optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from itertools import product\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator\n",
    "\n",
    "import gurobipy as grb\n",
    "from gurobipy import GRB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Input Problem Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import du problème"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import define_nums\n",
    "from utils.extract_parameters import extract_parameters\n",
    "from utils.define_nums import define_nums\n",
    "from utils.domination_3D import liste_dominants, graph_dominant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "################################\n",
    "######## TO DO #################\n",
    "################################\n",
    "\n",
    "# choose taille among: \"small\", \"medium\", \"large\"\n",
    "taille = \"small\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "################################\n",
    "######## DO NOT CHANGE #########\n",
    "################################\n",
    "map_employe_indice, map_job_indice, map_qualif_indice, conge, qualif, d, p, b, besoin = extract_parameters(taille)\n",
    "nombre_employes, horizon, nombre_qualifs, nombre_projets = define_nums(conge, qualif, d, p, b, besoin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Définissons les paramètres"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "## u_j, le projet j est réalisé\n",
    "u_shape = nombre_projets\n",
    "\n",
    "## x_i_j_k_n, l'employé k travaille sur le projet j avec la qualif i\n",
    "## au jour n\n",
    "x_shape = [(i,j,k, n) for i in range(nombre_qualifs) for j in range(nombre_projets) for k in range(nombre_employes) for n in range(horizon)]\n",
    "\n",
    "## t_k_j, l'employé k travaille sur le projet j\n",
    "t_shape = [(i,j) for i in range(nombre_employes) for j in range(nombre_projets)]\n",
    "\n",
    "## begin_j, la date de début effective\n",
    "begin_shape = nombre_projets\n",
    "\n",
    "## end_j, la date de fin effective = date de livraison du projet j\n",
    "end_shape = nombre_projets\n",
    "\n",
    "## delay_j, le nombre de jours de retard par projet j\n",
    "delay_shape = nombre_projets\n",
    "\n",
    "## longueur_j, la longueur du projet j\n",
    "longueur_shape = nombre_projets\n",
    "\n",
    "## projet_par_employe_k, le nombre de projet par employe\n",
    "projet_par_employe_shape = nombre_employes\n",
    "\n",
    "# majorant pour la contrainte de couverture\n",
    "maj = max([besoin[i][j] for j in range(nombre_projets) for i in range(nombre_qualifs)]) + 1\n",
    "\n",
    "# si le projet j est travaillé au jour n\n",
    "job_in_process_shape = [(j, n) for j in range(nombre_projets) for n in range(horizon)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model deployment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add the variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2023-12-29\n"
     ]
    }
   ],
   "source": [
    "model = grb.Model(\"Planning\")\n",
    "\n",
    "# L'affectation du planning, la variable clé\n",
    "x = model.addVars(x_shape, vtype=GRB.BINARY, name=\"x\")\n",
    "\n",
    "## Les dates de fin des projets\n",
    "dateFin = model.addVars(end_shape, lb = 0, ub = horizon, name = \"dateFin\")\n",
    "\n",
    "## Les dates de début des projets\n",
    "dateDebut = model.addVars(begin_shape, lb = 0, ub = horizon, name = \"dateDebut\")\n",
    "\n",
    "## Le nombre de jours de delai\n",
    "delay = model.addVars(delay_shape, lb = 0, ub = horizon, name = \"delay\")\n",
    "\n",
    "## Les longueurs des projets\n",
    "longueur = model.addVars(longueur_shape, lb = 0, ub = horizon, name = \"longueur\")\n",
    "\n",
    "## Nombre de projet par employé\n",
    "projet_par_employe = model.addVars(projet_par_employe_shape, lb = 0, ub = nombre_projets, name = \"projet_par_employe\")\n",
    "\n",
    "## L'affectation sur un projet d'un employé\n",
    "affectation = model.addVars(t_shape, vtype = GRB.BINARY, name = \"affectation\")\n",
    "\n",
    "## La réalisation ou non d'un projet\n",
    "u = model.addVars(u_shape, vtype = GRB.BINARY, name=\"u\")\n",
    "\n",
    "## Verification du projet\n",
    "job_in_process = model.addVars(job_in_process_shape, vtype = GRB.BINARY, name = \"job_in_process\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update le modele pour confirmer la création des variables\n",
    "model.update()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(nombre_qualifs):\n",
    "    for j in range(nombre_projets):\n",
    "        for k in range(nombre_employes):\n",
    "            for n in range(horizon):\n",
    "                ## La qualification du personnel\n",
    "                model.addConstr( x[i,j,k,n] <= qualif[i][k], name=\"QualificationPersonnel[{0}{1}{2}{3}]\".format(i,j,k,n))\n",
    "                model.addConstr( x[i,j,k,n] <= (besoin[i][j] >=1), name = \"BesoinQualifPersonnel[{0}{1}{2}{3}]\".format(i,j,k,n))\n",
