home	boolean logic	integer arithmetic	channeling constraints	scheduling	Using the CP-SAT solver	Model manipulation	Troubleshooting	Python API

Solving a CP-SAT model

https://developers.google.com/optimization/

Changing the parameters of the solver

The SatParameters protobuf encapsulates the set of parameters of a CP-SAT solver. The most useful one is the time limit.

Specifying the time limit in Python

#!/usr/bin/env python3
"""Solves a problem with a time limit."""

from ortools.sat.python import cp_model


def solve_with_time_limit_sample_sat():
    """Minimal CP-SAT example to showcase calling the solver."""
    # Creates the model.
    model = cp_model.CpModel()
    # Creates the variables.
    num_vals = 3
    x = model.new_int_var(0, num_vals - 1, "x")
    y = model.new_int_var(0, num_vals - 1, "y")
    z = model.new_int_var(0, num_vals - 1, "z")
    # Adds an all-different constraint.
    model.add(x != y)

    # Creates a solver and solves the model.
    solver = cp_model.CpSolver()

    # Sets a time limit of 10 seconds.
    solver.parameters.max_time_in_seconds = 10.0

    status = solver.solve(model)

    if status == cp_model.OPTIMAL:
        print(f"x = {solver.value(x)}")
        print(f"y = {solver.value(y)}")
        print(f"z = {solver.value(z)}")


solve_with_time_limit_sample_sat()

Specifying the time limit in C++

#include <stdlib.h>

#include "ortools/base/logging.h"
#include "ortools/sat/cp_model.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/sorted_interval_list.h"

namespace operations_research {
namespace sat {

void SolveWithTimeLimitSampleSat() {
  CpModelBuilder cp_model;

  const Domain domain(0, 2);
  const IntVar x = cp_model.NewIntVar(domain).WithName("x");
  const IntVar y = cp_model.NewIntVar(domain).WithName("y");
  const IntVar z = cp_model.NewIntVar(domain).WithName("z");

  cp_model.AddNotEqual(x, y);

  // Solving part.
  Model model;

  // Sets a time limit of 10 seconds.
  SatParameters parameters;
  parameters.set_max_time_in_seconds(10.0);
  model.Add(NewSatParameters(parameters));

  // Solve.
  const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);
  LOG(INFO) << CpSolverResponseStats(response);

  if (response.status() == CpSolverStatus::OPTIMAL) {
    LOG(INFO) << "  x = " << SolutionIntegerValue(response, x);
    LOG(INFO) << "  y = " << SolutionIntegerValue(response, y);
    LOG(INFO) << "  z = " << SolutionIntegerValue(response, z);
  }
}

}  // namespace sat
}  // namespace operations_research

int main() {
  operations_research::sat::SolveWithTimeLimitSampleSat();

  return EXIT_SUCCESS;
}

Specifying the time limit in Java

package com.google.ortools.sat.samples;

import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverStatus;
import com.google.ortools.sat.IntVar;

/** Solves a problem with a time limit. */
public final class SolveWithTimeLimitSampleSat {
  public static void main(String[] args) {
    Loader.loadNativeLibraries();
    // Create the model.
    CpModel model = new CpModel();
    // Create the variables.
    int numVals = 3;

    IntVar x = model.newIntVar(0, numVals - 1, "x");
    IntVar y = model.newIntVar(0, numVals - 1, "y");
    IntVar z = model.newIntVar(0, numVals - 1, "z");
    // Create the constraint.
    model.addDifferent(x, y);

    // Create a solver and solve the model.
    CpSolver solver = new CpSolver();
    solver.getParameters().setMaxTimeInSeconds(10.0);
    CpSolverStatus status = solver.solve(model);

    if (status == CpSolverStatus.OPTIMAL) {
      System.out.println("x = " + solver.value(x));
      System.out.println("y = " + solver.value(y));
      System.out.println("z = " + solver.value(z));
    }
  }

  private SolveWithTimeLimitSampleSat() {}
}

Specifying the time limit in C#.

