) const
+
+ +
+
+inline double part_time_fixed_wage_cost(unsigned int t_staff_index, unsigned int t_time_index) const
+
+ +
+
+inline double part_time_staff_hourly_wage_cost(unsigned int t_staff_index, unsigned int t_time_index) const
+
+ +
+
+inline double part_time_staff_minimum_number_of_shifts(unsigned int t_staff_index) const
+
+ +
+
+inline double part_time_staff_maximum_number_of_shifts(unsigned int t_staff_index) const
+
+ +
+
+inline double unmet_demand_penalty_cost(unsigned int t_time_index) const
+
+ +
+
+inline double demand(unsigned int t_time_index) const
+
+ +
+
+inline void set_regular_staff_shift_duration(unsigned int t_value)
+
+ +
+
+inline void set_regular_staff_fixed_wage_cost(unsigned int t_staff_index, unsigned int t_time_index, double t_value)
+
+ +
+
+inline void set_regular_staff_minimum_number_of_shifts(unsigned int t_staff_index, double t_value)
+
+ +
+
+inline void set_regular_staff_maximum_number_of_shifts(unsigned int t_staff_index, double t_value)
+
+ +
+
+inline void set_part_time_fixed_wage_cost(unsigned int t_staff_index, unsigned int t_time_index, double t_value)
+
+ +
+
+inline void set_part_time_staff_hourly_wage_cost(unsigned int t_staff_index, unsigned int t_time_index, double t_value)
+
+ +
+
+inline void set_part_time_staff_minimum_number_of_shifts(unsigned int t_staff_index, double t_value)
+
+ +
+
+inline void set_part_time_staff_maximum_number_of_shifts(unsigned int t_staff_index, double t_value)
+
+ +
+
+inline void set_unmet_demand_penalty_cost(unsigned int t_index_index, double t_value)
+
+ +
+
+inline void set_demand(unsigned int t_time_index, double t_value)
+
+ +
+
+

Friends

+
+
+friend std::ostream &operator<<(std::ostream&, const Instance&)
+
+ +
+
+friend Instance read_instance_from_file(const std::string&)
+
+ +
+
+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/problems/index.html b/api/problems/index.html new file mode 100644 index 00000000..6793e4c3 --- /dev/null +++ b/api/problems/index.html @@ -0,0 +1,141 @@ + + + + + + + Problems — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/api/tolerances.html b/api/tolerances.html new file mode 100644 index 00000000..6f075900 --- /dev/null +++ b/api/tolerances.html @@ -0,0 +1,190 @@ + + + + + + + Tolerances — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Tolerances

+
+
+namespace Tolerance
+

Stores the default high-level tolerances used in idol.

+

It is possible for optimizers to have additional tolerance parameters, yet, the tolerances defined in this namespace should always be taken into account by the optimizer. Apart from the Sparsity tolerance, users can also change tolerance values at a local level (i.e., at an optimizer level) rather than at a global level.

+
+

Variables

+
+
+static double Sparsity = 1e-6
+

Default: \( 10^{-6} \)

+

Recommended range: \( [ 10^{-10}, 10^{-5} ] \)

+

This tolerance is used when data is saved in a sparse manner. For instance, when a value close to zero should be stored or ignored when saving a primal point.

+
+ +
+
+static double MIPRelativeGap = 1e-4
+

Default: \( 10^{-4} \)

+

Recommended range: \( [ 0, +\infty ] \)

+

Used to declare optimality of a MIP solution by comparing with the current relative gap.

+

The relative gap is computed as follows:

+\[ RelativeGap := \frac{ |UB - LB| }{ 10^{-10} + |UB| }. \]
+

+
+ +
+
+static double MIPAbsoluteGap = 1e-10
+

Default: \( 10^{-10} \)

+

Recommended range: \( [ 0, \infty ] \)

+

Used to declare optimality of a MIP solution by comparing with the current absolute gap.

+

The absolute gap is computed as follows:

+\[ AbsoluteGap := |UB - LB| \]
+

+
+ +
+
+static double Integer = 10e-5
+

Default: \( 10^{-5} \)

+

Recommended range: \( [ 10^{-9}, 10^{-1} ] \)

+

Used to recognized integer values, i.e., a given value is considered integer when the closest integer point is closer than this tolerance.

+
+ +
+
+static double Feasibility = 10e-6
+

Default: \( 10^{-6} \)

+

Recommended range: \( [ 10^{-9}, 10^{-2} ] \)

+

Used to characterized constraint satisfaction, i.e., a constraint is satisfied if it is not violated by a larger amount than this tolerance.

+
+ +
+
+static double Optimality = 10e-6
+

Default: \( 10^{-6} \)

+

Recommended range: \( [ 10^{-9}, 10^{-2} ] \)

+

Used to characterize optimality, i.e., all reduced costs must be smaller than this tolerance.

+
+ +
+
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/developer_guide/build-the-doc.html b/developer_guide/build-the-doc.html new file mode 100644 index 00000000..6ba71f5b --- /dev/null +++ b/developer_guide/build-the-doc.html @@ -0,0 +1,168 @@ + + + + + + + Build the doc! — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Build the doc!

+

This page explains how to build the documentation on a local machine.

+
+

Dependencies

+
+

Description

+

The documentation is built using doxygen and a bunch of other tools, in particular:

+
    +

  • doxygen the C++ documentation generator;

    • +

  • Sphinx the python documentation generator;

    • +

  • sphinx-rtd-theme a Sphinx theme used to render the +HTML version of the documentation;

    • +

  • sphinx-sitemap a Sphinx extension +to generate multi-version and multi-language sitemaps.org compliant sitemaps for the HTML version +of a Sphinx documentation;

    • +

  • sphinx-copybutton a Sphinx extension which +automatically adds buttons on code-blocks environments to copy its content;

    • +

  • Breathe the Sphinx plugin for integrating doxygen outputs into Sphinx.

    • +
+

For a detailed description on how these tools interact, please refer to this article.

+
+
+

Installation guide (Ubuntu)

+
sudo apt-get install doxygen # installs the last version of doxygen
+
+sudo apt-get install python3-sphinx # installs the last version of Sphinx
+
+sudo apt-get install python3-breathe # installs the last version of Breathe
+
+pip3 install sphinx-sitemap sphinx-rtd-theme sphinx-copybutton # installs theme and extensions
+
+
+
+
+
+

Build instructions

+

By default, CMake automatically creates a doc target. All you have to do to build the documentation website +is to build this target. For instance, inside a build directory, the following command can be used.

+
cmake .. && make doc
+
+
+

Note that you do not need to use make and use the following generic command.

+
cmake --build . --target doc
+
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/developer_guide/index.html b/developer_guide/index.html new file mode 100644 index 00000000..0da24296 --- /dev/null +++ b/developer_guide/index.html @@ -0,0 +1,137 @@ + + + + + + + Developer guide — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/developer_guide/tests.html b/developer_guide/tests.html new file mode 100644 index 00000000..136589ce --- /dev/null +++ b/developer_guide/tests.html @@ -0,0 +1,187 @@ + + + + + + + Unit and integration tests — idol + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Unit and integration tests

+

This page explains how to build the unit and integration tests on a local machine.

+
+

Dependencies

+

Tests are managed by the C++ unit testing framework Catch2.

+

When CMake is told to create test targets, it will automatically look for an installation of Catch2 on your +machine. If it cannot be found, CMake will attempt to download Catch2 from its GitHub repository.

+
+

Installation guide (Ubuntu)

+
git clone https://github.com/catchorg/Catch2.git # Clone Catch2 repository
+
+cd Catch2 # go inside the new directory
+
+cmake -Bbuild -H. -DBUILD_TESTING=OFF # Create install target
+
+sudo cmake --build build/ --target install # Build and install
+
+
+
+
+
+

Build instructions

+

By default, CMake will not create test targets nor look for Catch2. To tell CMake to generate them, you +need to set the CMake option BUILD_TESTS to YES.

+
+

Example

+

The following will tell CMake to create targets for tests.

+
cmake -DBUILD_TESTS=YES ..
+
+
+

For instance, we can now build all the existing tests

+
make tests
+
+
+

and run them.

+
./tests/tests
+
+
+
+
+
+

Code coverage options

+

Code coverage is done via gcov.

+

If you want to active code coverage options, you shall set the CMake option WITH_TEST_COVERAGE to YES. +Note that this only has an effect when BUILD_TESTS is also set to YES.

+
+

Example

+

The following command will tell CMake to generate targets for tests with code coverage options.

+
cmake -DBUILD_TESTS=YES -DWITH_CODE_COVERAGE=YES ..
+
+
+

Then, you should build and run the tests.

+
make tests && ./tests/tests
+
+
+

Once you are there, you may generate a report to a file called coverage.info by using gcov.

+
lcov --directory . --capture --output-file coverage.info
+
+
+
+

Also note that this forces g++ to be used for compiling.

+
+

Tip

+

Code coverage reports are also automatically generated at every push action on idol’s GitHub repository and +are available on codecov.