    "                ## Contraintes des congés\n",
    "                model.addConstr( x[i,j,k,n] <= conge[k][n], name=f\"CongesPersonnel[{i}{j}{k}{n}]\")\n",
    "        \n",
    "        ## Contrainte d'unicité de réalisation d'un projet\n",
    "        model.addConstr(grb.quicksum(grb.quicksum(x[i,j,k,n] for n in range(horizon)) for k in range(nombre_employes)) == besoin[i][j]*u[j], name=f\"UniciteRealisation[{i}{j}]\")\n",
    "\n",
    "\n",
    "## Unicité de l'affectation quotidienne\n",
    "for k in range(nombre_employes):\n",
    "    for n in range(horizon):\n",
    "        model.addConstr(grb.quicksum(grb.quicksum(x[i,j,k,n] for j in range(nombre_projets)) for i in range(nombre_qualifs)) <= 1, name=f\"UniciteAffectation[{k}{n}]\")\n",
    "\n",
    "        \n",
    "for j in range(nombre_projets):\n",
    "    for n in range(horizon):\n",
    "        model.addConstrs(((job_in_process[j,n] >= x[i,j,k,n]) for i in range(nombre_qualifs) for k in range(nombre_employes)), name=f\"ContrainteJobInProcess[{j}{n}]\")\n",
    "    # start date\n",
    "    model.addConstrs(((dateDebut[j] <= job_in_process[j,n]*n) for n in range(horizon)), name = f\"ContrainteDateDebut[{j}]\")\n",
    "\n",
    "    # end date\n",
    "    model.addConstrs(((job_in_process[j,n]*n <= dateFin[j]) for n in range(horizon)), name=f\"FinProjet[{j}]\")\n",
    "\n",
    "    ## longueur\n",
    "    model.addConstr(longueur[j] == dateFin[j] - dateDebut[j], name=f\"LongueurProjet[{j}]\")\n",
    "\n",
    "    ## delay\n",
    "    model.addConstr(delay[j] >= dateFin[j] - (d[j] - 1), name=f\"DelaiProjet_difference[{j}]\")    \n",
    "\n",
    "## projet_par_employe\n",
    "for k in range(nombre_employes):\n",
    "    model.addConstr(projet_par_employe[k] == grb.quicksum( affectation[k,j] for j in range(nombre_projets)), name=f\"FinProjet[{j}]\")\n",
    "    \n",
    "    \n",
    "## Contrainte de l'affectation à un projet selon les jours de travail\n",
    "for k in range(nombre_employes):\n",
    "    for j in range(nombre_projets):\n",
    "        model.addConstr(affectation[k,j] <= grb.quicksum(grb.quicksum(x[i,j,k,n] for i in range(nombre_qualifs)) for n in range(horizon)), name=f\"AffectationProjetQuicksum[{k}{j}]\")    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fonctions objectif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## bénéfice total\n",
    "benefice_tot = grb.quicksum( (b[j]*u[j] - delay[j]*p[j]) for j in range(nombre_projets) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: <gurobi.Constr *Awaiting Model Update*>,\n",
       " 1: <gurobi.Constr *Awaiting Model Update*>,\n",
       " 2: <gurobi.Constr *Awaiting Model Update*>,\n",
       " 3: <gurobi.Constr *Awaiting Model Update*>,\n",
       " 4: <gurobi.Constr *Awaiting Model Update*>}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lignes pour optimiser le problème suivant\n",
    "## les trois fonctions objectif voulues\n",
    "\n",
    "# Nombre de projet maximum par personne\n",
    "projet_max = model.addVar(lb= 0, ub=nombre_projets, name=\"projet_max\")\n",
    "model.addConstrs(projet_max>=projet_par_employe[k] for k in range(nombre_employes))\n",
    "\n",
    "# Compacité des projets\n",
    "longueur_max = model.addVar(lb = 0, ub=horizon, name=\"longueur_max\")\n",
    "model.addConstrs(longueur_max>=longueur[j] for j in range(nombre_projets))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1018 rows, 295 columns and 1976 nonzeros\n",
      "Model fingerprint: 0x6790b0ab\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 966 rows and 190 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 52 rows, 105 columns, 270 nonzeros\n",
      "Variable types: 0 continuous, 105 integer (102 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 7.200000e+01, 79 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   72.00000    0   16   20.00000   72.00000   260%     -    0s\n",
      "H    0     0                      62.0000000   72.00000  16.1%     -    0s\n",
      "     0     0   67.00000    0   16   62.00000   67.00000  8.06%     -    0s\n",
      "H    0     0                      64.0000000   66.72222  4.25%     -    0s\n",
      "H    0     0                      65.0000000   66.72222  2.65%     -    0s\n",
      "     0     0   66.72222    0   36   65.00000   66.72222  2.65%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 3\n",
      "  Cover: 1\n",
      "  Implied bound: 1\n",
      "  Clique: 2\n",
      "  RLT: 2\n",
      "  Relax-and-lift: 1\n",
      "\n",
      "Explored 1 nodes (170 simplex iterations) in 0.03 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 5: 65 64 62 ... -0\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 6.500000000000e+01, best bound 6.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1020 rows, 295 columns and 1978 nonzeros\n",
      "Model fingerprint: 0x7738f755\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 968 rows and 190 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 52 rows, 105 columns, 270 nonzeros\n",