Parameters must be passed as string to the solver.

using System;
using Google.OrTools.Sat;

public class SolveWithTimeLimitSampleSat
{
    static void Main()
    {
        // Creates the model.
        CpModel model = new CpModel();
        // Creates the variables.
        int num_vals = 3;

        IntVar x = model.NewIntVar(0, num_vals - 1, "x");
        IntVar y = model.NewIntVar(0, num_vals - 1, "y");
        IntVar z = model.NewIntVar(0, num_vals - 1, "z");
        // Adds a different constraint.
        model.Add(x != y);

        // Creates a solver and solves the model.
        CpSolver solver = new CpSolver();

        // Adds a time limit. Parameters are stored as strings in the solver.
        solver.StringParameters = "max_time_in_seconds:10.0";

        CpSolverStatus status = solver.Solve(model);

        if (status == CpSolverStatus.Optimal)
        {
            Console.WriteLine("x = " + solver.Value(x));
            Console.WriteLine("y = " + solver.Value(y));
            Console.WriteLine("z = " + solver.Value(z));
        }
    }
}

Specifying the time limit in Go

// The solve_with_time_limit_sample_sat command is an example of setting a time limit on the model.
package main

import (
	"fmt"

	log "github.com/golang/glog"
	"github.com/google/or-tools/ortools/sat/go/cpmodel"
	cmpb "github.com/google/or-tools/ortools/sat/proto/cpmodel"
	sppb "github.com/google/or-tools/ortools/sat/proto/satparameters"
	"google.golang.org/protobuf/proto"
)

func solveWithTimeLimitSampleSat() error {
	model := cpmodel.NewCpModelBuilder()

	domain := cpmodel.NewDomain(0, 2)
	x := model.NewIntVarFromDomain(domain).WithName("x")
	y := model.NewIntVarFromDomain(domain).WithName("y")
	z := model.NewIntVarFromDomain(domain).WithName("z")

	model.AddNotEqual(x, y)

	m, err := model.Model()
	if err != nil {
		return fmt.Errorf("failed to instantiate the CP model: %w", err)
	}

	// Sets a time limit of 10 seconds.
	params := &sppb.SatParameters{
		MaxTimeInSeconds: proto.Float64(10.0),
	}

	// Solve.
	response, err := cpmodel.SolveCpModelWithParameters(m, params)
	if err != nil {
		return fmt.Errorf("failed to solve the model: %w", err)
	}

	fmt.Printf("Status: %v\n", response.GetStatus())

	if response.GetStatus() == cmpb.CpSolverStatus_OPTIMAL {
		fmt.Printf(" x = %v\n", cpmodel.SolutionIntegerValue(response, x))
		fmt.Printf(" y = %v\n", cpmodel.SolutionIntegerValue(response, y))
		fmt.Printf(" z = %v\n", cpmodel.SolutionIntegerValue(response, z))
	}

	return nil
}

func main() {
	if err := solveWithTimeLimitSampleSat(); err != nil {
		log.Exitf("solveWithTimeLimitSampleSat returned with error: %v", err)
	}
}

Printing intermediate solutions

In an optimization model, you can print intermediate solutions. For all languages except Go, you need to register a callback on the solver that will be called at each solution. For Go, callbacks are not implemented, but you can still get the intermediate solutions in the response.

The exact implementation depends on the target language.

Python code

#!/usr/bin/env python3
"""Solves an optimization problem and displays all intermediate solutions."""

from ortools.sat.python import cp_model


# You need to subclass the cp_model.CpSolverSolutionCallback class.
class VarArrayAndObjectiveSolutionPrinter(cp_model.CpSolverSolutionCallback):
    """Print intermediate solutions."""

    def __init__(self, variables: list[cp_model.IntVar]):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__solution_count = 0

    def on_solution_callback(self) -> None:
        print(f"Solution {self.__solution_count}")
        print(f"  objective value = {self.objective_value}")
        for v in self.__variables:
            print(f"  {v}={self.value(v)}", end=" ")
        print()
        self.__solution_count += 1

    @property
    def solution_count(self) -> int:
        return self.__solution_count


def solve_and_print_intermediate_solutions_sample_sat():
    """Showcases printing intermediate solutions found during search."""
    # Creates the model.
    model = cp_model.CpModel()

    # Creates the variables.
    num_vals = 3
    x = model.new_int_var(0, num_vals - 1, "x")
    y = model.new_int_var(0, num_vals - 1, "y")
    z = model.new_int_var(0, num_vals - 1, "z")

    # Creates the constraints.
    model.add(x != y)

    model.maximize(x + 2 * y + 3 * z)

