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Using the CP-SAT solver

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

Documentation structure

This document presents modeling recipes for the CP-SAT solver.

Code samples are given in C++, Python, Java, C#, and Go. Each language has different requirements for the code samples.

Searching for one (optimal) solution of a CP-SAT model

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 code samples

The Python interface to the CP-SAT solver is implemented using two classes.

• The CpModel class proposes modeling methods that creates variables, or add constraints. This class completely hides the underlying CpModelProto used to store the model.
• The CpSolver class encapsulates the solve API and offers helpers to access the solution found by the solve.

#!/usr/bin/env python3
"""Simple solve."""
from ortools.sat.python import cp_model


def simple_sat_program():
    """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")

    # 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.OPTIMAL or status == cp_model.FEASIBLE:
        print(f"x = {solver.value(x)}")
        print(f"y = {solver.value(y)}")
        print(f"z = {solver.value(z)}")
    else:
        print("No solution found.")


simple_sat_program()

C++ code samples

The interface to the C++ CP-SAT solver is implemented through the CpModelBuilder class described in ortools/sat/cp_model.h. This class is just a helper to fill in the cp_model protobuf.

Calling Solve() method 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 <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/util/sorted_interval_list.h"

namespace operations_research {
namespace sat {

void SimpleSatProgram() {
  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.
  const CpSolverResponse response = Solve(cp_model.Build());

  if (response.status() == CpSolverStatus::OPTIMAL ||
      response.status() == CpSolverStatus::FEASIBLE) {
    // Get the value of x in the solution.
    LOG(INFO) << "x = " << SolutionIntegerValue(response, x);
    LOG(INFO) << "y = " << SolutionIntegerValue(response, y);
    LOG(INFO) << "z = " << SolutionIntegerValue(response, z);
  } else {
    LOG(INFO) << "No solution found.";
  }
}

}  // namespace sat
}  // namespace operations_research

int main() {
  operations_research::sat::SimpleSatProgram();
  return EXIT_SUCCESS;
}

Java code samples

The Java code implements the same interface as the Python code, with a CpModel and a CpSolver class.

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;

/** Minimal CP-SAT example to showcase calling the solver. */
public final class SimpleSatProgram {
  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();
    CpSolverStatus status = solver.solve(model);

    if (status == CpSolverStatus.OPTIMAL || status == CpSolverStatus.FEASIBLE) {
      System.out.println("x = " + solver.value(x));
      System.out.println("y = " + solver.value(y));
      System.out.println("z = " + solver.value(z));
    } else {
      System.out.println("No solution found.");
    }
  }

  private SimpleSatProgram() {}
}

C# code samples

The C# code implements the same interface as the Python code, with a CpModel and a CpSolver class.

using System;
using Google.OrTools.Sat;

public class SimpleSatProgram
{
    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 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.Optimal || status == CpSolverStatus.Feasible)
        {
            Console.WriteLine("x = " + solver.Value(x));
            Console.WriteLine("y = " + solver.Value(y));
            Console.WriteLine("z = " + solver.Value(z));
        }
        else
        {
            Console.WriteLine("No solution found.");
        }
    }
}

Go code samples

The interface to the CP-SAT solver is implemented through the CpModelBuilder described in the package cpmodel in ortools/sat/go/cp_model.go. This class is a helper to fill in the cp_model protobuf.

Also within the cpmodel package is ortools/sat/go/cp_model.go which provides functions to solve the model along with helpers to access the solution found by the solver.

// The simple_sat_program command is an example of a simple sat program.
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"
)

func simpleSatProgram() 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)
	}
	response, err := cpmodel.SolveCpModel(m)
	if err != nil {
		return fmt.Errorf("failed to solve the model: %w", err)
	}

	switch response.GetStatus() {
	case cmpb.CpSolverStatus_OPTIMAL, cmpb.CpSolverStatus_FEASIBLE:
		fmt.Printf("x = %d\n", cpmodel.SolutionIntegerValue(response, x))
		fmt.Printf("y = %d\n", cpmodel.SolutionIntegerValue(response, y))
		fmt.Printf("z = %d\n", cpmodel.SolutionIntegerValue(response, z))
	default:
		fmt.Println("No solution found.")
	}

	return nil
}

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