      "Variable types: 0 continuous, 105 integer (102 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 7.200000e+01, 79 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   72.00000    0   16   20.00000   72.00000   260%     -    0s\n",
      "H    0     0                      62.0000000   72.00000  16.1%     -    0s\n",
      "     0     0   67.00000    0   16   62.00000   67.00000  8.06%     -    0s\n",
      "H    0     0                      64.0000000   66.72222  4.25%     -    0s\n",
      "H    0     0                      65.0000000   66.72222  2.65%     -    0s\n",
      "     0     0   66.72222    0   36   65.00000   66.72222  2.65%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 3\n",
      "  Cover: 1\n",
      "  Implied bound: 1\n",
      "  Clique: 2\n",
      "  RLT: 2\n",
      "  Relax-and-lift: 1\n",
      "\n",
      "Explored 1 nodes (170 simplex iterations) in 0.04 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 5: 65 64 62 ... -0\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 6.500000000000e+01, best bound 6.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1022 rows, 295 columns and 1980 nonzeros\n",
      "Model fingerprint: 0x4f874483\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 970 rows and 190 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 52 rows, 105 columns, 270 nonzeros\n",
      "Variable types: 0 continuous, 105 integer (102 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 7.200000e+01, 79 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   72.00000    0   16   20.00000   72.00000   260%     -    0s\n",
      "H    0     0                      62.0000000   72.00000  16.1%     -    0s\n",
      "     0     0   67.00000    0   16   62.00000   67.00000  8.06%     -    0s\n",
      "H    0     0                      64.0000000   66.72222  4.25%     -    0s\n",
      "H    0     0                      65.0000000   66.72222  2.65%     -    0s\n",
      "     0     0   66.72222    0   36   65.00000   66.72222  2.65%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 3\n",
      "  Cover: 1\n",
      "  Implied bound: 1\n",
      "  Clique: 2\n",
      "  RLT: 2\n",
      "  Relax-and-lift: 1\n",
      "\n",
      "Explored 1 nodes (170 simplex iterations) in 0.03 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 5: 65 64 62 ... -0\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 6.500000000000e+01, best bound 6.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1024 rows, 295 columns and 1982 nonzeros\n",
      "Model fingerprint: 0xf5610caf\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 972 rows and 190 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 52 rows, 105 columns, 270 nonzeros\n",
      "Variable types: 0 continuous, 105 integer (102 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 7.200000e+01, 79 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   72.00000    0   16   20.00000   72.00000   260%     -    0s\n",
      "H    0     0                      62.0000000   72.00000  16.1%     -    0s\n",
      "     0     0   67.00000    0   16   62.00000   67.00000  8.06%     -    0s\n",
      "H    0     0                      64.0000000   66.72222  4.25%     -    0s\n",
      "H    0     0                      65.0000000   66.72222  2.65%     -    0s\n",
      "     0     0   66.72222    0   36   65.00000   66.72222  2.65%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 3\n",
      "  Cover: 1\n",
      "  Implied bound: 1\n",
      "  Clique: 2\n",
      "  RLT: 2\n",
      "  Relax-and-lift: 1\n",
      "\n",
      "Explored 1 nodes (170 simplex iterations) in 0.03 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 5: 65 64 62 ... -0\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 6.500000000000e+01, best bound 6.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1026 rows, 295 columns and 1984 nonzeros\n",
      "Model fingerprint: 0x41e685bf\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 996 rows and 217 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 30 rows, 78 columns, 180 nonzeros\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable types: 0 continuous, 78 integer (78 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 6.000000e+01, 49 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   60.00000    0    1   20.00000   60.00000   200%     -    0s\n",
      "H    0     0                      55.0000000   60.00000  9.09%     -    0s\n",
      "     0     0   60.00000    0    7   55.00000   60.00000  9.09%     -    0s\n",
      "     0     0   55.00000    0    3   55.00000   55.00000  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 2\n",
      "  Cover: 1\n",
      "  Zero half: 1\n",
      "\n",
      "Explored 1 nodes (62 simplex iterations) in 0.03 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 55 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 5.500000000000e+01, best bound 5.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1028 rows, 295 columns and 1986 nonzeros\n",