+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/examples/facility-location-problem.html b/examples/facility-location-problem.html new file mode 100644 index 00000000..4637ddcc --- /dev/null +++ b/examples/facility-location-problem.html @@ -0,0 +1,188 @@ + + + + + + + Facility Location Problem / Branch-and-Bound — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Facility Location Problem / Branch-and-Bound

+
//
+// Created by henri on 06/04/23.
+//
+#include <iostream>
+#include "modeling.h"
+#include "problems/facility-location-problem/FLP_Instance.h"
+#include "optimizers/branch-and-bound/BranchAndBound.h"
+#include "optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "optimizers/solvers/gurobi/Gurobi.h"
+#include "optimizers/branch-and-bound/node-selection-rules/factories/BestBound.h"
+
+int main(int t_argc, const char** t_argv) {
+
+    using namespace idol;
+
+    Env env;
+
+    // Read instance
+    const auto instance = Problems::FLP::read_instance_1991_Cornuejols_et_al("instance.txt");
+    const unsigned int n_customers = instance.n_customers();
+    const unsigned int n_facilities = instance.n_facilities();
+
+    // Make model
+
+    Model model(env);
+
+    auto x = model.add_vars(Dim<1>(n_facilities), 0., 1., Binary, "x");
+    auto y = model.add_vars(Dim<2>(n_facilities, n_customers), 0., 1., Continuous, "y");
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        model.add_ctr(idol_Sum(j, Range(n_customers), instance.demand(j) * y[i][j]) <= instance.capacity(i) * x[i]);
+    }
+
+    for (unsigned int j = 0 ; j < n_customers ; ++j) {
+        model.add_ctr(idol_Sum(i, Range(n_facilities), y[i][j]) == 1);
+    }
+
+    model.set_obj_expr(idol_Sum(i, Range(n_facilities),
+                                instance.fixed_cost(i) * x[i]
+                                + idol_Sum(j, Range(n_customers),
+                                             instance.per_unit_transportation_cost(i, j) *
+                                             instance.demand(j) *
+                                             y[i][j]
+                                         )
+                                 )
+                         );
+
+    // Set backend options
+    model.use(
+            BranchAndBound()
+                    .with_node_optimizer(Gurobi::ContinuousRelaxation())
+                .with_branching_rule(MostInfeasible())
+                .with_node_selection_rule(BestBound())
+                .with_log_level(Trace, Blue)
+    );
+
+    model.optimize();
+
+    std::cout << model.get_status() << std::endl;
+
+    return 0;
+}
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/examples/generalized-assignment-problem.html b/examples/generalized-assignment-problem.html new file mode 100644 index 00000000..614674d3 --- /dev/null +++ b/examples/generalized-assignment-problem.html @@ -0,0 +1,205 @@ + + + + + + + Generalized Assignment Problem / Branch-and-Price — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Generalized Assignment Problem / Branch-and-Price

+
//
+// Created by henri on 13/03/23.
+//
+#include <iostream>
+#include "modeling.h"
+#include "problems/generalized-assignment-problem/GAP_Instance.h"
+#include "optimizers/column-generation/Optimizers_ColumnGeneration.h"
+#include "optimizers/column-generation/ColumnGeneration.h"
+#include "optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "optimizers/branch-and-bound/node-selection-rules/factories/WorstBound.h"
+#include "optimizers/branch-and-bound/BranchAndBound.h"
+#include "optimizers/solvers/GLPK.h"
+#include "optimizers/dantzig-wolfe/DantzigWolfeDecomposition.h"
+#include "optimizers/column-generation/IntegerMasterHeuristic.h"
+
+int main(int t_argc, const char** t_argv) {
+
+    using namespace idol;
+
+    const auto instance = Problems::GAP::read_instance("instance.txt");
+
+    const unsigned int n_agents = instance.n_agents();
+    const unsigned int n_jobs = instance.n_jobs();
+
+    // Create optimization environment
+    Env env;
+
+    // Create model
+    Model model(env);
+
+    // Create decomposition annotation
+    Annotation<Ctr> decomposition(env, "decomposition", MasterId);
+
+    // Create assignment variables (x_ij binaries)
+    auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, "x");
+
+    // Create knapsack constraints (i.e., capacity constraints)
+    for (unsigned int i = 0 ; i < n_agents ; ++i) {
+        auto capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+
+        capacity.set(decomposition, i); // Assign constraint to i-th subproblem
+    }
+
+    // Create assignment constraints
+    for (unsigned int j = 0 ; j < n_jobs ; ++j) {
+        model.add_ctr(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j));
+    }
+
+    // Set the objective function
+    model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j])));
+
+    // Set optimizer
+    model.use(BranchAndBound()
+
+                      .with_node_optimizer(
+                              DantzigWolfeDecomposition(decomposition)
+                                      .with_master_optimizer(GLPK::ContinuousRelaxation())
+                                      .with_pricing_optimizer(GLPK())
+                                      .with_log_level(Info, Yellow)
+                                      .with_farkas_pricing(false)
+                                      .with_artificial_variables_cost(1e+4)
+                                      .with_branching_on_master(true)
+                                      .with_dual_price_smoothing_stabilization(.3)
+                                      .with_column_pool_clean_up(1e+8, .75)
+                      )
+                .with_branching_rule(MostInfeasible())
+                .with_node_selection_rule(WorstBound())
+                .with_log_level(Info, Blue)
+                .with_callback(IntegerMasterHeuristic().with_optimizer(GLPK()))
+            );
+
+    // Solve
+    model.optimize();
+
+    // Print solution
+    std::cout << save_primal(model) << std::endl;
+
+    return 0;
+}
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/examples/index.html b/examples/index.html new file mode 100644 index 00000000..533eb60b --- /dev/null +++ b/examples/index.html @@ -0,0 +1,133 @@ + + + + + + + Examples — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/examples/knapsack-problem.html b/examples/knapsack-problem.html new file mode 100644 index 00000000..8b16737c --- /dev/null +++ b/examples/knapsack-problem.html @@ -0,0 +1,178 @@ + + + + + + + Knapsack Problem / Gurobi — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Knapsack Problem / Gurobi

+
//
+// Created by henri on 06/04/23.
+//
+#include <iostream>
+#include <gurobi_c++.h>
+#include "problems/knapsack-problem/KP_Instance.h"
+#include "modeling.h"
+#include "optimizers/solvers/gurobi/Gurobi.h"
+#include "optimizers/branch-and-bound/BranchAndBound.h"
+#include "optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "optimizers/branch-and-bound/node-selection-rules/factories/BestBound.h"
+#include "optimizers/branch-and-bound/cutting-planes/CoverCuts.h"
+
+int main(int t_argc, const char** t_argv) {
+
+    using namespace idol;
+
+    const auto instance = Problems::KP::read_instance("instance.txt");
+    //const auto instance = Problems::KP::read_instance("/home/henri/CLionProjects/optimize/examples/knapsack-problem/instance50.txt");
+
+    const auto n_items = instance.n_items();
+
+    Env env;
+
+    // Create model
+    Model model(env);
+
+    auto x = model.add_vars(Dim<1>(n_items), 0, 1, Binary, "x");
+
+    model.add_ctr(idol_Sum(j, Range(n_items), instance.weight(j) * x[j]) <= instance.capacity());
+
+    model.set_obj_expr(idol_Sum(j, Range(n_items), -instance.profit(j) * x[j]));
+
+    // Set optimizer
+    //model.use(Gurobi());
+    model.use(
+            BranchAndBound()
+                    .with_node_optimizer(Gurobi::ContinuousRelaxation())
+                    .with_branching_rule(MostInfeasible())
+                    .with_node_selection_rule(BestBound())
+                    //.with_cutting_planes(CoverCuts().with_optimizer(Gurobi()))
+                    .with_log_level(Info, Blue)
+    );
+    // Solve
+    model.optimize();
+
+    std::cout << "Objective value = " << model.get_best_obj() << std::endl;
+
+    std::cout << save_primal(model) << std::endl;
+
+    return 0;
+}
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/genindex.html b/genindex.html new file mode 100644 index 00000000..8c3ac9d2 --- /dev/null +++ b/genindex.html @@ -0,0 +1,1191 @@ + + + + + + Index — idol + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Index
    • +
  • +
    • +
+
+
+
+
+ + +

Index

+ +
+ I + +
+

I

+ + + +
+ + + +
+
+
+ +
+ +
+

© Copyright 2023, Henri Lefebvre.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 00000000..3f8d87f7 --- /dev/null +++ b/index.html @@ -0,0 +1,277 @@ + + + + + + + Welcome to idol! — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Welcome to idol!

+https://img.shields.io/github/license/hlefebvr/idol +https://img.shields.io/github/v/tag/hlefebvr/idol?label=version +https://img.shields.io/github/actions/workflow/status/hlefebvr/idol/cmake.yml?branch=main +https://img.shields.io/github/issues-raw/hlefebvr/idol +https://www.repostatus.org/badges/latest/wip.svghttps://codecov.io/github/hlefebvr/idol/branch/main/graph/badge.svg?token=BWMH5522QP)](https://app.codecov.io/gh/hlefebvr/idol +
+
+

Idol is a C++ library for implementing complex decomposition algorithms for +mathematical optimization.

+

Its main goal is to ease the development of new mathematical optimization techniques to +solve complex optimization problems. It offers a user-friendly interface to build new algorithms +on top of state-of-the-art methods like Dantzig-Wolfe decomposition, Benders decomposition or +column-and-constraint generation.

+
+

New to idol?

+

If you are new to idol, I advise you to visit our installation guideline. +In particular, have a look at the local installation guideline. +It is the easiest installation process one could think of since it automatically downloads the latest version of idol and +installs it in a local folder. It’s really a mater of seconds before you can start using idol.

+
+

Example

+

Idol has a user-friendly interface which should look natural to people working in optimization. For instance, +here is how one solves a Knapsack Problem using the Gurobi solver.

+
using namespace idol;
+
+const unsigned int n_items = 5;
+const double[] profit = { 40., 50., 100., 95., 30., };
+const double[] weight = { 2., 3.14, 1.98, 5., 3., };
+const double capacity = 10.;
+
+Env env;
+
+Model model(env);
+
+auto x = model.add_vars(Dim<1>(n_items), 0., 1., Binary, "x");
+
+model.add_ctr(idol_Sum(j, Range(n_items), weight[j] * x[j]) <= capacity);
+
+model.set_obj_expr(idol_Sum(j, Range(n_items), -profits[j] * x[j]);
+
+model.use(Gurobi());
+
+model.optimize();
+
+
+
+

If you want to learn more about idol’s modeling interface, be sure to visit beginner tutorials.

+

If you are more experienced, you may want to have a look at our decomposition methods tutorials.

+
+
+

Is this a MIP solver?

+

The idol library is not a MIP solver in itself. Indeed, it typically needs to call external +solvers (e.g., GLPK or Gurobi) +as a sub-routine of more complex algorithmic schemes (e.g., column generation). +The idea is to work hand in hand with existing fine-tuned and well-engineered optimization +softwares to enhance their possibilities to solve e.g., larger problems or problems which +cannot directly be modeled as MIPs (e.g., \(\Sigma_i^P\)-hard problems).

+

Each subproblem is then solved by an external and dedicated solver. +Currently, the following external solvers can be interfaced:

+ +
+
+

Current features

+
+

Warning

+

Handling quadratic expressions is an experimental feature and extreme care should be taken if used.