    # Creates a solver and solves.
    solver = cp_model.CpSolver()
    solution_printer = VarArrayAndObjectiveSolutionPrinter([x, y, z])
    status = solver.solve(model, solution_printer)

    print(f"Status = {solver.status_name(status)}")
    print(f"Number of solutions found: {solution_printer.solution_count}")


solve_and_print_intermediate_solutions_sample_sat()

C++ code

#include <stdlib.h>

#include "ortools/base/logging.h"
#include "ortools/sat/cp_model.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/util/sorted_interval_list.h"

namespace operations_research {
namespace sat {

void SolveAndPrintIntermediateSolutionsSampleSat() {
  CpModelBuilder cp_model;

  const Domain domain(0, 2);
  const IntVar x = cp_model.NewIntVar(domain).WithName("x");
  const IntVar y = cp_model.NewIntVar(domain).WithName("y");
  const IntVar z = cp_model.NewIntVar(domain).WithName("z");

  cp_model.AddNotEqual(x, y);

  cp_model.Maximize(x + 2 * y + 3 * z);

  Model model;
  int num_solutions = 0;
  model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& r) {
    LOG(INFO) << "Solution " << num_solutions;
    LOG(INFO) << "  objective value = " << r.objective_value();
    LOG(INFO) << "  x = " << SolutionIntegerValue(r, x);
    LOG(INFO) << "  y = " << SolutionIntegerValue(r, y);
    LOG(INFO) << "  z = " << SolutionIntegerValue(r, z);
    num_solutions++;
  }));

  const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);

  LOG(INFO) << "Number of solutions found: " << num_solutions;
}

}  // namespace sat
}  // namespace operations_research

int main() {
  operations_research::sat::SolveAndPrintIntermediateSolutionsSampleSat();

  return EXIT_SUCCESS;
}

Java code

package com.google.ortools.sat.samples;

import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverSolutionCallback;
import com.google.ortools.sat.CpSolverStatus;
import com.google.ortools.sat.IntVar;
import com.google.ortools.sat.LinearExpr;
import java.util.function.Consumer;

/** Solves an optimization problem and displays all intermediate solutions. */
public final class SolveAndPrintIntermediateSolutionsSampleSat {
  static class VarArraySolutionPrinterWithObjective extends CpSolverSolutionCallback {
    public VarArraySolutionPrinterWithObjective(IntVar[] variables) {
      variableArray = variables;
    }

    @Override
    public void onSolutionCallback() {
      System.out.printf("Solution #%d: time = %.02f s%n", solutionCount, wallTime());
      System.out.printf("  objective value = %f%n", objectiveValue());
      for (IntVar v : variableArray) {
        System.out.printf("  %s = %d%n", v.getName(), value(v));
      }
      solutionCount++;
    }

    public int getSolutionCount() {
      return solutionCount;
    }

    private int solutionCount;
    private final IntVar[] variableArray;
  }

  static class BestBoundCallback implements Consumer<Double> {
    public BestBoundCallback() {
      bestBound = 0.0;
      numImprovements = 0;
    }

    @Override
    public void accept(Double bound) {
      bestBound = bound;
      numImprovements++;
    }

    public double getBestBound() {
      return bestBound;
    }

    double bestBound;
    int numImprovements;
  }


  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    // Create the model.
    CpModel model = new CpModel();

    // Create the variables.
    int numVals = 3;

    IntVar x = model.newIntVar(0, numVals - 1, "x");
    IntVar y = model.newIntVar(0, numVals - 1, "y");
    IntVar z = model.newIntVar(0, numVals - 1, "z");

    // Create the constraint.
    model.addDifferent(x, y);

    // Maximize a linear combination of variables.
    model.maximize(LinearExpr.weightedSum(new IntVar[] {x, y, z}, new long[] {1, 2, 3}));

    // Create a solver and solve the model.
    CpSolver solver = new CpSolver();
    VarArraySolutionPrinterWithObjective cb =
        new VarArraySolutionPrinterWithObjective(new IntVar[] {x, y, z});
    solver.getParameters().setNumWorkers(1);
    solver.getParameters().setLinearizationLevel(2);
    BestBoundCallback bestBoundCallback = new BestBoundCallback();

    solver.setBestBoundCallback(bestBoundCallback);
    CpSolverStatus unusedStatus = solver.solve(model, cb);