      "Model fingerprint: 0x3eee421d\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 998 rows and 217 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 30 rows, 78 columns, 180 nonzeros\n",
      "Variable types: 0 continuous, 78 integer (78 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 6.000000e+01, 49 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   60.00000    0    1   20.00000   60.00000   200%     -    0s\n",
      "H    0     0                      55.0000000   60.00000  9.09%     -    0s\n",
      "     0     0   60.00000    0    7   55.00000   60.00000  9.09%     -    0s\n",
      "     0     0   55.00000    0    3   55.00000   55.00000  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 2\n",
      "  Cover: 1\n",
      "  Zero half: 1\n",
      "\n",
      "Explored 1 nodes (62 simplex iterations) in 0.02 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 55 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 5.500000000000e+01, best bound 5.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1030 rows, 295 columns and 1988 nonzeros\n",
      "Model fingerprint: 0xcca1edd9\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1000 rows and 217 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 30 rows, 78 columns, 180 nonzeros\n",
      "Variable types: 0 continuous, 78 integer (78 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 6.000000e+01, 49 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   60.00000    0    1   20.00000   60.00000   200%     -    0s\n",
      "H    0     0                      55.0000000   60.00000  9.09%     -    0s\n",
      "     0     0   60.00000    0    7   55.00000   60.00000  9.09%     -    0s\n",
      "     0     0   55.00000    0    3   55.00000   55.00000  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 2\n",
      "  Cover: 1\n",
      "  Zero half: 1\n",
      "\n",
      "Explored 1 nodes (62 simplex iterations) in 0.03 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 55 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 5.500000000000e+01, best bound 5.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1032 rows, 295 columns and 1990 nonzeros\n",
      "Model fingerprint: 0xe7a12312\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1002 rows and 217 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 30 rows, 78 columns, 180 nonzeros\n",
      "Variable types: 0 continuous, 78 integer (78 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 6.000000e+01, 49 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   60.00000    0    1   20.00000   60.00000   200%     -    0s\n",
      "H    0     0                      55.0000000   60.00000  9.09%     -    0s\n",
      "     0     0   60.00000    0    7   55.00000   60.00000  9.09%     -    0s\n",
      "     0     0   55.00000    0    3   55.00000   55.00000  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 2\n",
      "  Cover: 1\n",
      "  Zero half: 1\n",
      "\n",
      "Explored 1 nodes (62 simplex iterations) in 0.04 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 55 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 5.500000000000e+01, best bound 5.500000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1034 rows, 295 columns and 1992 nonzeros\n",
      "Model fingerprint: 0x492e5f53\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1017 rows and 240 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 17 rows, 55 columns, 110 nonzeros\n",
      "Variable types: 0 continuous, 55 integer (55 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 4.500000e+01, 26 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   45.00000    0    5   20.00000   45.00000   125%     -    0s\n",
      "H    0     0                      40.0000000   45.00000  12.5%     -    0s\n",
      "     0     0   45.00000    0    5   40.00000   45.00000  12.5%     -    0s\n",
      "\n",
      "Explored 1 nodes (30 simplex iterations) in 0.01 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 40 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 4.000000000000e+01, best bound 4.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1036 rows, 295 columns and 1994 nonzeros\n",
      "Model fingerprint: 0x33f223a3\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Presolve removed 1019 rows and 240 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 17 rows, 55 columns, 110 nonzeros\n",
      "Variable types: 0 continuous, 55 integer (55 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 4.500000e+01, 26 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   45.00000    0    5   20.00000   45.00000   125%     -    0s\n",
      "H    0     0                      40.0000000   45.00000  12.5%     -    0s\n",
      "     0     0   45.00000    0    5   40.00000   45.00000  12.5%     -    0s\n",
      "\n",