+
+
+

Interfacing external optimization solvers

+

The idol library can be used to interface external solvers like GLPK +or Gurobi to solve standalone MI(N)LPs. It offers a unified and common +interface to every solver including standard parameters and branch-and-bound callbacks. +Thus, you can write your code once and test it with different solvers!

+
+
+

Generic Branch-and-Bound algorithms

+

Idol allows its user to create custom branch-and-bound scheme very easily where almost everything can be tweaked.

+
    +

  • Node agnostic implementation. The branch-and-bound algorithm can work with any node type as long as the user properly +defines how nodes must be updated. A default node type is already implemented for classical variable branching. This +node type can also be inherited, e.g., to enrich the information carried out from each parent node to its children.

    • +

  • Customizable branching rule. The default branching rules include: most-infeasible rule.

    • +

  • Customizable node selection rule. The default node selection rules include: best-bound, worst-bound, depth-first, breadth-first.

    • +

  • Callbacks. The user can specify its own callback to locally or globally modify a node’s problem, submit heuristic solutions, +or influence the execution of the overall algorithm.

    • +

  • Branch-and-bound with phases. Independently on any of the above settings, the B&B algorithm supports sub-trees exploration +to reach valid solutions to the original problem as quick as possible.

    • +
+

Features to come/desired features

+
    +

  • Parallelization of the algorithm.

    • +

  • New branching rules: pseudo-cost, strong-branching and reliability branching.

    • +

  • Default cutting planes.

    • +
+
+
+

Generic Column Generation and Dantzig-Wolfe decomposition

+

Idol can be used to build and custom column-generation algorithms with the following features.

+
    +

  • Infeasible master problem procedures. Idol can handle an infeasible master problem by resorting to Farkas pricing or +by adding artificial variables to the original problem (note that if this fails, idol will then switch to pure phase I +so as to exactly prove infeasibility).

    • +

  • Automatic pool clean up. If the master problem contains too many variables, they can be automatically removed. This can be +all controlled by user parameters.

    • +

  • Stabilization via dual price smoothing. The column generation procedure can be stabilized using dual price smoothing +controlled by user inputs.

    • +

  • Parallel pricing. Each pricing problem can be solved in parallel by means of a single parameter.

    • +

  • Nested column generation. A key idea of idol is that every optimizer is seen as a black-box to solve a given optimization model. +As such, a column-generation algorithm can easily be “plugged in” any algorithmic phase. For instance, solving the pricing of +a column-generation algorithm can be done by yet another column-generation algorithm.

    • +
+

Features to come/desired features

+
    +

  • Handling identical sub-systems.

    • +

  • Ryan-and-Foster branching rule.

    • +
+
+
+
+

Table of contents

+
+ +
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/installation/global_installation.html b/installation/global_installation.html new file mode 100644 index 00000000..9c1a3b19 --- /dev/null +++ b/installation/global_installation.html @@ -0,0 +1,199 @@ + + + + + + + Global installation — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Global installation

+

The installation process is managed by the CMake build system. You will therefore need to have it +installed on your computer (at least version 3.22 is required but it may work with earlier versions).

+
+

Hint

+

If you simply want to “try out” idol, we advise you to opt for a local installation.

+
+
+

Creating the install target

+

The first step is to create a build directory. +This is where the library will be compiled before being installed (i.e., copied) on your system.

+
mkdir build
+cd build
+
+
+

Then, you should call CMake in order to create some targets (in particular, the idol and the install target). +To do so, we recommend you to specify some options in order to link with external solvers that you may have +already installed on your computer.

+
+

Attention

+

By default, (i.e., if no options are given to CMake) idol will not be linked with any external solver. +See the last section on this page for more details.

+
+
cmake <YOUR_CMAKE_OPTIONS_SHOULD_GO_HERE> ..
+
+
+
+

Example for Gurobi

+

Here is an example of possible CMake command which will create the necessary targets for installing idol with Gurobi.

+
cmake -DUSE_GUROBI=YES ..
+
+
+

Note that this example assumes that your environment variable GUROBI_HOME has been correctly configured +(see this official Gurobi page).

+
+
+
+

Building

+

Now that targets have been created, we can build idol by running the following command.

+
make idol
+
+
+

This will compile the idol C++ library and make it ready to be installed (i.e., copied) on your computer.

+
+
+

Installing

+

If you want to install idol on your computer, run the following command.

+
sudo make install
+
+
+
+

Hint

+

Here, you need superuser rights in order to install idol globally. If you want to install idol on a specific folder, +you may also use the CMAKE_INSTALL_PREFIX CMake option to change the destination folder.

+
cmake -CMAKE_INSTALL_PREFIX=/my/custom/installation/folder <YOUR_CMAKE_OPTIONS_SHOULD_GO_HERE> ..
+make install
+
+
+
+
+
+

Linking with external solvers

+

To link idol with external solvers, specific options need to be passed to CMake. +A detailed list of such options can be found on this page.

+
+

Hint

+

Here is a quick guide on how to pass options to CMake. Say you want +to pass the option MY_OPTION to CMake with the value MY_VALUE. Then, you should run the following +command (inside build/).

+
cmake -DMY_OPTION=MY_VALUE ..
+
+
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/installation/index.html b/installation/index.html new file mode 100644 index 00000000..3b2d6c53 --- /dev/null +++ b/installation/index.html @@ -0,0 +1,147 @@ + + + + + + + Installation guidelines — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Installation guidelines

+

Welcome to idol! You are here on the installation guidelines.

+
+

Installation types

+

There are two ways of installing idol:

+
    +

  • A global installation installs idol globally on your computer (e.g., in /usr/lib).

    • +

  • A local installation lets CMake automatically download and manage idol’s installation on a sub-folder of your +CMake project.

    • +
+
+
+

Table of contents

+
+ +
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/installation/linking.html b/installation/linking.html new file mode 100644 index 00000000..8c7b2a6d --- /dev/null +++ b/installation/linking.html @@ -0,0 +1,160 @@ + + + + + + + Linking your C++ project with idol — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Linking your C++ project with idol

+

Idol is built with and for CMake (even though it is still possible to link using Makefile or pure gcc, clang, ...).

+

If you are using CMake, here is a minimal CMakeLists.txt which creates a new executable target linked with idol.

+
cmake_minimum_required(VERSION 3.22)
+project(my_project)
+
+set(CMAKE_CXX_STANDARD 17)
+
+add_executable(my_target main.cpp)
+
+find_package(idol REQUIRED) ## Here, we search for the installed library idol
+
+target_link_library(my_target PUBLIC idol) ## Here, we ask CMake to link with idol
+
+
+

Note that this will also work when idol is linked with an external solver like Gurobi, Mosek or GLPK.

+

The following main.cpp is then a minimal example.

+
#include <iostream>
+#include <idol/modeling.h>
+
+int main(int t_argc, const char** t_argv) {
+
+    Env env;
+
+    Model model(env);
+
+    Var x(env, 0., 1., Binary, "x");
+    model.add(x);
+
+    // ...
+
+    return 0;
+}
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/installation/local_installation.html b/installation/local_installation.html new file mode 100644 index 00000000..0c9a0bb9 --- /dev/null +++ b/installation/local_installation.html @@ -0,0 +1,197 @@ + + + + + + + Local installation — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Local installation

+

This page is dedicated to local installations of idol. This is the easiest way to get your project working with +idol without installing it globally on your computer.

+
+

Hint

+

If you want to install idol globally, please read our global installation guide.

+
+

The idea behind local installations is to let CMake download and manage the installation of idol in a sub-folder of your +project. This is done by using the CMake FetchContent_* directives.

+

Using this method, you can also explicitly specify the desired version of idol which you want to use.

+

We provide here a minimal CMakeLists.txt.

+
cmake_minimum_required(VERSION 3.23)
+project(my_project)
+
+set(CMAKE_CXX_STANDARD 17)
+
+include(FetchContent)
+
+# Define your CMake options here
+set(USE_GUROBI YES) # For instance, tell CMake to link idol with Gurobi
+
+# Tell CMake which version of idol you desire
+FetchContent_Declare(
+        idol
+        GIT_REPOSITORY https://github.com/hlefebvr/idol.git
+        GIT_TAG        origin/main # You may also use a tag, e.g., v0.2.4-alpha
+)
+
+# Ask CMake to download idol and install it to a sub-folder
+FetchContent_MakeAvailable(idol)
+
+# Normal executable definition
+add_executable(my_target main.cpp)
+
+# Link your CMake target with idol as classically done
+target_link_libraries(my_target PUBLIC idol)
+
+
+
+

Hint

+

As you have seen, some options must be set in CMake in order to tell it to link idol with external solvers. +This is done with the set CMake function. Say you want +to set the option MY_OPTION to the value MY_VALUE. Then, you should add the following +function call.

+
set(MY_OPTION MY_VALUE)
+
+
+
+
+

See also

+

A list of all possible options which can be set can be found on the global installation guide. +In particular, you will find options to link with Gurobi, Mosek and GLPK.

+
+

Then, here is a starting main.cpp.

+
#include <iostream>
+#include <modeling.h> // Note that we do not include <idol/modeling.h>
+
+int main(int t_argc, const char** t_argv) {
+
+    Env env;
+
+    Model model(env);
+
+    Var x(env, 0., 1., Binary, "x");
+    model.add(x);
+
+    // ...
+
+    return 0;
+}
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/installation/mosek-and-socp.html b/installation/mosek-and-socp.html new file mode 100644 index 00000000..e9ca9c8b --- /dev/null +++ b/installation/mosek-and-socp.html @@ -0,0 +1,163 @@ + + + + + + + Using idol with Eigen — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Using idol with Eigen

+

This page elaborates on some operations made by idol which require usage of the Eigen +C++ library.

+

We first explain how to link idol with Eigen, then discuss several operations which require the use of Eigen.

+
+

Warning

+

Calling functionalities which require Eigen without have linked idol with Eigen will result in an Exception being +thrown.

+
+
+

“Linking” with Eigen

+

Eigen is header-only C++ library. In that sense, no installation is required. One only needs to download Eigen’s source +code in order to make their header files accessible.

