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Solving a CP-SAT model

Searching for one (optimal) solution

By default, searching for one solution will return the first solution found if the model has no objective, or the optimal solution if the model has an objective.

Python solver code

The CpSolver class encapsulates searching for a solution of a model.

"""Simple solve."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from ortools.sat.python import cp_model


def SimpleSolve():
  """Minimal CP-SAT example to showcase calling the solver."""
  # Creates the model.
  model = cp_model.CpModel()
  # Creates the variables.
  num_vals = 3
  x = model.NewIntVar(0, num_vals - 1, 'x')
  y = model.NewIntVar(0, num_vals - 1, 'y')
  z = model.NewIntVar(0, num_vals - 1, 'z')
  # Creates the constraints.
  model.Add(x != y)

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

  if status == cp_model.FEASIBLE:
    print('x = %i' % solver.Value(x))
    print('y = %i' % solver.Value(y))
    print('z = %i' % solver.Value(z))


SimpleSolve()

C++ solver code

Calling SolveCpModel() will return a CpSolverResponse protobuf that contains the solve status, the values for each variable in the model if solve was successful, and some metrics.

#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/model.h"

namespace operations_research {
namespace sat {

void SimpleSolve() {
  CpModelProto cp_model;

  // Trivial model with just one variable and no constraint.
  auto new_variable = [&cp_model](int64 lb, int64 ub) {
    CHECK_LE(lb, ub);
    const int index = cp_model.variables_size();
    IntegerVariableProto* const var = cp_model.add_variables();
    var->add_domain(lb);
    var->add_domain(ub);
    return index;
  };

  const int x = new_variable(0, 3);

  // Solving part.
  Model model;
  LOG(INFO) << CpModelStats(cp_model);
  const CpSolverResponse response = SolveCpModel(cp_model, &model);
  LOG(INFO) << CpSolverResponseStats(response);

  if (response.status() == CpSolverStatus::FEASIBLE) {
    // Get the value of x in the solution.
    const int64 value_x = response.solution(x);
    LOG(INFO) << "x = " << value_x;
  }
}

}  // namespace sat
}  // namespace operations_research

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

  return EXIT_SUCCESS;
}

Java code

As in Python, the CpSolver class encapsulates searching for a solution.

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

/** Solve a simple problem with three variables and one different constraint. */
public class SimpleSolve {

  static { System.loadLibrary("jniortools"); }

  public static void main(String[] args) throws Exception {
    // 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();
    CpSolverStatus status = solver.solve(model);

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

C# code

As in Python, the CpSolver class encapsulates searching for a solution of a model.

using System;
using Google.OrTools.Sat;

public class CodeSamplesSat
{
  static void SimpleSolve()
  {
    // 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 the constraints.
    model.Add(x != y);

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

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

  static void Main()
  {
    SimpleSolve();
  }
}

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

"""Solves a problem with a time limit."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from ortools.sat.python import cp_model


def MinimalCpSatWithTimeLimit():
  """Minimal CP-SAT example to showcase calling the solver."""
  # Creates the model.
  model = cp_model.CpModel()
  # Creates the variables.
  num_vals = 3
  x = model.NewIntVar(0, num_vals - 1, 'x')
  y = model.NewIntVar(0, num_vals - 1, 'y')
  z = model.NewIntVar(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.FEASIBLE:
    print('x = %i' % solver.Value(x))
    print('y = %i' % solver.Value(y))
    print('z = %i' % solver.Value(z))


MinimalCpSatWithTimeLimit()

Specifying the time limit in C++

#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"

namespace operations_research {
namespace sat {

void SolveWithTimeLimit() {
  CpModelProto cp_model;

  // Trivial model with just one variable and no constraint.
  auto new_variable = [&cp_model](int64 lb, int64 ub) {
    CHECK_LE(lb, ub);
    const int index = cp_model.variables_size();
    IntegerVariableProto* const var = cp_model.add_variables();
    var->add_domain(lb);
    var->add_domain(ub);
    return index;
  };

  const int x = new_variable(0, 3);

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

  if (response.status() == CpSolverStatus::FEASIBLE) {
    // Get the value of x in the solution.
    const int64 value_x = response.solution(x);
    LOG(INFO) << "value_x = " << value_x;
  }
}

}  // namespace sat
}  // namespace operations_research

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

  return EXIT_SUCCESS;
}

Specifying the time limit in Java

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

public class SolveWithTimeLimit {

  static { System.loadLibrary("jniortools"); }

  public static void main(String[] args) throws Exception {
    // 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.FEASIBLE) {
      System.out.println("x = " + solver.value(x));
      System.out.println("y = " + solver.value(y));
      System.out.println("z = " + solver.value(z));
    }
  }
}

Specifying the time limit in C#.