      "Explored 1 nodes (30 simplex iterations) in 0.02 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 40 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 4.000000000000e+01, best bound 4.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1038 rows, 295 columns and 1996 nonzeros\n",
      "Model fingerprint: 0xbe14d70e\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1021 rows and 240 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 17 rows, 55 columns, 110 nonzeros\n",
      "Variable types: 0 continuous, 55 integer (55 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 4.500000e+01, 26 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   45.00000    0    5   20.00000   45.00000   125%     -    0s\n",
      "H    0     0                      40.0000000   45.00000  12.5%     -    0s\n",
      "     0     0   45.00000    0    5   40.00000   45.00000  12.5%     -    0s\n",
      "\n",
      "Explored 1 nodes (30 simplex iterations) in 0.02 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 40 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 4.000000000000e+01, best bound 4.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1040 rows, 295 columns and 1998 nonzeros\n",
      "Model fingerprint: 0x9639e16a\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1023 rows and 240 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 17 rows, 55 columns, 110 nonzeros\n",
      "Variable types: 0 continuous, 55 integer (55 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 4.500000e+01, 26 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   45.00000    0    5   20.00000   45.00000   125%     -    0s\n",
      "H    0     0                      40.0000000   45.00000  12.5%     -    0s\n",
      "     0     0   45.00000    0    5   40.00000   45.00000  12.5%     -    0s\n",
      "\n",
      "Explored 1 nodes (30 simplex iterations) in 0.01 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 40 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 4.000000000000e+01, best bound 4.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1042 rows, 295 columns and 2000 nonzeros\n",
      "Model fingerprint: 0xba035ef4\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1028 rows and 260 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 14 rows, 35 columns, 70 nonzeros\n",
      "Variable types: 0 continuous, 35 integer (35 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 2.666667e+01, 20 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   26.66667    0    5   20.00000   26.66667  33.3%     -    0s\n",
      "     0     0 infeasible    0        20.00000   20.00000  0.00%     -    0s\n",
      "\n",
      "Explored 1 nodes (24 simplex iterations) in 0.01 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.000000000000e+01, best bound 2.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1044 rows, 295 columns and 2002 nonzeros\n",
      "Model fingerprint: 0x7ea0a50d\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1030 rows and 260 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 14 rows, 35 columns, 70 nonzeros\n",
      "Variable types: 0 continuous, 35 integer (35 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 2.666667e+01, 20 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   26.66667    0    5   20.00000   26.66667  33.3%     -    0s\n",
      "     0     0 infeasible    0        20.00000   20.00000  0.00%     -    0s\n",
      "\n",
      "Explored 1 nodes (24 simplex iterations) in 0.01 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.000000000000e+01, best bound 2.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1046 rows, 295 columns and 2004 nonzeros\n",
      "Model fingerprint: 0x68f7271c\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1032 rows and 260 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 14 rows, 35 columns, 70 nonzeros\n",
      "Variable types: 0 continuous, 35 integer (35 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 2.666667e+01, 20 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   26.66667    0    5   20.00000   26.66667  33.3%     -    0s\n",
      "     0     0 infeasible    0        20.00000   20.00000  0.00%     -    0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Explored 1 nodes (24 simplex iterations) in 0.01 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.000000000000e+01, best bound 2.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n",
      "Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (mac64[x86])\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i5-8257U CPU @ 1.40GHz\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 1048 rows, 295 columns and 2006 nonzeros\n",
      "Model fingerprint: 0xe37cd777\n",
      "Variable types: 25 continuous, 270 integer (270 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 4e+00]\n",
      "  Objective range  [3e+00, 2e+01]\n",
      "  Bounds range     [1e+00, 5e+00]\n",