+

Then, all you have to do in order to “link” with Eigen is to set the USE_EIGEN CMake +option to YES.

+
+

Example

+

This example shows you have to create an install target for idol with Mosek and Eigen.

+
cmake -DUSE_MOSEK=YES -DUSE_EIGEN=YES ..
+
+
+
+
+
+

Interfacing Mosek for solving QPs and SOCPs

+

The interface of idol +is based on functional expressions, e.g., like

+
+\[\sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^ix_jx_k \le b_i.\]
+

The C++ Mosek interface, instead, is based on conic expressions, e.g., like

+
+\[(x_0, \textbf{Fx}) \in \mathcal Q^n,\]
+

where \(\mathcal Q^n\) denotes the second-order cone and \(F\) is some matrix related to \(Q^i\).

+

In order to compute \(F\) and thus, to make the conversion between the Mosek interface and +the idol interface, one needs to compute an eigen value decomposition.

+

This is automatically done by idol using Eigen.

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/installation/options.html b/installation/options.html new file mode 100644 index 00000000..18239221 --- /dev/null +++ b/installation/options.html @@ -0,0 +1,219 @@ + + + + + + + List of CMake options — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

List of CMake options

+
+

Linking with external solvers

+
+

For Gurobi (commercial solver)

+

To link with Gurobi, you will need to pass the USE_GUROBI CMake option with value YES.

+

By default, CMake will look for Gurobi inside the folder indicated by the environment variable GUROBI_HOME +(see this official Gurobi page). +Note that it is also possible to pass the CMake option GUROBI_DIR=/path/to/gurobi/install/dir in order to specify +another directory to look for Gurobi.

+
+

Example

+

The following will create an install target which will install idol with Gurobi.

+
cmake -DUSE_GUROBI=YES -DGUROBI_DIR=/path/to/gurobi/install/dir ..
+
+
+

If you are doing a local installation, then the same can be achieved as follows.

+
set(USE_GUROBI YES)
+set(GUROBI_DIR /path/to/gurobi/install/dir)
+
+
+
+
+
+

For Mosek (commercial solver)

+

To link with Mosek, you will need to pass the USE_MOSEK CMake option with value YES.

+

By default, CMake will look for Mosek inside the folder indicated by the environment variable MOSEK_HOME. +Note that it is also possible to pass the CMake option MOSEK_DIR=/path/to/mosek/install/dir in order to specify +another directory to look for Mosek.

+

Note that MOSEK_HOME (or equivalently MOSEK_DIR) should point to the Mosek installation folder where +folders h and bin can be found. For instance, MOSEK_HOME=/home/<MY_USERNAME>/mosek/10.0/tools/platform/linux64x86.

+
+

Example

+

The following will create an install target which will install idol with Mosek.

+
cmake -DUSE_MOSEK=YES -DMOSEK_DIR=/path/to/mosek/install/dir ..
+
+
+

If you are doing a local installation, then the same can be achieved as follows.

+
set(USE_MOSEK YES)
+set(MOSEK_DIR /path/to/mosek/install/dir)
+
+
+
+
+

Attention

+

If you intend to use Mosek for solving QPs or SOCPs, please read this.

+
+
+
+

For GLPK (open-source solver)

+

To link with GLPK, you will need to pass the USE_GLPK CMake option with value YES.

+

By default, CMake will look for GLPK inside the folder indicated by the environment variable GLPK_HOME as well +as in the default installation folders /usr/include and /usr/lib. +Note that it is also possible to pass the CMake option GLPK_DIR=/path/to/glpk/install/dir in order to specify +another directory to look for GLPK.

+
+

Example

+

The following will create an install target which will install idol with GLPK.

+
cmake -DUSE_GLPK=YES -GLPK_DIR=/path/to/glpk/install/dir ..
+
+
+

If you are doing a local installation, then the same can be achieved as follows.

+
set(USE_GLPK YES)
+set(GLPK_DIR /path/to/glpk/install/dir)
+
+
+
+
+
+
+

Building examples

+

Examples : can be found at the root level of the idol repository, inside the directory examples.

+

By default, CMake will not generate targets to build these example. To tell CMake to generate them, you +need to set the CMake option BUILD_EXAMPLE to YES.

+
+

Example

+

The following will tell CMake to create targets for examples.

+
cmake -DBUILD_EXAMPLES=YES ..
+
+
+

For instance, we can now build the Knapsack Problem example,

+
make ex_knapsack_problem
+
+
+

and run it.

+
./examples/knapsack-problem/ex_knapsack_problem
+
+
+
+
+
+

Building unit and integration tests

+

To build tests for idol, please refer to this developer page.

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/objects.inv b/objects.inv new file mode 100644 index 00000000..7fba2188 Binary files /dev/null and b/objects.inv differ diff --git a/search.html b/search.html new file mode 100644 index 00000000..13d8264e --- /dev/null +++ b/search.html @@ -0,0 +1,129 @@ + + + + + + Search — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
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  • Search
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+
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+ +
+ +
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+ +
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+

© Copyright 2023, Henri Lefebvre.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
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+
+
+ + + + + + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js new file mode 100644 index 00000000..a0ef2b05 --- /dev/null +++ b/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"docnames": ["api/index", "api/modeling/Annotation", "api/modeling/Column", "api/modeling/Constant", "api/modeling/Ctr", "api/modeling/Env", "api/modeling/Expr", "api/modeling/LinExpr", "api/modeling/Model", "api/modeling/Param", "api/modeling/QuadExpr", "api/modeling/Row", "api/modeling/SolutionDual", "api/modeling/SolutionPrimal", "api/modeling/TempCtr", "api/modeling/TempVar", "api/modeling/Var", "api/modeling/index", "api/optimizers/branch-and-bound/BranchAndBound", "api/optimizers/branch-and-bound/BranchAndBoundCallback", "api/optimizers/branch-and-bound/branching-rules/MostInfeasible", "api/optimizers/branch-and-bound/branching-rules/index", "api/optimizers/branch-and-bound/index", "api/optimizers/branch-and-bound/node-selection-rules/BestBound", 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\ No newline at end of file diff --git a/tutorials/decomposition_methods/benders.html b/tutorials/decomposition_methods/benders.html new file mode 100644 index 00000000..28b0350f --- /dev/null +++ b/tutorials/decomposition_methods/benders.html @@ -0,0 +1,254 @@ + + + + + + + Benders Decomposition (with LazyCutCallback) — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Benders Decomposition (with LazyCutCallback)

+

In this section, we will show how to use the LazyCutCallback callback to implement a simple Benders Decomposition +algorithm.

+
+

Hint

+

This tutorial regards the advanced topic of Benders Decomposition. +Rudimentary notions in the following subjects are recommended:

+ +
+
+

Mathematical Model

+
+

Original formulation

+

We will base our example on the following model taken from Blanco, V., (2016), Benders Decomposition, MINLP School: Theory +and Applications.

+
+\[\begin{split}\begin{align} + \min_{x,y} \ & 2 x_0 + 3x_1 + 2y \\ + \text{s.t.} \ & x_0 + 2x_1 + y \ge 3, \\ + & 2x_0 - x_1 + 3y \ge 4, \\ + & x,y\ge 0. +\end{align}\end{split}\]
+
+
+

Benders reformulation

+

We apply a Benders reformulation to this problem by considering \(y\) as the complicating variable. +The Benders reformulation reads:

+
+\[\begin{split}\begin{align} + \min_{y,z} \ & 2y + z \\ + \text{s.t.} \ & z \ge \lambda_1 ( 3 - y ) + \lambda_2(4 - 3y) \quad \lambda \in \Lambda, \\ + & z \ge 0, +\end{align}\end{split}\]
+

with \(\Lambda\) defined as the set of all \(\lambda\in\mathbb R^2_+\) such that

+
+\[\begin{split}\begin{align} + & \lambda_0 + 2 \lambda_1 \le 2, \\ + & 2\lambda_0 - \lambda_1 \le 3. +\end{align}\end{split}\]
+
+
+
+

Implementation

+

We are now ready to implement our decomposition method. We will need to define three different things:

+
    +

  • the master problem;

    • +

  • the dual space \(\Lambda\);

    • +

  • the shape of the cuts to be added.

    • +
+
+

The master problem

+

The master problem is created like any optimization model; see our Modeling tutorial.

+
Env env;
+
+Model master(env);
+
+auto y = master.add_var(0, Inf, Continuous, "y");
+auto z = master.add_var(0, Inf, Continuous, "z");
+
+master.set_obj_expr(2 * y + z);
+
+
+
+
+

The dual space \(\Lambda\)

+

To provide the description of the dual space \(\Lambda\), we use another Model object which will contain the variables +and constraints defining \(\Lambda\). The objective function is not used and can be left to zero.

+
Model dual_space(env);
+
+auto lambda = dual_space.add_vars(Dim<1>(2), 0, Inf, Continuous, "lambda");
+
+dual_space.add_ctr(lambda[0] + 2 + lambda[1] <= 2);
+dual_space.add_ctr(2 * lambda[0] - lambda[1] <= 3);
+
+
+
+
+

The cuts to be added

+

Finally, we need to define the cuts to be added to the master problem for a given dual variable \(\lambda\). +The cuts are always expressed in the “master space”. What we mean by this is that, here, \(y\) should be a variable +in the constraint while \(\lambda\) should be a constant.

+

This is done as follows.

+
auto benders_cut = z >= !lambda[0] * (3 - y) + !lambda[1] * (4 - 3 * y);
+
+
+

See how the lambda variables are “turned into” constants by prepending them with an “!” symbol.

+
+
+
+

Solving the model

+

In this section, we solve our model using GLPK and the LazyCutCallback from idol.

+

This is done as follows.

+
master.use(
+    GLPK()
+        .with_callback(
+            LazyCutCallback(dual_space, benders_cut)
+                .with_separation_optimizer(GLPK())
+        )
+);
+
+master.optimize();
+
+std::cout << save_primal(master) << std::endl;
+
+
+

See how we specified also an optimizer for solving the separation problem. Here, we use GLPK.