    System.out.println("solution count: " + cb.getSolutionCount());
    System.out.println("best bound count: " + bestBoundCallback.numImprovements);
  }

  private SolveAndPrintIntermediateSolutionsSampleSat() {}
}

C# code

using System;
using Google.OrTools.Sat;

public class VarArraySolutionPrinterWithObjective : CpSolverSolutionCallback
{
    public VarArraySolutionPrinterWithObjective(IntVar[] variables)
    {
        variables_ = variables;
    }

    public override void OnSolutionCallback()
    {
        Console.WriteLine(String.Format("Solution #{0}: time = {1:F2} s", solution_count_, WallTime()));
        Console.WriteLine(String.Format("  objective value = {0}", ObjectiveValue()));
        foreach (IntVar v in variables_)
        {
            Console.WriteLine(String.Format("  {0} = {1}", v.ToString(), Value(v)));
        }
        solution_count_++;
    }

    public int SolutionCount()
    {
        return solution_count_;
    }

    private int solution_count_;
    private IntVar[] variables_;
}

public class SolveAndPrintIntermediateSolutionsSampleSat
{
    static void Main()
    {
        // Creates the model.
        CpModel model = new CpModel();

        // Creates the variables.
        int num_vals = 3;

        IntVar x = model.NewIntVar(0, num_vals - 1, "x");
        IntVar y = model.NewIntVar(0, num_vals - 1, "y");
        IntVar z = model.NewIntVar(0, num_vals - 1, "z");

        // Adds a different constraint.
        model.Add(x != y);

        // Maximizes a linear combination of variables.
        model.Maximize(x + 2 * y + 3 * z);

        // Creates a solver and solves the model.
        CpSolver solver = new CpSolver();
        VarArraySolutionPrinterWithObjective cb = new VarArraySolutionPrinterWithObjective(new IntVar[] { x, y, z });
        solver.Solve(model, cb);

        Console.WriteLine(String.Format("Number of solutions found: {0}", cb.SolutionCount()));
    }
}

Go code

// The solve_and_print_intermediate_solutions_sample_sat command
package main

import (
	"fmt"

	log "github.com/golang/glog"
	"github.com/google/or-tools/ortools/sat/go/cpmodel"
	sppb "github.com/google/or-tools/ortools/sat/proto/satparameters"
	"google.golang.org/protobuf/proto"
)

func solveAndPrintIntermediateSolutionsSampleSat() error {
	model := cpmodel.NewCpModelBuilder()

	domain := cpmodel.NewDomain(0, 2)
	x := model.NewIntVarFromDomain(domain).WithName("x")
	y := model.NewIntVarFromDomain(domain).WithName("y")
	z := model.NewIntVarFromDomain(domain).WithName("z")

	model.AddNotEqual(x, y)

	model.Maximize(cpmodel.NewLinearExpr().Add(x).AddTerm(y, 2).AddTerm(z, 3))

	// Create a solver and solve with a fixed search.
	m, err := model.Model()
	if err != nil {
		return fmt.Errorf("failed to instantiate the CP model: %w", err)
	}

	// Currently, the CpModelBuilder does not allow for callbacks, so intermediate solutions
	// cannot be printed while solving. However, the CP-SAT solver does allow for returning
	// the intermediate solutions found while solving in the response.
	params := &sppb.SatParameters{
		FillAdditionalSolutionsInResponse: proto.Bool(true),
		SolutionPoolSize:                  proto.Int32(10),
	}
	response, err := cpmodel.SolveCpModelWithParameters(m, params)
	if err != nil {
		return fmt.Errorf("failed to solve the model: %w", err)
	}

	fmt.Println("Number of intermediate solutions found: ", len(response.GetAdditionalSolutions()))

	fmt.Println("Optimal solution:")
	fmt.Printf("  x = %v\n", cpmodel.SolutionIntegerValue(response, x))
	fmt.Printf("  y = %v\n", cpmodel.SolutionIntegerValue(response, y))
	fmt.Printf("  z = %v\n", cpmodel.SolutionIntegerValue(response, z))

	return nil
}

func main() {
	if err := solveAndPrintIntermediateSolutionsSampleSat(); err != nil {
		log.Exitf("solveAndPrintIntermediateSolutionsSampleSat returned with error: %v", err)
	}
}

Searching for all solutions in a satisfiability model

In an non-optimization model, you can search for all solutions. For all languages except Go, you need to register a callback on the solver that will be called at each solution. For Go, callbacks are not implemented, but you can still get the intermediate solutions in the response.