      "  RHS range        [1e+00, 4e+00]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 1034 rows and 260 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 14 rows, 35 columns, 70 nonzeros\n",
      "Variable types: 0 continuous, 35 integer (35 binary)\n",
      "Found heuristic solution: objective 20.0000000\n",
      "\n",
      "Root relaxation: objective 2.666667e+01, 20 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0   26.66667    0    5   20.00000   26.66667  33.3%     -    0s\n",
      "     0     0 infeasible    0        20.00000   20.00000  0.00%     -    0s\n",
      "\n",
      "Explored 1 nodes (24 simplex iterations) in 0.01 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 20 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.000000000000e+01, best bound 2.000000000000e+01, gap 0.0000%\n",
      "Discarded solution information including additional information\n"
     ]
    }
   ],
   "source": [
    "res = pd.DataFrame(columns = [\"Benefice\", \"longueur max\", \"projets max\"])\n",
    "\n",
    "for l in range(horizon-1, 0 , -1):\n",
    "    for p in range(nombre_projets-1, 0, -1):\n",
    "        # contrainte sur la longueur des projets\n",
    "        model.addConstr(longueur_max<=l)\n",
    "        # contrainte sur le nombre de projets\n",
    "        model.addConstr(projet_max<=p)\n",
    "\n",
    "        model.ModelSense = GRB.MAXIMIZE\n",
    "        model.setObjective(benefice_tot)\n",
    "        model.optimize()\n",
    "\n",
    "        res.loc[len(res)] = [model.objVal, int(longueur_max.x), int(projet_max.x)]\n",
    "        \n",
    "        model.reset(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model optimisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "res.to_excel(\"results/final/\"+taille+\"/res.xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Unknown projection '3d'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/projections/__init__.py\u001b[0m in \u001b[0;36mget_projection_class\u001b[0;34m(projection)\u001b[0m\n\u001b[1;32m     57\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mprojection_registry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_projection_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     59\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/projections/__init__.py\u001b[0m in \u001b[0;36mget_projection_class\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m     24\u001b[0m         \"\"\"\n\u001b[0;32m---> 25\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_all_projection_types\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: '3d'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-14-0902b07287c2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmpl_toolkits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maxes_grid1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmake_axes_locatable\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubplot_kw\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m\"projection\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m\"3d\"\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmeshgrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"projets max\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"longueur max\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36msubplots\u001b[0;34m(nrows, ncols, sharex, sharey, squeeze, subplot_kw, gridspec_kw, **fig_kw)\u001b[0m\n\u001b[1;32m   1210\u001b[0m     axs = fig.subplots(nrows=nrows, ncols=ncols, sharex=sharex, sharey=sharey,\n\u001b[1;32m   1211\u001b[0m                        \u001b[0msqueeze\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msqueeze\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubplot_kw\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msubplot_kw\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1212\u001b[0;31m                        gridspec_kw=gridspec_kw)\n\u001b[0m\u001b[1;32m   1213\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1214\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/figure.py\u001b[0m in \u001b[0;36msubplots\u001b[0;34m(self, nrows, ncols, sharex, sharey, squeeze, subplot_kw, gridspec_kw)\u001b[0m\n\u001b[1;32m   1573\u001b[0m                 \u001b[0msubplot_kw\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"sharex\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mshared_with\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msharex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1574\u001b[0m                 \u001b[0msubplot_kw\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"sharey\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mshared_with\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msharey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1575\u001b[0;31m                 \u001b[0maxarr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcol\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_subplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcol\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0msubplot_kw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1576\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1577\u001b[0m         \u001b[0;31m# turn off redundant tick labeling\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/figure.py\u001b[0m in \u001b[0;36madd_subplot\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1394\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1395\u001b[0m             \u001b[0mprojection_class\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1396\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_process_projection_requirements\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1397\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1398\u001b[0m             \u001b[0;31m# try to find the axes with this key in the stack\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/figure.py\u001b[0m in \u001b[0;36m_process_projection_requirements\u001b[0;34m(self, polar, projection, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1118\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1119\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mprojection\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1120\u001b[0;31m             \u001b[0mprojection_class\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprojections\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_projection_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1121\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'_as_mpl_axes'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1122\u001b[0m             \u001b[0mprojection_class\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_kwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprojection\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_as_mpl_axes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/matplotlib/projections/__init__.py\u001b[0m in \u001b[0;36mget_projection_class\u001b[0;34m(projection)\u001b[0m\n\u001b[1;32m     58\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mprojection_registry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_projection_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     59\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 60\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Unknown projection %r\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mprojection\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     61\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Unknown projection '3d'"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"})\n",
    "\n",
    "X, Y = np.meshgrid(res[\"projets max\"], res[\"longueur max\"])\n",
    "Z = res[\"Benefice\"]\n",
    "\n",
    "X = np.array(res[\"projets max\"])\n",
    "Y = np.array(res[\"longueur max\"])\n",
    "Z = np.array(res[\"Benefice\"])\n",
    "\n",
    "# Plot the surface.\n",
    "surf = ax.plot_trisurf(X, Y, Z, cmap = 'Spectral')\n",
    "\n",
    "# Add a color bar which maps values to colors.\n",
    "fig.colorbar(surf, pad=0.2)\n",
    "\n",
    "ax.set_xlabel('projets max')\n",
    "ax.set_ylabel('longueur max')\n",
    "ax.set_zlabel('bénéfice')\n",
    "\n",
    "fig.set_size_inches(7, 5)\n",
    "\n",
    "plt.savefig(\"results/sys_preference/\"+taille+\".png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(res[\"longueur max\"])\n",
    "Y = np.array(res[\"projets max\"])\n",
    "Z = np.array(res[\"Benefice\"])\n",
    "\n",
    "#longueur/projet\n",
    "plt.scatter(X,Y,label=\"longueur/projet\", marker='+')\n",
    "plt.title(\"Projets max en fonction de longueur\")\n",
    "plt.savefig(\"results/graphs_biobjectifs/Domination longueur_max projet_max\"+taille)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sur le plot précédent, on remarque que la seule solution non dominée lorsqu'on regarde les critères longueur_max et projet_max correspond à (1,1).\n",
    "Introduire un système de préférence sur ces deux critères n'est pas nécessaire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#longueur/projet\n",
    "plt.scatter(Y, Z,label=\"Bénéfice en fonction de projets max\", marker='+', c=X)\n",
    "plt.title(\"Bénéfice en fonction de projets max\")\n",
    "plt.colorbar()\n",
    "plt.savefig(\"results/graphs_biobjectifs/Domination Benefice projet_max\"+taille)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sur le plot précédent, on remarque que la seule solution non dominée lorsqu'on regarde les critères bénéfice et projet_max.\n",
    "Introduire un système de préférence sur ces deux critères n'est pas nécessaire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#longueur/benefice\n",
    "plt.scatter(X,Z,label=\"Bénéfice en fonction de longueur max\", marker = '+', c=Y)\n",
    "plt.colorbar()\n",
    "plt.title(\"Bénéfice en fonction de longueur max\")\n",
    "plt.savefig(\"results/graphs_biobjectifs/Domination longueur_max bénéfice\"+taille)\n",
    "plt.show()"
   ]
  }
 ],
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