+
+

Warning

+

If you are using Gurobi with the LazyCutCallback, make sure to call the Gurobi::with_lazy_cuts method. +This is necessary to turn off some parameters of Gurobi which would otherwise lead to wrong solutions.

+
master.use(
+        Gurobi()
+            .with_lazy_cuts(true)
+            .with_callback(
+                LazyCutCallback(dual_space, benders_cut)
+                    .with_separation_optimizer(Gurobi())
+            )
+    );
+
+
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/decomposition_methods/dantzig_wolfe.html b/tutorials/decomposition_methods/dantzig_wolfe.html new file mode 100644 index 00000000..c2314380 --- /dev/null +++ b/tutorials/decomposition_methods/dantzig_wolfe.html @@ -0,0 +1,367 @@ + + + + + + + Dantzig-Wolfe Decomposition (Automatic) — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Dantzig-Wolfe Decomposition (Automatic)

+

In this section, we will show how to use the Branch-and-Price solver to solve the Generalized Assignment Problem (GAP) +using an external solver to solve each sub-problem.

+
+

Hint

+

This tutorial regards the advanced topic of Column Generation and Dantzig-Wolfe decomposition. +Rudimentary notions in the following subjects are recommended:

+ +
+
+

See also

+

A Benchmark on Generalized Assignemnt Problem is +available. +This includes a comparison with Coluna.jl.

+
+
+

Mathematical models

+

In this section, we assume that the reader is familiar with GAP. +Let \(m\) be a given of agents and let \(n\) be a set of tasks to perform. Let \(c_{ij}\) be the cost for +assigning task \(j\) to agent \(i\), \(w_{ij}\) be the resource consumption of task \(j\) when performed +by agent \(i\) and let \(t_i\) be the resource capacity of agent \(i\).

+
+

Direct model

+

The Generalized Assignment Problem (GAP) can be modeled as

+
+\[\begin{split}\min \ & \sum_{i=1}^m\sum_{j=1}^n c_{ij} x_{ij} \\ +\textrm{s.t. } & \sum_{j=1}^n w_{ij} x_{ij} \le t_i & i=1,...,m \\ +& \sum_{i=1}^m x_{ij} = 1 & j = 1,...,n \\ +& x_{ij}\in\{0,1\} & i=1,...,m, j=1,...,n\end{split}\]
+

Here, variable \(x_{ij}\) encodes the assignment decision and equals 1 if and only if task \(j\) is assigned to +agent \(i\).

+
+
+

Dantzig-Wolfe reformulation

+

Let us enumerate the list of all feasible assignments, i.e., let

+
+\[\{\bar x^e_{ij} \}_{e\in E} = \{ x \in \{ 0,1 \}^{mn} : \sum_{j=1}^n w_{ij}x_{ij} \le t_i \quad i=1,...,m \},\]
+

where \(E\) denotes a list for their indices. The Dantzig-Wolfe reformulation of GAP reads

+
+\[\begin{split}\min \ & \sum_{e\in E} \lambda_e\left( \sum_{i=1}^m\sum_{j=1}^n c_{ij}\bar x_{ij}^e \right) \\ +\textrm{s.t. } & \sum_{e\in E} \lambda_e \left( \sum_{i=1}^m \bar x_{ij}^e \right) = 1 & j=1,...,n \\ +& \sum_{e\in E} \lambda_e = 1 \\ +& \lambda_e \in \{ 0, 1 \} & \forall e\in E\end{split}\]
+

Though this model contains an exponential number of variables (i.e., columns) it can be solved efficiently using +Column Generation and Branch-and-price. In such case, the pricing problem is a Knapsack Problem.

+
+
+
+

Automatic reformulation in idol

+

The simplest way to solve a problem using column generation and idol is through its automatic reformulation feature. +To use this, one simply needs to give the original space formulation of the problem (here, the so-called direct model) +and to indicate which constraints should be moved to the pricing problem (here, the knapsack constraints).

+
+

Implementing the direct model with idol

+

To read an instance for GAP, we first need to include the header file located in "idol/problems/generalized-assignment-problem/GAP_Instance.h". +This will allow us to use idol’s instance parser for GAP. +Assuming that the instance file is named instance.txt, it can be loaded as follows.

+
const auto instance = Problems::GAP::read_instance("instance.txt");
+
+const unsigned int n_agents = instance.n_agents();
+const unsigned int n_jobs = instance.n_jobs();
+
+
+

We are now ready to model our problem (for more details, refer to this tutorial on modeling)

+
// Create optimization environment
+Env env;
+
+// Create model
+Model model(env);
+
+// Create assignment variables (x_ij binaries)
+auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, "x");
+
+// Create knapsack constraints (i.e., capacity constraints)
+for (unsigned int i = 0 ; i < n_agents ; ++i) {
+    model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+}
+
+// Create assignment constraints
+for (unsigned int j = 0 ; j < n_jobs ; ++j) {
+    model.add(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j));
+}
+
+// Set the objective function
+model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j])));
+
+
+
+
+

Giving decomposition instructions

+

We are now at the crucial step of indicating which constraint should be moved to the pricing problem. In idol, this is done by using +annotations. Annotations are additional information associated to an optimization object (e.g., a constraint or a variable). +Note that annotations are global, i.e., they do not relate to a given optimization model.

+

Every annotation is formed with two template arguments: an optimization object type and a value type. Here, we want to add +annotations to constraints, thus, the optimization object type must be Ctr. The value type can typically be any desired +type. Here, however, the Dantzig-Wolfe decomposition needs an annotation corresponding to an unsigned int. Thus, we create +the annotation as follows.

+
Annotation<Ctr, unsigned int> decomposition(env, "decomposition", MasterId);
+
+
+

Here, we pass three arguments to the constructor of Annotation<Ctr, unsigned int>. First, we pass the optimization +environment which will store the annotation. Then, a name (mandatory) is given to the annotation, here, “decomposition”. +Finally, a default value is given and equals “MasterId”. This will tell idol that constraints which have not been annotated +should remain in the master problem.

+

Now, observe how the annotation is applied to the capacity constraints.

+
for (unsigned int i = 0 ; i < n_agents ; ++i) {
+    Ctr capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+    capacity.set(decomposition, i); // <-- Annotating the capacity constraint
+}
+
+
+

Here, the first capacity constraint is moved to the first pricing problem (id: 0), +the second constraint to the second pricing problem (id: 1), and so on.

+

Note that another decomposition would be materialized as follows.

+
for (unsigned int i = 0 ; i < n_agents ; ++i) {
+    Ctr capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+    capacity.set(decomposition, 0); // <-- Annotating the capacity constraint
+}
+
+
+

Here, all the knapsack constraints are moved to the same pricing problem (id: 0).

+
+
+
+

Decomposing and solving the model

+

Now that the desired decomposition has been specified, we can specify the desired optimizer to solve our model. +Here, we want to solve our problem using a branch-and-price algorithm, i.e., a branch-and-bound algorithm where each relaxation +in the branch-and-bound tree is solved by a Dantzig-Wolfe decomposition. This is done as follows.

+
model.use(
+    /* The overall algorithm is a branch-and-bound */
+    BranchAndBound()
+
+        /* Each node is solved with a Dantzig-Wolfe decomposition algorithm */
+        .with_node_optimizer(
+
+            /* The annotation "decomposition" is used to automatically decompose the problem */
+            DantzigWolfeDecomposition(decomposition1)
+
+                /* The master problem is solved using Gurobi */
+                .with_master_optimizer(Gurobi::ContinuousRelaxation())
+
+                /* Each pricing problem is solved by Gurobi as well */
+                .with_pricing_optimizer(Gurobi())
+
+        )
+
+        /* Variables are selected for branching using the most-infeasible rule */
+        .with_branching_rule(MostInfeasible())
+
+        /* Nodes are selected using the best-bound rule */
+        .with_node_selection_rule(BestBound()
+
+        /* The algorithm will run with a time limit of 3600 */
+        .with_time_limit(3600)
+
+);
+
+
+

Then, one can simply call the Model::optimize method as follows.

+
model.optimize();
+
+
+

That’s it! The problem is being solved by column generation, and possibly branching on fractional variables.

+
+

Hint

+

Note that it is possible to obtain logs using the with_log_level method on the desired optimizer. +For instance, one may want to have +logs for the branch-and-bound optimizer. Then, one should do as follows.

+
model.use(
+    BranchAndBound()
+
+        /* ... omitting identical details */
+
+        .with_log_level(Info, Blue)
+);
+
+
+
+

The rest remains unchanged and one can use Model::optimize to solve the problem and retrieve the solution +through methods like Model::get_status and Model::get_var_primal.

+
+

Example

+

Here, we can solve our model using a Dantzig-Wolfe decomposition.

+
model.optimize();
+
+std::cout << save_primal(model) << std::endl;
+
+
+

This will produce the following output (e.g.).