Parameters must be passed as string to the solver.

using System;
using Google.OrTools.Sat;

public class CodeSamplesSat
{
  static void MinimalCpSatWithTimeLimit()
  {
    // 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.Feasible)
    {
      Console.WriteLine("x = " + solver.Value(x));
      Console.WriteLine("y = " + solver.Value(y));
      Console.WriteLine("z = " + solver.Value(z));
    }
  }

  static void Main()
  {
    MinimalCpSatWithTimeLimit();
  }
}

Printing intermediate solutions

In an optimization model, you can print intermediate solutions. You need to register a callback on the solver that will be called at each solution.

The exact implementation depends on the target language.

Python code

"""Solves an optimization problem and displays all intermediate solutions."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

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):
    cp_model.CpSolverSolutionCallback.__init__(self)
    self.__variables = variables
    self.__solution_count = 0

  def OnSolutionCallback(self):
    print('Solution %i' % self.__solution_count)
    print('  objective value = %i' % self.ObjectiveValue())
    for v in self.__variables:
      print('  %s = %i' % (v, self.Value(v)), end=' ')
    print()
    self.__solution_count += 1

  def SolutionCount(self):
    return self.__solution_count


def MinimalCpSatPrintIntermediateSolutions():
  """Showcases printing intermediate solutions found during search."""
  # Creates the model.
  model = cp_model.CpModel()
  # Creates the variables.
  num_vals = 3
  x = model.NewIntVar(0, num_vals - 1, 'x')
  y = model.NewIntVar(0, num_vals - 1, 'y')
  z = model.NewIntVar(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.SolveWithSolutionCallback(model, solution_printer)

  print('Status = %s' % solver.StatusName(status))
  print('Number of solutions found: %i' % solution_printer.SolutionCount())


MinimalCpSatPrintIntermediateSolutions()

C++ code

#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/model.h"

namespace operations_research {
namespace sat {

void MinimalSatPrintIntermediateSolutions() {
  CpModelProto cp_model;

  auto new_variable = [&cp_model](int64 lb, int64 ub) {
    CHECK_LE(lb, ub);
    const int index = cp_model.variables_size();
    IntegerVariableProto* const var = cp_model.add_variables();
    var->add_domain(lb);
    var->add_domain(ub);
    return index;
  };

  auto add_different = [&cp_model](const int left_var, const int right_var) {
    LinearConstraintProto* const lin =
        cp_model.add_constraints()->mutable_linear();
    lin->add_vars(left_var);
    lin->add_coeffs(1);
    lin->add_vars(right_var);
    lin->add_coeffs(-1);
    lin->add_domain(kint64min);
    lin->add_domain(-1);
    lin->add_domain(1);
    lin->add_domain(kint64max);
  };

  auto maximize = [&cp_model](const std::vector<int>& vars,
                              const std::vector<int64>& coeffs) {
    CpObjectiveProto* const obj = cp_model.mutable_objective();
    for (const int v : vars) {
      obj->add_vars(v);
    }
    for (const int64 c : coeffs) {
      obj->add_coeffs(-c);  // Maximize.
    }
    obj->set_scaling_factor(-1.0);  // Maximize.
  };

  const int kNumVals = 3;
  const int x = new_variable(0, kNumVals - 1);
  const int y = new_variable(0, kNumVals - 1);
  const int z = new_variable(0, kNumVals - 1);

  add_different(x, y);

  maximize({x, y, z}, {1, 2, 3});

  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 = " << r.solution(x);
    LOG(INFO) << "  y = " << r.solution(y);
    LOG(INFO) << "  z = " << r.solution(z);
    num_solutions++;
  }));
  const CpSolverResponse response = SolveCpModel(cp_model, &model);
  LOG(INFO) << "Number of solutions found: " << num_solutions;
}