Please note that it does not work in parallel (i. e. parameter num_search_workers > 1).

It also does not work if the model contains an objective.

The method will return the following:

FEASIBLE if some solutions have been found
INFEASIBLE if the solver has proved there are no solution
OPTIMAL if all solutions have been found

The exact implementation depends on the target language.

Python code

To search for all solutions, use the Solve() method after setting the correct parameter.

#!/usr/bin/env python3
"""Code sample that solves a model and displays all solutions."""

from ortools.sat.python import cp_model


class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
    """Print intermediate solutions."""

    def __init__(self, variables: list[cp_model.IntVar]):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__solution_count = 0

    def on_solution_callback(self) -> None:
        self.__solution_count += 1
        for v in self.__variables:
            print(f"{v}={self.value(v)}", end=" ")
        print()

    @property
    def solution_count(self) -> int:
        return self.__solution_count


def search_for_all_solutions_sample_sat():
    """Showcases calling the solver to search for all solutions."""
    # Creates the model.
    model = cp_model.CpModel()

    # Creates the variables.
    num_vals = 3
    x = model.new_int_var(0, num_vals - 1, "x")
    y = model.new_int_var(0, num_vals - 1, "y")
    z = model.new_int_var(0, num_vals - 1, "z")

    # Create the constraints.
    model.add(x != y)

    # Create a solver and solve.
    solver = cp_model.CpSolver()
    solution_printer = VarArraySolutionPrinter([x, y, z])
    # Enumerate all solutions.
    solver.parameters.enumerate_all_solutions = True
    # Solve.
    status = solver.solve(model, solution_printer)

    print(f"Status = {solver.status_name(status)}")
    print(f"Number of solutions found: {solution_printer.solution_count}")


search_for_all_solutions_sample_sat()

C++ code

To search for all solutions, a parameter of the SAT solver must be changed.

#include <stdlib.h>

#include "ortools/base/logging.h"
#include "ortools/sat/cp_model.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/sorted_interval_list.h"

namespace operations_research {
namespace sat {

void SearchAllSolutionsSampleSat() {
  CpModelBuilder cp_model;

  const Domain domain(0, 2);
  const IntVar x = cp_model.NewIntVar(domain).WithName("x");
  const IntVar y = cp_model.NewIntVar(domain).WithName("y");
  const IntVar z = cp_model.NewIntVar(domain).WithName("z");

  cp_model.AddNotEqual(x, y);

  Model model;

  int num_solutions = 0;
  model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& r) {
    LOG(INFO) << "Solution " << num_solutions;
    LOG(INFO) << "  x = " << SolutionIntegerValue(r, x);
    LOG(INFO) << "  y = " << SolutionIntegerValue(r, y);
    LOG(INFO) << "  z = " << SolutionIntegerValue(r, z);
    num_solutions++;
  }));

  // Tell the solver to enumerate all solutions.
  SatParameters parameters;
  parameters.set_enumerate_all_solutions(true);
  model.Add(NewSatParameters(parameters));
  const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);

  LOG(INFO) << "Number of solutions found: " << num_solutions;
}

}  // namespace sat
}  // namespace operations_research

int main() {
  operations_research::sat::SearchAllSolutionsSampleSat();

  return EXIT_SUCCESS;
}

Java code

As in Python, CpSolver.solve() must be called after setting the correct parameter.

package com.google.ortools.sat.samples;

import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverSolutionCallback;
import com.google.ortools.sat.CpSolverStatus;
import com.google.ortools.sat.IntVar;

/** Code sample that solves a model and displays all solutions. */
public class SearchForAllSolutionsSampleSat {
  static class VarArraySolutionPrinter extends CpSolverSolutionCallback {
    public VarArraySolutionPrinter(IntVar[] variables) {
      variableArray = variables;
    }

    @Override
    public void onSolutionCallback() {
      System.out.printf("Solution #%d: time = %.02f s%n", solutionCount, wallTime());
      for (IntVar v : variableArray) {
        System.out.printf("  %s = %d%n", v.getName(), value(v));
      }
      solutionCount++;
    }

    public int getSolutionCount() {
      return solutionCount;
    }

    private int solutionCount;
    private final IntVar[] variableArray;
  }

  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    // Create the model.
    CpModel model = new CpModel();

    // Create the variables.
    int numVals = 3;