+
[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=110000> <NGen=0> <BestBnd=-inf> <BestObj=110000.00> <RGap=90909090909090928.00 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-50093.00000> <NGen=0> <BestBnd=-inf> <BestObj=110000.00000> <RGap=90909090909090928.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-40096.00000> <NGen=0> <BestBnd=-inf> <BestObj=110000.00000> <RGap=90909090909090928.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-30068.00000> <NGen=0> <BestBnd=-inf> <BestObj=110000.00000> <RGap=90909090909090928.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=-242.5> <NGen=1> <BestBnd=-277.86> <BestObj=-242.50> <RGap=14.58 %> <AGap=35.36>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-7.90269> <NGen=1> <BestBnd=-277.85653> <BestObj=-242.50000> <RGap=14.58001 %> <AGap=35.35653>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-14.49817> <NGen=1> <BestBnd=-277.85653> <BestObj=-242.50000> <RGap=14.58001 %> <AGap=35.35653>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-1.36131> <NGen=1> <BestBnd=-277.85653> <BestObj=-242.50000> <RGap=14.58001 %> <AGap=35.35653>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=16> <TimT=0.02> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=-242.5> <NGen=0> <BestBnd=-242.51> <BestObj=-242.50> <RGap=0.00 %> <AGap=0.01>
+[2023-04-07 13:45:44]   [info]  [branch-and-bound]      <Node=   0 > <TimT=   0.02> <TimI=   0.02> <Levl=  0> <Stat=1> <Reas=0> <ObjVal=  -242.50> <BestBnd=     -inf> <BestObj=     +inf> <RelGap=200.00> <AbsGap= +inf>
+[2023-04-07 13:45:44]   [info]  [branch-and-bound]      <Node=   H-> <TimT=   0.02> <TimI=   0.02> <Levl=  0> <Stat=1> <Reas=1> <ObjVal=  -233.00> <BestBnd=     -inf> <BestObj=  -233.00> <RelGap=42918454935603896320.00> <AbsGap= +inf>
+[2023-04-07 13:45:44]   [info]  [branch-and-bound]      <Node=   0+> <TimT=   0.02> <TimI=   0.02> <Levl=  0> <Stat=1> <Reas=0> <ObjVal=  -242.50> <BestBnd=  -242.50> <BestObj=  -233.00> <RelGap= 4.08> <AbsGap= 9.50>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=-233> <NGen=0> <BestBnd=-inf> <BestObj=-233.00> <RGap=42918454935603896320.00 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-22579.50000> <NGen=0> <BestBnd=-inf> <BestObj=-233.00000> <RGap=42918454935603896320.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-17547.50000> <NGen=0> <BestBnd=-inf> <BestObj=-233.00000> <RGap=42918454935603896320.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-17552.50000> <NGen=0> <BestBnd=-inf> <BestObj=-233.00000> <RGap=42918454935603896320.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=-233> <NGen=2> <BestBnd=-235.81> <BestObj=-233.00> <RGap=1.21 %> <AGap=2.81>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-0.25760> <NGen=2> <BestBnd=-235.80933> <BestObj=-233.00000> <RGap=1.20572 %> <AGap=2.80933>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-0.22397> <NGen=2> <BestBnd=-235.80933> <BestObj=-233.00000> <RGap=1.20572 %> <AGap=2.80933>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=10> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-0.36123> <NGen=2> <BestBnd=-235.80933> <BestObj=-233.00000> <RGap=1.20572 %> <AGap=2.80933>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=13> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=-233> <NGen=2> <BestBnd=-233.02> <BestObj=-233.00> <RGap=0.01 %> <AGap=0.02>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=4747> <NGen=0> <BestBnd=-inf> <BestObj=4747.00> <RGap=2106593638087168512.00 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-12451.00000> <NGen=0> <BestBnd=-inf> <BestObj=4747.00000> <RGap=2106593638087168512.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=-7492.00000> <NGen=0> <BestBnd=-inf> <BestObj=4747.00000> <RGap=2106593638087168512.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Pricing> <Iter=0> <TimT=0.00> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <Obj=0.00000> <NGen=0> <BestBnd=-inf> <BestObj=4747.00000> <RGap=2106593638087168512.00000 %> <AGap=+inf>
+[2023-04-07 13:45:44]   [info]  [dantzig-wolfe] <Type=Master> <Iter=8> <TimT=0.01> <TimI=0.00> <Stat=Optimal> <Reas=Proved> <ObjVal=-218> <NGen=1> <BestBnd=-224.13> <BestObj=-218.00> <RGap=2.81 %> <AGap=6.13>
+
++-----------------------
+| Status: Optimal
+| Reason: Proved
+| ObjVal: -233.00
+| Values:
+|       x_1_7 = 1.00
+|       x_2_0 = 1.00
+|       x_2_1 = 1.00
+|       x_1_4 = 1.00
+|       x_1_5 = 1.00
+|       x_0_6 = 1.00
+|       x_0_2 = 1.00
+|       x_0_3 = 1.00
++-----------------------
+
+
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/decomposition_methods/index.html b/tutorials/decomposition_methods/index.html new file mode 100644 index 00000000..d6230bcc --- /dev/null +++ b/tutorials/decomposition_methods/index.html @@ -0,0 +1,134 @@ + + + + + + + Decomposition methods — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/getting_started/index.html b/tutorials/getting_started/index.html new file mode 100644 index 00000000..b5c09432 --- /dev/null +++ b/tutorials/getting_started/index.html @@ -0,0 +1,134 @@ + + + + + + + Getting started — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Getting started

+
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/getting_started/modeling_optimization_problems.html b/tutorials/getting_started/modeling_optimization_problems.html new file mode 100644 index 00000000..804c5ce0 --- /dev/null +++ b/tutorials/getting_started/modeling_optimization_problems.html @@ -0,0 +1,302 @@ + + + + + + + Modeling optimization problems — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Modeling optimization problems

+

On this page, we discuss the very basic ideas of idol’s modeling API. +All classes which are used for modeling an optimization problem can be accessed by including #include <idol/modeling.h>. +Let’s get started.

+
+

Warning

+

The idol library can be found inside the idol namespace, thus, be sure to add using namespace idol; +where desired or to explicitly refer to classes using this namespace, e.g., by using idol::Model instead of Model.

+
+
+

Env

+

Every optimization object (like variables and constraints) are managed by an “optimization environment”. Essentially, +it is the environment that controls the death and lives of such objects. It is through the environment that idol +manages the different versions each optimization object may have during the execution of your program.

+

Typically, only one environment should be used by your code, though it is possible to instantiate many environment (not advised).

+

Environments are objects of the Env class and can be created as follows.

+
Env env; // Creates a new optimization environment.
+
+
+
+
+

Model

+

The Model class is used to represent an optimization model of the following form.

+
+\[\begin{split}\begin{array}{lll} + \min\ & \displaystyle \sum_{j=1}^n c_jx_j + \sum_{j=1}^n\sum_{k=1}^n d_{jk}x_jx_k \\ + \textrm{s.t. } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\ + & l_j \le x_j \le u_j & j=1,...,m \\ + & x_j\in\mathbb Z & j\in J_I +\end{array}\end{split}\]
+

Here, \(x_j\) are the variables of this optimization problem while \(c_j, d_{jk}, a_{ij}\) and \(q_{jk}^i\) are given +input parameters for this model. Optionally, \(J_I\subseteq\{1,...,n\}\) is a set of variable indices +whose value must be integral.

+

Constructors of Model can be used to create a new optimization model in idol. The most common takes a single argument +which is the optimization environment to be used.

+
int main(int t_argc, const char** t_argv) {
+
+    Env env;
+
+    Model model(env);
+
+    // The model has been created!
+
+    return 0;
+}
+
+
+

Now, we can define optimization variables and constraints.

+
+
+

Variables

+

Any variable in idol is associated to at least one Model object. Typically, exactly one. +We can easily create a new variable by using the constructor of the Var class and add it to a model by calling the Model::add method. +For instance, the following piece of code +will create a new variable, called “x”, which is continuous and non-negative.

+
Var x(env, 0., Inf, Continuous, "x");
+
+model.add(x); // Variable x is added to the model
+
+
+

A more straightforward way of creating variables is by directly calling the method add_var of the Model class. +For instance, the following piece of code is equivalent to the previous one.

+
model.add_var(0, Inf, Continuous, "x");
+
+
+

Note that we did not need to repeat the environment since the model’s environment is used by default.

+

The idol library also offers simple ways for creating multiple variables at once. +For instance, one can call the Var::make_vector function. This function requires +an extra parameter specifying the dimension of the new variable. For instance, the following code creates variables \(y_{ij}\) +with \(i=1,...,K\) and \(j=1,...,T\).

+
auto y = Var::array(env, Dim<2>(K, T), 0., Inf, Continuous, "y");
+
+model.add_array<Var, 2>(y); // Variables y_ij are added to the model
+
+std::cout << y[0][0] << std::endl; // "y_0_0"
+
+
+

Alternatively, one can use the Model::add_vars method.

+
auto y= model.add_vars(Dim<2>(K, T), 0., Inf, Continuous, "y");
+
+std::cout << y[0][0] << std::endl; // "y_0_0"
+
+
+
+
+

Constraints

+

Similarly to variables, constraints are easily created and added to a given Model.

+

Constraints can be created by calling the constructor of the Ctr class and added to a model by means of Model::add. +See for instance.

+
Env env;
+Model model(env);
+
+Var x_0(env, 0., Inf, Continuous, "x_0");
+Var x_1(env, 0., Inf, Continuous, "x_1");
+Ctr constraint(env, x_0 + x_1 >= 1);
+
+model.add(x_0);
+model.add(x_1);
+model.add(constraint);
+
+
+

A more compact of this code is obtained by making use of the Model::add_vars and Model::add_ctr methods.

+
Env env;
+Model model(env);
+
+auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, "x");
+auto constraint = model.add_ctr(x + y >= 1);
+
+
+

As you can see, a constraint is created using the pattern {expression} {sign} {expression} where

+
    +

  • {sign} is one of <=, >= and ==;

    • +

  • {expression} is an instance of Expr.

    • +
+

The Expr class is used to represent a mathematical expression in idol. An expression is composed of three parts:

+
    +

  • Expr::linear will give you access to the linear part of the expression (it is an instance of LinExpr);

    • +

  • Expr::quadratic will give you access to the quadratic part of the expression (it is an instance of QuadExpr);

    • +

  • Expr::constant will return the constant (or offset) of the expression (it is an instance of Constant).

    • +
+

Typically, however, you will not really care about what composes an expression since an Expr object can be created +quite naturally. See for instance the following code.

+
Expr expr = 1 + 3 * x[0];
+expr += x[1];
+expr += x[0] + 2 * x[0] * x[1];
+
+std::cout << expr << std::endl; // "1 + 4 * x[0] + 1 * x[1] + 2 * x[0] * x[1]"
+
+
+

As mentioned, you can access parts of an expression as follows.

+
for (const auto& [var, coefficient] : expr.linear()) {
+    std::cout << var << " is multiplied by " << coefficient << std::endl;
+}
+
+/*
+    "x_0 is multiplied by 4"
+    "x_1 is multiplied by 1"
+*/
+
+
+
+

About constants in expressions

+

Without diving into too much detail, we should here precise that each constant multiplying a variable in an Expr +can actually be composite (e.g., a coefficient in the expression may refer to external optimization variables whose +value is considered fixed in the current model).

+

Fixing variables in an optimization problem can be achieved thanks to the ! symbol.