}  // namespace sat
}  // namespace operations_research

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

  return EXIT_SUCCESS;
}

Java code

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

public class SolveWithIntermediateSolutions {

  static { System.loadLibrary("jniortools"); }

  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;
  }

  public static void main(String[] args) throws Exception {
    // 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.maximizeScalProd(new IntVar[] {x, y, z}, new int[] {1, 2, 3});

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

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

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.ShortString(), Value(v)));
    }
    solution_count_++;
  }

  public int SolutionCount()
  {
    return solution_count_;
  }

  private int solution_count_;
  private IntVar[] variables_;
}

public class CodeSamplesSat
{
  static void MinimalCpSatPrintIntermediateSolutions()
  {
    // 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.SolveWithSolutionCallback(model, cb);
    Console.WriteLine(String.Format("Number of solutions found: {0}",
          cb.SolutionCount()));
  }

  static void Main()
  {
    MinimalCpSatPrintIntermediateSolutions();
  }
}

Searching for all solutions in a satisfiability model

In an non-optimization model, you can search for all solutions. You need to register a callback on the solver that will be called at each solution.

The exact implementation depends on the target language.

Python code

To search for all solutions, use the SearchForAllSolutions method.

"""Code sample that solves a model and displays all solutions."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from ortools.sat.python import cp_model


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

  def __init__(self, variables):
    cp_model.CpSolverSolutionCallback.__init__(self)
    self.__variables = variables
    self.__solution_count = 0

  def OnSolutionCallback(self):
    self.__solution_count += 1
    for v in self.__variables:
      print('%s=%i' % (v, self.Value(v)), end=' ')
    print()

  def SolutionCount(self):
    return self.__solution_count


def SolveAllSolutions():
  """Showcases calling the solver to search for all solutions."""
  # Creates the model.
  model = cp_model.CpModel()
  # Creates the variables.
  num_vals = 3
  x = model.NewIntVar(0, num_vals - 1, 'x')
  y = model.NewIntVar(0, num_vals - 1, 'y')
  z = model.NewIntVar(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])
  status = solver.SearchForAllSolutions(model, solution_printer)
  print('Status = %s' % solver.StatusName(status))
  print('Number of solutions found: %i' % solution_printer.SolutionCount())


SolveAllSolutions()

C++ code

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

#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"

namespace operations_research {
namespace sat {

void MinimalSatSearchForAllSolutions() {
  CpModelProto cp_model;

  auto new_variable = [&cp_model](int64 lb, int64 ub) {
    CHECK_LE(lb, ub);
    const int index = cp_model.variables_size();
    IntegerVariableProto* const var = cp_model.add_variables();
    var->add_domain(lb);
    var->add_domain(ub);
    return index;
  };

  auto add_different = [&cp_model](const int left_var, const int right_var) {
    LinearConstraintProto* const lin =
        cp_model.add_constraints()->mutable_linear();
    lin->add_vars(left_var);
    lin->add_coeffs(1);
    lin->add_vars(right_var);
    lin->add_coeffs(-1);
    lin->add_domain(kint64min);
    lin->add_domain(-1);
    lin->add_domain(1);
    lin->add_domain(kint64max);
  };

  const int kNumVals = 3;
  const int x = new_variable(0, kNumVals - 1);
  const int y = new_variable(0, kNumVals - 1);
  const int z = new_variable(0, kNumVals - 1);

  add_different(x, y);

  Model model;

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

  int num_solutions = 0;
  model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& r) {
    LOG(INFO) << "Solution " << num_solutions;
    LOG(INFO) << "  x = " << r.solution(x);
    LOG(INFO) << "  y = " << r.solution(y);
    LOG(INFO) << "  z = " << r.solution(z);
    num_solutions++;
  }));
  const CpSolverResponse response = SolveCpModel(cp_model, &model);
  LOG(INFO) << "Number of solutions found: " << num_solutions;
}

}  // namespace sat
}  // namespace operations_research

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

  return EXIT_SUCCESS;
}

Java code

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

public class SolveAllSolutions {

  static { System.loadLibrary("jniortools"); }

  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 {
    // 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});
    solver.searchAllSolutions(model, cb);

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

C# code

As in Python, CpSolver.SearchAllSolutions() must be called.