    IntVar x = model.newIntVar(0, numVals - 1, "x");
    IntVar y = model.newIntVar(0, numVals - 1, "y");
    IntVar z = model.newIntVar(0, numVals - 1, "z");

    // Create the constraints.
    model.addDifferent(x, y);

    // Create a solver and solve the model.
    CpSolver solver = new CpSolver();
    VarArraySolutionPrinter cb = new VarArraySolutionPrinter(new IntVar[] {x, y, z});
    // Tell the solver to enumerate all solutions.
    solver.getParameters().setEnumerateAllSolutions(true);
    // And solve.
    CpSolverStatus unusedStatus = solver.solve(model, cb);

    System.out.println(cb.getSolutionCount() + " solutions found.");
  }
}

C# code

As in Python, CpSolver.Solve() must be called after setting the correct string parameter.

using System;
using Google.OrTools.Sat;

public class VarArraySolutionPrinter : CpSolverSolutionCallback
{
    public VarArraySolutionPrinter(IntVar[] variables)
    {
        variables_ = variables;
    }

    public override void OnSolutionCallback()
    {
        {
            Console.WriteLine(String.Format("Solution #{0}: time = {1:F2} s", solution_count_, WallTime()));
            foreach (IntVar v in variables_)
            {
                Console.WriteLine(String.Format("  {0} = {1}", v.ToString(), Value(v)));
            }
            solution_count_++;
        }
    }

    public int SolutionCount()
    {
        return solution_count_;
    }

    private int solution_count_;
    private IntVar[] variables_;
}

public class SearchForAllSolutionsSampleSat
{
    static void Main()
    {
        // Creates the model.
        CpModel model = new CpModel();

        // Creates the variables.
        int num_vals = 3;

        IntVar x = model.NewIntVar(0, num_vals - 1, "x");
        IntVar y = model.NewIntVar(0, num_vals - 1, "y");
        IntVar z = model.NewIntVar(0, num_vals - 1, "z");

        // Adds a different constraint.
        model.Add(x != y);

        // Creates a solver and solves the model.
        CpSolver solver = new CpSolver();
        VarArraySolutionPrinter cb = new VarArraySolutionPrinter(new IntVar[] { x, y, z });
        // Search for all solutions.
        solver.StringParameters = "enumerate_all_solutions:true";
        // And solve.
        solver.Solve(model, cb);

        Console.WriteLine($"Number of solutions found: {cb.SolutionCount()}");
    }
}

Go code

To search for all solutions, a parameter of the SAT solver must be changed.

// The search_for_all_solutions_sample_sat command is an example for how to search for
// all solutions.
package main

import (
	"fmt"

	log "github.com/golang/glog"
	"github.com/google/or-tools/ortools/sat/go/cpmodel"
	sppb "github.com/google/or-tools/ortools/sat/proto/satparameters"
	"google.golang.org/protobuf/proto"
)

func searchForAllSolutionsSampleSat() error {
	model := cpmodel.NewCpModelBuilder()

	domain := cpmodel.NewDomain(0, 2)
	x := model.NewIntVarFromDomain(domain).WithName("x")
	y := model.NewIntVarFromDomain(domain).WithName("y")
	z := model.NewIntVarFromDomain(domain).WithName("z")

	model.AddNotEqual(x, y)

	m, err := model.Model()
	if err != nil {
		return fmt.Errorf("failed to instantiate the CP model: %w", err)
	}
	// Currently, the CpModelBuilder does not allow for callbacks, so each feasible solution cannot
	// be printed while solving. However, the CP Solver can return all of the enumerated solutions
	// in the response by setting the following parameters.
	params := &sppb.SatParameters{
		EnumerateAllSolutions:             proto.Bool(true),
		FillAdditionalSolutionsInResponse: proto.Bool(true),
		SolutionPoolSize:                  proto.Int32(27),
	}
	response, err := cpmodel.SolveCpModelWithParameters(m, params)
	if err != nil {
		return fmt.Errorf("failed to solve the model: %w", err)
	}

	for i, solution := range response.GetAdditionalSolutions() {
		vs := solution.GetValues()
		fmt.Printf("Solution %v: x = %v, y = %v, z = %v\n", i, vs[x.Index()], vs[y.Index()], vs[z.Index()])
	}

	fmt.Println("Number of solutions found: ", len(response.GetAdditionalSolutions()))

	return nil
}

func main() {
	if err := searchForAllSolutionsSampleSat(); err != nil {
		log.Exitf("searchForAllSolutionsSampleSat returned with error: %v", err)
	}
}

Stopping search early

Sometimes, you might decide that the current solution is good enough. In this section, we will enumerate all possible combinations of three variables, and stop after the fifth combination found.