+

For instance, here is an expression where xi_0 and xi_1 are seen as parameters.

+
Expr expr = (1 + 2 * !xi_0) * x + 3 * !xi_1 * y;
+
+
+

Here, 1 + 2 * !xi_0 is an instance of the Constant object and can be used as follows.

+
Constant constant = 1 + 2 * !xi_0;
+
+std::cout << constant.numerical() << std::endl; // output: 1
+
+for (const auto& [param, coeff] : constant) {
+    std::cout << coeff << " * " << param << std::endl; // output: 2 * !xi_0
+}
+
+
+
+
+
+

Objective function

+

The objective function of an optimization model can specified by the Model::set_obj_expr method.

+

Here is an example which sets the objective function to \(-x_0 + 2 * x_1\);

+
model.set_obj_expr(-x_0 + 2 * x_1);
+
+
+

In the following tutorial, we will dive into a more practical way to build expressions by considering the simple example +of the combinatorial Knapsack problem. We will also see how to call an external solver like Gurobi or GLPK using idol. +See you there!

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/getting_started/using_an_external_solver.html b/tutorials/getting_started/using_an_external_solver.html new file mode 100644 index 00000000..3c097581 --- /dev/null +++ b/tutorials/getting_started/using_an_external_solver.html @@ -0,0 +1,321 @@ + + + + + + + Using an external solver — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Using an external solver

+

In this tutorial, we will see how to use an external optimization solver like GLPK or GLPK to solve +a small combinatorial problem. +The considered problem is the Knapsack Problem (see the Knapsack Problem wikipedia page).

+
+

Modeling

+

The first step is to model our problem using idol. Recall the standard model for the knapsack problem:

+
+\[\begin{split}\begin{array}{lll} + \max\ & \displaystyle \sum_{j=1}^n p_jx_j \\ + \textrm{s.t. } & \displaystyle \sum_{j=1}^n w_jx_j \le W \\ + & x_j \in \{ 0, 1 \} & j=1,...,n +\end{array}\end{split}\]
+

where \(n\) denotes the number of items and for each item \(j\in\{1,...,n\}\), \(p_j\) denotes its profit while +\(w_j\) denotes its weight. Finally, we let \(W\) denote the knapsack capacity.

+

We will assume to have the following input data at hand.

+
const unsigned int n = 5; // 5 items
+const std::vector<double> p = { 40., 50., 100., 95., 30. }; // profits
+const std::vector<double> w = { 2., 3.14, 1.98, 5., 3. }; // weights
+const double W = 10; // capacity
+
+
+

Then, using idol’s modeling API contained in #include <api/modeling.h>, we can create our model easily. +We will first present a naive implementation using only the knowledge introduced in the previous tutorial. +Then, we will show a more compact way of implementing it.

+
+

A first approach

+

A first approach to model our knapsack problem in idol is as follows.

+
// Create environemnt
+Env env;
+
+// Create a new model
+Model model(env);
+
+// Create a vector for storing the x variables
+std::vector<Var> x;
+x.reserve(n);
+
+// Create x variables as binary with p_j as objective coefficient
+for (unsigned int j = 0 ; j < n ; ++j) {
+    Var x_j(env, 0., 1., Binary, Column(p[j]), "x_" + std::to_string(j));
+    model.add(x_j);
+    x.emplace_back( x_j );
+}
+
+// Create expression for the knapsack constraint
+Expr knapsack_constraint;
+for (unsigned int j = 0 ; j < n ; ++j) {
+    knapsack_constraint += w[j] * x[j];
+}
+
+// Create the knapsack constraint
+Ctr c(knapsack_constraint <= W);
+model.add(c);
+
+// Define objective sense
+model.set_obj_sense(Maximize);
+
+
+

Here, we used the Model::set_obj_sense method to set the objective sense of our model. By default, all models are +assumed to be minimization problems.

+
+
+

A more elegant approach

+

Though our first approach works well, its size and readability can greatly be reduced by using the predefined macro idol_Sum +and calls to methods of the Model class.

+
// Create environemnt
+Env env;
+
+// Create a new model
+Model model(env);
+
+// Create x variables
+model.add_vars(Dim<1>(n), 0., 1., Binary, "x");
+
+// Create the knapsack constraint
+model.add(idol_Sum(j, Range(n), w[j] * x[j] ) <= W);
+
+// Define objective sense
+model.set_obj_sense(Maximize);
+model.set_obj_expr(idol_Sum(j, Range(n), p[i] * x[i]);
+
+
+

Here, we directly add \(n\) variables with the right types and bounds.

+

Then, we use the idol_Sum macro to create the knapsack constraint. +This macro is used as follows idol_Sum({name}, {iteratable}, {expression}) where {name} will be the name of an index +taking value in the {iteratable} (here, Range(n)) while {expression} is the piece of expression which will be accumulated.

+
+

About Range

+

In the above example, Range is used to define an iterable ranging from \(0\) to \(n\) (note that it is also possible to range from \(l\) to \(n\) for \(l < n\) +by calling Range(l, n)). The objective function is created similarly.

+
+
+
+
+

Solving the problem using an external solver

+

The idol library offers different ways for solving optimization problems. +To select the desired approach for a given model, one must call the Model::use method and specify the +“optimizer” to be used.

+

For instance, the following will set the optimizer to GLPK for solving our model.

+
model.use(GLPK());
+
+
+
+

Hint

+

Here, GLPK is actually an OptimizerFactory which will eventually create an optimizer to solve our model. +Indeed, the “real” optimizer in this case will be an instance of Optimizers::GLPK which will be created when necessary.

+

If you want to learn more about optimizers and optimizer factories, please refer to this page.

+
+

Now that the optimizer has been configure, we can solve our problem by calling the Model::optimize method.

+
model.optimize();
+
+
+
+
+

Accessing the solution

+

Finally, you may access pieces of information regarding the solution by using one of the following methods:

+
    +

  • get_status returns the current solution status (e.g., Optimal, Infeasible, Unbounded, …).

    • +

  • get_reason returns the reason for the solution status (e.g., the solution reports Infeasible because of +TimeLimit).

    • +

  • get_best_obj returns the best objective value found (i.e., the best objective cost among feasible solutions +considered during the execution of the algorithm).

    • +

  • get_best_bound returns the best objective value bound (e.g., a dual bound).

    • +

  • get_relative_gap returns the relative optimality gap computed as

    • +
+
+\[\textrm{relative_gap} = \left| \frac{ \textrm{best_obj} - \textrm{best_bound} }{ 1e^{-10} + \textrm{best_obj} } \right|.\]
+
    +

  • get_absolute_gap returns the absolute optimality gap computed as

    • +
+
+\[\textrm{absolute_gap} = | \textrm{best_obj} - \textrm{best_bound} |.\]
+
    +

  • get_var_primal returns the primal value (when status is Optimal or Feasible) of a given variable.

    • +

  • get_var_ray returns the ray value (when status Unbounded) of a given variable.

    • +

  • get_ctr_dual returns the dual value (when status is Optimal or Feasible for continuous problems) of a given +constraint.

    • +

  • get_ctr_farkas returns the Farkas certificate value (when status is Infeasible for continuous problems) of a given +constraint.

    • +
+

Additionally, functions save_primal, save_ray, save_dual and save_farkas will create objects of the class +Solution::Primal and Solution::Dual storing the results of corresponding calls to get_var_* and get_ctr_* +methods.

+
+

Example

+

This example shows how to solve a model using GLPK and retrieves some piece of information about its solution.

+
model.use(GLPK());
+
+model.optimize();
+
+const SolutionStatus status = model.get_status();
+
+if (status == Optimal) {
+
+    std::cout << "Optimal solution found!" << std::endl;
+
+    Solution::Primal primal_values = save_primal(model);
+
+    std::cout << primal_values << std::endl;
+
+} else {
+
+    std::cout << "An optimal solution could not be found" << std::endl;
+
+    std::cout << "GLPK returned status " << status << std::endl;
+
+    std::cout << "The reason for this status is " << get_reason(model) << std::endl;
+
+    if (status == Feasible) {
+
+        std::cout << "The optimality gap is " << get_relative_gap(model) * 100 << " %" << std::endl;
+
+    } else if (status == Unbounded) {
+
+        std::cout << "An unbounded ray is" << std::endl;
+
+        std::cout << save_ray(model) << std::endl;
+
+    } else if (status == Infeasible) {
+
+        std::cout << "A Farkas certificate is" << std::endl;
+
+        std::cout << save_farkas(model) << std::endl;
+
+    }
+
+}
+
+
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/index.html b/tutorials/index.html new file mode 100644 index 00000000..11359d4a --- /dev/null +++ b/tutorials/index.html @@ -0,0 +1,167 @@ + + + + + + + Tutorials — idol + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/tutorials/robust_optimization/dualizing.html b/tutorials/robust_optimization/dualizing.html new file mode 100644 index 00000000..d02ecedd --- /dev/null +++ b/tutorials/robust_optimization/dualizing.html @@ -0,0 +1,313 @@ + + + + + + + Dualization — idol + + + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Dualization

+

Dualization plays a prominent role in robust optimization. In this tutorial we show how one can derive the dual problem +of any convex quadratic problem. This is done both from the theoretical and computational side. In the first section, +the mathematical expression of the dual is derived while we show how it can automatically be obtained by using Idol.

+
+

Dual of a convex quadratic problem

+

Recall that Idol considers convex problems with quadratic expressions of the following form:

+
+\[\begin{split}\begin{array}{lll} + \textrm{minimize } & \displaystyle \sum_{j=1}^n c_jx_j + \sum_{j=1}^n\sum_{k=1}^n d_{jk}x_jx_k \\ + \textrm{subject to } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\ + & l_j \le x_j \le u_j & j=1,...,m \\ + & x_j\in\mathbb Z & j\in J_I, +\end{array}\end{split}\]
+

where it is assumed that \(C^i\cap[l,u]\) are convex sets, with

+
+\[C^i = \{ x\in\mathbb R^n : \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i \}`\]
+

and \(i=1,...,m\), and that the objective function \(f(x) = \sum_{j=1}^n c_jx_j + \sum_{j=1}^n\sum_{k=1}^n d_{jk}x_jx_k\) +is convex over \(\mathbb R^n\). The bounds \(l_j\) and \(u_j\) (with \(j=1,...,n\)) belong to the extended real number line.