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.ShortString(), Value(v)));
      }
      solution_count_++;
    }
  }

  public int SolutionCount()
  {
    return solution_count_;
  }

  private int solution_count_;
  private IntVar[] variables_;
}


public class CodeSamplesSat
{
  static void MinimalCpSatAllSolutions()
  {
    // 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 });
    solver.SearchAllSolutions(model, cb);
    Console.WriteLine(String.Format("Number of solutions found: {0}",
                                    cb.SolutionCount()));
  }

  static void Main()
  {
    MinimalCpSatAllSolutions();
  }
}

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().

"""Code sample that solves a model and displays a small number of solutions."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from ortools.sat.python import cp_model


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

  def __init__(self, variables, limit):
    cp_model.CpSolverSolutionCallback.__init__(self)
    self.__variables = variables
    self.__solution_count = 0
    self.__solution_limit = limit

  def OnSolutionCallback(self):
    self.__solution_count += 1
    for v in self.__variables:
      print('%s=%i' % (v, self.Value(v)), end=' ')
    print()
    if self.__solution_count >= self.__solution_limit:
      print('Stop search after %i solutions' % self.__solution_limit)
      self.StopSearch()

  def SolutionCount(self):
    return self.__solution_count


def StopAfterNSolutions():
  """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.NewIntVar(0, num_vals - 1, 'x')
  y = model.NewIntVar(0, num_vals - 1, 'y')
  z = model.NewIntVar(0, num_vals - 1, 'z')

  # Create a solver and solve.
  solver = cp_model.CpSolver()
  solution_printer = VarArraySolutionPrinterWithLimit([x, y, z], 5)
  status = solver.SearchForAllSolutions(model, solution_printer)
  print('Status = %s' % solver.StatusName(status))
  print('Number of solutions found: %i' % solution_printer.SolutionCount())
  assert solution_printer.SolutionCount() == 5


StopAfterNSolutions()

C++ code

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


#include <atomic>
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/time_limit.h"

namespace operations_research {
namespace sat {

void StopAfterNSolutions() {
  CpModelProto cp_model;

  auto new_variable = [&cp_model](int64 lb, int64 ub) {
    CHECK_LE(lb, ub);
    const int index = cp_model.variables_size();
    IntegerVariableProto* const var = cp_model.add_variables();
    var->add_domain(lb);
    var->add_domain(ub);
    return index;
  };

  const int kNumVals = 3;
  const int x = new_variable(0, kNumVals - 1);
  const int y = new_variable(0, kNumVals - 1);
  const int z = new_variable(0, kNumVals - 1);

  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 = " << r.solution(x);
    LOG(INFO) << "  y = " << r.solution(y);
    LOG(INFO) << "  z = " << r.solution(z);
    num_solutions++;
    if (num_solutions >= kSolutionLimit) {
      stopped = true;
      LOG(INFO) << "Stop search after " << kSolutionLimit << " solutions.";
    }
  }));
  const CpSolverResponse response = SolveCpModel(cp_model, &model);
  LOG(INFO) << "Number of solutions found: " << num_solutions;
  CHECK_EQ(num_solutions, kSolutionLimit);
}

}  // namespace sat
}  // namespace operations_research

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

  return EXIT_SUCCESS;
}

Java code

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

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

public class StopAfterNSolutions {

  static { System.loadLibrary("jniortools"); }

  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) throws Exception {
    // 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);
    solver.searchAllSolutions(model, cb);

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

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.ShortString(), 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 CodeSamplesSat
{
  static void StopAfterNSolutions()
  {
    // 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.SearchAllSolutions(model, cb);
    Console.WriteLine(String.Format("Number of solutions found: {0}",
          cb.SolutionCount()));
  }

  static void Main()
  {
    StopAfterNSolutions();
  }
}

31 KiB Raw Blame History

Solving a CP-SAT model

Searching for one (optimal) solution

Python solver code

C++ solver code

Java code

C# code

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#.

Printing intermediate solutions

Python code

C++ code

Java code

C# code

Searching for all solutions in a satisfiability model

Python code

C++ code

Java code

C# code

Stopping search early

Python code

C++ code

Java code

C# code

31 KiB

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