Python code

You can stop the search by calling StopSearch() inside of CpSolverSolutionCallback.OnSolutionCallback().

#!/usr/bin/env python3
"""Code sample that solves a model and displays a small number of solutions."""

from ortools.sat.python import cp_model


class VarArraySolutionPrinterWithLimit(cp_model.CpSolverSolutionCallback):
    """Print intermediate solutions."""

    def __init__(self, variables: list[cp_model.IntVar], limit: int):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__solution_count = 0
        self.__solution_limit = limit

    def on_solution_callback(self) -> None:
        self.__solution_count += 1
        for v in self.__variables:
            print(f"{v}={self.value(v)}", end=" ")
        print()
        if self.__solution_count >= self.__solution_limit:
            print(f"Stop search after {self.__solution_limit} solutions")
            self.stop_search()

    @property
    def solution_count(self) -> int:
        return self.__solution_count


def stop_after_n_solutions_sample_sat():
    """Showcases calling the solver to search for small number of solutions."""
    # Creates the model.
    model = cp_model.CpModel()
    # Creates the variables.
    num_vals = 3
    x = model.new_int_var(0, num_vals - 1, "x")
    y = model.new_int_var(0, num_vals - 1, "y")
    z = model.new_int_var(0, num_vals - 1, "z")

    # Create a solver and solve.
    solver = cp_model.CpSolver()
    solution_printer = VarArraySolutionPrinterWithLimit([x, y, z], 5)
    # Enumerate all solutions.
    solver.parameters.enumerate_all_solutions = True
    # Solve.
    status = solver.solve(model, solution_printer)
    print(f"Status = {solver.status_name(status)}")
    print(f"Number of solutions found: {solution_printer.solution_count}")
    assert solution_printer.solution_count == 5


stop_after_n_solutions_sample_sat()

C++ code

Stopping search is done by registering an atomic bool on the model-owned time limit, and setting that bool to true.

#include <stdlib.h>

#include <atomic>

#include "ortools/base/logging.h"
#include "ortools/sat/cp_model.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/sorted_interval_list.h"
#include "ortools/util/time_limit.h"

namespace operations_research {
namespace sat {

void StopAfterNSolutionsSampleSat() {
  CpModelBuilder cp_model;

  const Domain domain(0, 2);
  const IntVar x = cp_model.NewIntVar(domain).WithName("x");
  const IntVar y = cp_model.NewIntVar(domain).WithName("y");
  const IntVar z = cp_model.NewIntVar(domain).WithName("z");

  Model model;

  // Tell the solver to enumerate all solutions.
  SatParameters parameters;
  parameters.set_enumerate_all_solutions(true);
  model.Add(NewSatParameters(parameters));

  // Create an atomic Boolean that will be periodically checked by the limit.
  std::atomic<bool> stopped(false);
  model.GetOrCreate<TimeLimit>()->RegisterExternalBooleanAsLimit(&stopped);

  const int kSolutionLimit = 5;
  int num_solutions = 0;
  model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& r) {
    LOG(INFO) << "Solution " << num_solutions;
    LOG(INFO) << "  x = " << SolutionIntegerValue(r, x);
    LOG(INFO) << "  y = " << SolutionIntegerValue(r, y);
    LOG(INFO) << "  z = " << SolutionIntegerValue(r, z);
    num_solutions++;
    if (num_solutions >= kSolutionLimit) {
      stopped = true;
      LOG(INFO) << "Stop search after " << kSolutionLimit << " solutions.";
    }
  }));
  const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);
  LOG(INFO) << "Number of solutions found: " << num_solutions;
  CHECK_EQ(num_solutions, kSolutionLimit);
}

}  // namespace sat
}  // namespace operations_research

int main() {
  operations_research::sat::StopAfterNSolutionsSampleSat();

  return EXIT_SUCCESS;
}

Java code

Stopping search is performed by calling stopSearch() inside of CpSolverSolutionCallback.onSolutionCallback().

package com.google.ortools.sat.samples;

import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverSolutionCallback;
import com.google.ortools.sat.CpSolverStatus;
import com.google.ortools.sat.IntVar;