+

We start by re-writing our problem in term of indicator functions. We recall here that the indicator function of a set \(C\) +is noted \(\delta(\bullet|C)\) and is defined as

+
+\[\begin{split}\delta(x|C) = \begin{cases} + 0 & \textrm{if } x\in C \\ + +\infty & \textrm{otherwise} +\end{cases}.\end{split}\]
+

Our (primal) problem reads

+
+\[\min_{x\in\mathbb R^n} f(x) + \sum_{i=1}^m\delta(x|C^i) + \delta(x|[l,u]).\]
+

As long as \(f\) and \(C^i\cap [l, u]\) are convex, this problem is convex and, assuming constraint qualification holds, the following +equality holds (see Fenchel duality).

+
+\[\begin{split}\begin{multline} +\min_{x\in\mathbb R^n} \sum_{i=1}^m\delta(x|C^i) + \delta(x|[l,u]) - (-f)(x) \\ + = +\max_{\pi\in\mathbb R^n} (-f)_*(\pi) - \left( \sum_{i=1}^m\delta(\bullet|C^i) + \delta(\bullet|[l,u]) \right)^*(\pi) +\end{multline}\end{split}\]
+

Refering to this cheatsheet on convex conjugates, +one sees that \((-f)_*(\pi) = -f^*(-\pi)\). Moreover, refering to the “Non-separable sum” formula, one obtains the followig problem:

+
+\[\begin{split}\begin{array}{lll} + \textrm{maximize } & -f^*(-\pi) - \sum_{i=1}^m \delta^*(u^i|C^i) - \delta^*(v|[l,u]) \\ + \textrm{subject to } & v + \sum_{i=1}^m u^i = \pi \\ + & \pi\in\mathbb R^n +\end{array}\end{split}\]
+
+

Conjugate of the indicator function of bound restrictions

+

We start by computing \(\delta^*(v|[l,u])\). By definition, this equals

+
+\[\begin{split}\delta^*(v|[l,u]) = +\begin{array}[t]{lll} + \max\ & v^\top x \\ + \textrm{s.t. } & x \le u & (\lambda^u \ge 0) \\ + & -x \le -l & (\lambda^l \ge 0) \\ + & x\in \mathbb R^n. +\end{array}\end{split}\]
+

By standard LP duality, one has

+
+\[\begin{split}\begin{array}{lll} + \min\ & u^\top\lambda^u - l^\top\lambda^l \\ + \textrm{s.t. } & \lambda^u - \lambda^l = v & (x\in\mathbb R^n)\\ + & \lambda^u \ge 0 \\ + & \lambda^l \ge 0. +\end{array}\end{split}\]
+

We end with some useful remarks:

+
    +

  • Assume \(l_j = -\infty\) for some j, then one should remove \(\lambda^l_j\) from this model;

    • +

  • Assume \(u_j = +\infty\) for some j, then one should remove \(\lambda^u_j\) from this model;

    • +
+
+
+

Conjugate of convex sets defined by quadratic expressions

+

We may now take interest in \(\delta^*(u^i|C^i)\). Now, observe that there must +exist a symmetric matrix \(\tilde Q^i\) such that

+
+\[\sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k - b_i += +a_{(i)}x + x^\top \tilde Q^ix - b_i\]
+

Since \(\tilde Q^i\) is a real symmetric matrix, it is diagonalizable by orthogonal matrices. Thus, there exists matrices \(P^i\) and \(D^i\) such that +\(\tilde Q^i = {P^i}^\top D^iP^i\) where \(D^i\) is diagonal.

+

There, idol considers two cases:

+
    +

  • If \(D^i\succeq 0\), then \(C^i\) is a convex set and the following holds

    +
    +
    +\[\begin{split}\begin{align} + \delta^*(u^i|C^i) &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & a_{(i)}x + x^\top P^iD^i{P^i}^\top x \le b_i \\ + & x\in\mathbb R^n + \end{array} \\ + &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & || {D^i}^{\frac 12}{P^i}^\top x ||_2^2 \le b_i - a_{(i)} x \\ + & x\in\mathbb R^n + \end{array} + \\ + &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & (\frac 12, b_i - a_{(i)} x, {D^i}^{\frac 12}{P^i}^\top x ) \in \mathcal Q_r^{n+2} \\ + & x\in\mathbb R^n + \end{array} +\end{align}\end{split}\]
    +
    +

    where \(\mathcal Q_r^n\) denotes the \(n\)-dimensional quadratic rotated cone. +By conic duality (see e.g., here), we obtain

    +
    +
    +\[\begin{split}\begin{array}{lll} + \min\ & \frac 12\pi_1 + b_i\pi_2 \\ + \textrm{s.t. } & -a_{(i)}^\top\pi_2 + P^i{D^i}^{\frac 12}\lambda = - u^i \\ + & \sum_{j=1}^n \lambda_i^2 \le \pi_1\pi_2 \\ + & \pi_1, \pi_2 \ge 0 +\end{array}\end{split}\]
    +
    +

    In the special case where \(D^i = 0\), \(\pi_1\) can be fixed to 0 and one recovers LP duality.

    +
    • +

  • Otherwise, Idol expects \(\tilde Q^i\) to have one negative eigen value, \(a = 0\) and \(b_i = 0\). +We have,

    +
    +\[\tilde Q^i = PD^iP^\top = d_{kk}p^{(k)}{p^{(k)}}^\top + \sum_{j\neq k} d_{jj}p^{(j)}{p^{(j)}}^\top\]
    +

    with \(d_{kk} < 0\) and \(d_{jj} \ge 0\) (with \(j\neq k\)). For simplicity, we will assume that \(k = 1\). +Then, constraint \(x^\top\tilde Q^ix \le 0\) can written as

    +
    +\[\sum_{j=2}^n d_{jj}( {p^{(j)}}^\top x )^2 \le d_{11}( {p^{(1)}}^\top x )^2\]
    +

    which can be expressed with a quadratic cone provided that \({p^{(1)}}^\top x \ge 0\) over \([l,u]\). We obtain

    +
    +\[(\sqrt{-d_{11}} {p^{(1)}}^\top x, \sqrt{d_{22}} {p^{(2)}}^\top x, \sqrt{d_{33}} {p^{(3)}}^\top x, ..., \sqrt{d_{nn}} {p^{(n)}}^\top x) \in \mathcal Q^{n}\]
    +

    where \(\mathcal Q^n\) denotes the \(n\)-dimensional quadratic cone. Finally, we obtain the following result.

    +
    +
    +\[\begin{split}\begin{align} + \delta^*(u^i|C^i) &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & x^\top P^iD^i{P^i}^\top x \le 0 \\ + & x\in\mathbb R^n + \end{array} \\ + &= + \begin{array}[t]{lll} + \max\ & {u^i}^\top x \\ + \textrm{s.t. } & (\sqrt{-d_{11}} {p^{(1)}}^\top x, \sqrt{d_{22}} {p^{(2)}}^\top x, \sqrt{d_{33}} {p^{(3)}}^\top x, ..., \sqrt{d_{nn}} {p^{(n)}}^\top x) \in \mathcal Q^{n} \\ + & {p^{(1)}}^\top x \ge 0 \\ + & x\in\mathbb R^n + \end{array} + \\ + &= + \begin{array}[t]{lll} + \min\ & 0 \\ + \textrm{s.t. } & \sqrt{-d_{11}}p^{(1)}(\lambda_1 + \pi) + \sum_{j=2}^n \sqrt{ d_{jj} }p^{(j)}\lambda_j = -u^{i} \\ + & \sum_{j=2}^n \lambda_j^2 \le \lambda_1 \\ + & \pi \ge 0 + \end{array} +\end{align}\end{split}\]
    +
    +
    • +
+
+
+

Conjugate of the objective function

+

The conjugate function of \(f\) is well known to equal to

+
+\[\begin{split}f^*(\pi) = +\begin{array}[t]{lll} + \min\ & \frac 14 (\pi - c)^\top \tilde D^{\dagger} (\pi - c) \\ + \textrm{s.t. } & \pi - b \in \textrm{span}(\tilde D) +\end{array}\end{split}\]
+

where \(\tilde D\) is the symmetric matrix associated to \(f\).

+
+
+

Final result

+

For now, we may assume that all \(C^i\) are convex sets.

+
+\[\begin{split}\begin{array}{lll} + \max\ & \frac 14 (\mu + c)^\top\tilde D^{-1}(\mu + c) + \sum_{i=1}^m(-\frac 12\pi_1^i - b_i\pi_2^i) - u^\top\lambda^u + l^\top\lambda^l \\ + \textrm{s.t. } & \lambda^u - \lambda^l + \sum_{i=1}^m ( a_{(i)}^\top\pi_2^i - P^i{D^i}^{\frac 12}\lambda^i ) = \mu \\ + & \sum_{j=1}^n \lambda_j^i \le \pi_1^i\pi_2^i & i=1,...,m \\ + & \lambda^u, \lambda^l \ge 0 \\ + & \pi_1^i, \pi_2^i \ge 0 & i=1,...,m +\end{array}\end{split}\]
+
+
+
+ + +
+
+ +
+
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Robust Optimization

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Single-stage robust optimization

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+\[\begin{split}\begin{align} + \min \ & c^\top x \\ + \textrm{s.t. } & A(\xi)x \ge b & \forall \xi\in\Xi \\ + & x\in X +\end{align}\end{split}\]
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Two-stage robust optimization

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+\[\begin{split}\begin{align} + \min \ & c^\top x + x_0 \\ + \textrm{s.t. } & \forall \xi\in\Xi, \exists y\in Y, + \begin{cases} + x_0 \ge d^\top y \\ + T(\xi)x + W(\xi) \ge h(\xi) + \end{cases} \\ + & (x_0,X) \in \mathbb R\times X +\end{align}\end{split}\]
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+\[\begin{align} + \min_{x\in X}\left\{ c^\top x + \max_{\xi\in\Xi}\min_{y\in Y(x,\xi)} d^\top y \right\} +\end{align}\]
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