/** Code sample that solves a model and displays a small number of solutions. */
public final class StopAfterNSolutionsSampleSat {
  static class VarArraySolutionPrinterWithLimit extends CpSolverSolutionCallback {
    public VarArraySolutionPrinterWithLimit(IntVar[] variables, int limit) {
      variableArray = variables;
      solutionLimit = limit;
    }

    @Override
    public void onSolutionCallback() {
      System.out.printf("Solution #%d: time = %.02f s%n", solutionCount, wallTime());
      for (IntVar v : variableArray) {
        System.out.printf("  %s = %d%n", v.getName(), value(v));
      }
      solutionCount++;
      if (solutionCount >= solutionLimit) {
        System.out.printf("Stop search after %d solutions%n", solutionLimit);
        stopSearch();
      }
    }

    public int getSolutionCount() {
      return solutionCount;
    }

    private int solutionCount;
    private final IntVar[] variableArray;
    private final int solutionLimit;
  }

  public static void main(String[] args) {
    Loader.loadNativeLibraries();
    // Create the model.
    CpModel model = new CpModel();
    // Create the variables.
    int numVals = 3;

    IntVar x = model.newIntVar(0, numVals - 1, "x");
    IntVar y = model.newIntVar(0, numVals - 1, "y");
    IntVar z = model.newIntVar(0, numVals - 1, "z");

    // Create a solver and solve the model.
    CpSolver solver = new CpSolver();
    VarArraySolutionPrinterWithLimit cb =
        new VarArraySolutionPrinterWithLimit(new IntVar[] {x, y, z}, 5);
    // Tell the solver to enumerate all solutions.
    solver.getParameters().setEnumerateAllSolutions(true);
    // And solve.
    CpSolverStatus unusedStatus = solver.solve(model, cb);

    System.out.println(cb.getSolutionCount() + " solutions found.");
    if (cb.getSolutionCount() != 5) {
      throw new RuntimeException("Did not stop the search correctly.");
    }
  }

  private StopAfterNSolutionsSampleSat() {}
}

C# code

Stopping search is performed by calling StopSearch() inside of CpSolverSolutionCallback.OnSolutionCallback().

using System;
using Google.OrTools.Sat;

public class VarArraySolutionPrinterWithLimit : CpSolverSolutionCallback
{
    public VarArraySolutionPrinterWithLimit(IntVar[] variables, int solution_limit)
    {
        variables_ = variables;
        solution_limit_ = solution_limit;
    }

    public override void OnSolutionCallback()
    {
        Console.WriteLine(String.Format("Solution #{0}: time = {1:F2} s", solution_count_, WallTime()));
        foreach (IntVar v in variables_)
        {
            Console.WriteLine(String.Format("  {0} = {1}", v.ToString(), Value(v)));
        }
        solution_count_++;
        if (solution_count_ >= solution_limit_)
        {
            Console.WriteLine(String.Format("Stopping search after {0} solutions", solution_limit_));
            StopSearch();
        }
    }

    public int SolutionCount()
    {
        return solution_count_;
    }

    private int solution_count_;
    private IntVar[] variables_;
    private int solution_limit_;
}

public class StopAfterNSolutionsSampleSat
{
    static void Main()
    {
        // Creates the model.
        CpModel model = new CpModel();
        // Creates the variables.
        int num_vals = 3;

        IntVar x = model.NewIntVar(0, num_vals - 1, "x");
        IntVar y = model.NewIntVar(0, num_vals - 1, "y");
        IntVar z = model.NewIntVar(0, num_vals - 1, "z");

        // Creates a solver and solves the model.
        CpSolver solver = new CpSolver();
        VarArraySolutionPrinterWithLimit cb = new VarArraySolutionPrinterWithLimit(new IntVar[] { x, y, z }, 5);
        solver.StringParameters = "enumerate_all_solutions:true";
        solver.Solve(model, cb);
        Console.WriteLine(String.Format("Number of solutions found: {0}", cb.SolutionCount()));
    }
}

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Solving a CP-SAT model

Changing the parameters of the solver

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Solving a CP-SAT model

Changing the parameters of the solver

Specifying the time limit in Python

Specifying the time limit in C++

Specifying the time limit in Java

Specifying the time limit in C#.

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Printing intermediate solutions

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Searching for all solutions in a satisfiability model

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