LinearSolverTests.cs

// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

using System;
using Xunit;
using Google.OrTools.LinearSolver;

namespace Google.OrTools.Tests
{
public class LinearSolverTest
{
    [Fact]
    public void VarOperator()
    {
        Solver solver = Solver.CreateSolver("CLP");
        Variable x = solver.MakeNumVar(0.0, 100.0, "x");
        Assert.Equal(0.0, x.Lb());
        Assert.Equal(100.0, x.Ub());

        Constraint ct1 = solver.Add(x >= 1);
        Assert.Equal(1.0, ct1.GetCoefficient(x));
        Assert.Equal(1.0, ct1.Lb());
        Assert.Equal(double.PositiveInfinity, ct1.Ub());

        Constraint ct2 = solver.Add(x <= 1);
        Assert.Equal(1.0, ct2.GetCoefficient(x));
        Assert.Equal(double.NegativeInfinity, ct2.Lb());
        Assert.Equal(1.0, ct2.Ub());

        Constraint ct3 = solver.Add(x == 1);
        Assert.Equal(1.0, ct3.GetCoefficient(x));
        Assert.Equal(1.0, ct3.Lb());
        Assert.Equal(1.0, ct3.Ub());

        Constraint ct4 = solver.Add(1 >= x);
        Assert.Equal(1.0, ct4.GetCoefficient(x));
        Assert.Equal(double.NegativeInfinity, ct4.Lb());
        Assert.Equal(1.0, ct4.Ub());

        Constraint ct5 = solver.Add(1 <= x);
        Assert.Equal(1.0, ct5.GetCoefficient(x));
        Assert.Equal(1.0, ct5.Lb());
        Assert.Equal(double.PositiveInfinity, ct5.Ub());

        Constraint ct6 = solver.Add(1 == x);
        Assert.Equal(1.0, ct6.GetCoefficient(x));
        Assert.Equal(1.0, ct6.Lb());
        Assert.Equal(1.0, ct6.Ub());
    }

    [Fact]
    public void VarAddition()
    {
        Solver solver = Solver.CreateSolver("CLP");
        Variable x = solver.MakeNumVar(0.0, 100.0, "x");
        Assert.Equal(0.0, x.Lb());
        Assert.Equal(100.0, x.Ub());

        Variable y = solver.MakeNumVar(0.0, 100.0, "y");
        Assert.Equal(0.0, y.Lb());
        Assert.Equal(100.0, y.Ub());

        Constraint ct1 = solver.Add(x + y == 1);
        Assert.Equal(1.0, ct1.GetCoefficient(x));
        Assert.Equal(1.0, ct1.GetCoefficient(y));

        Constraint ct2 = solver.Add(x + x == 1);
        Assert.Equal(2.0, ct2.GetCoefficient(x));

        Constraint ct3 = solver.Add(x + (y + x) == 1);
        Assert.Equal(2.0, ct3.GetCoefficient(x));
        Assert.Equal(1.0, ct3.GetCoefficient(y));

        Constraint ct4 = solver.Add(x + (y + x + 3) == 1);
        Assert.Equal(2.0, ct4.GetCoefficient(x));
        Assert.Equal(1.0, ct4.GetCoefficient(y));
        Assert.Equal(-2.0, ct4.Lb());
        Assert.Equal(-2.0, ct4.Ub());
    }

    [Fact]
    public void VarMultiplication()
    {
        Solver solver = Solver.CreateSolver("CLP");
        Variable x = solver.MakeNumVar(0.0, 100.0, "x");
        Assert.Equal(0.0, x.Lb());
        Assert.Equal(100.0, x.Ub());

        Variable y = solver.MakeNumVar(0.0, 100.0, "y");
        Assert.Equal(0.0, y.Lb());
        Assert.Equal(100.0, y.Ub());

        Constraint ct1 = solver.Add(3 * x == 1);
        Assert.Equal(3.0, ct1.GetCoefficient(x));

        Constraint ct2 = solver.Add(x * 3 == 1);
        Assert.Equal(3.0, ct2.GetCoefficient(x));

        Constraint ct3 = solver.Add(x + (2 * y + 3 * x) == 1);
        Assert.Equal(4.0, ct3.GetCoefficient(x));
        Assert.Equal(2.0, ct3.GetCoefficient(y));

        Constraint ct4 = solver.Add(x + 5 * (y + x + 3) == 1);
        Assert.Equal(6.0, ct4.GetCoefficient(x));
        Assert.Equal(5.0, ct4.GetCoefficient(y));
        Assert.Equal(-14.0, ct4.Lb());
        Assert.Equal(-14.0, ct4.Ub());

        Constraint ct5 = solver.Add(x + (2 * y + x + 3) * 3 == 1);
        Assert.Equal(4.0, ct5.GetCoefficient(x));
        Assert.Equal(6.0, ct5.GetCoefficient(y));
        Assert.Equal(-8.0, ct5.Lb());
        Assert.Equal(-8.0, ct5.Ub());
    }

    [Fact]
    public void BinaryOperator()
    {
        Solver solver = Solver.CreateSolver("CLP");
        Variable x = solver.MakeNumVar(0.0, 100.0, "x");
        Assert.Equal(0.0, x.Lb());
        Assert.Equal(100.0, x.Ub());

        Variable y = solver.MakeNumVar(0.0, 100.0, "y");
        Assert.Equal(0.0, y.Lb());
        Assert.Equal(100.0, y.Ub());

        Constraint ct1 = solver.Add(x == y);
        Assert.Equal(1.0, ct1.GetCoefficient(x));
        Assert.Equal(-1.0, ct1.GetCoefficient(y));

        Constraint ct2 = solver.Add(x == 3 * y + 5);
        Assert.Equal(1.0, ct2.GetCoefficient(x));
        Assert.Equal(-3.0, ct2.GetCoefficient(y));
        Assert.Equal(5.0, ct2.Lb());
        Assert.Equal(5.0, ct2.Ub());

        Constraint ct3 = solver.Add(2 * x - 9 == y);
        Assert.Equal(2.0, ct3.GetCoefficient(x));
        Assert.Equal(-1.0, ct3.GetCoefficient(y));
        Assert.Equal(9.0, ct3.Lb());
        Assert.Equal(9.0, ct3.Ub());

        Assert.True(x == x);
        Assert.True(!(x != x));
        Assert.True((x != y));
        Assert.True(!(x == y));
    }

    [Fact]
    public void Inequalities()
    {
        Solver solver = Solver.CreateSolver("CLP");
        Variable x = solver.MakeNumVar(0.0, 100.0, "x");
        Assert.Equal(0.0, x.Lb());
        Assert.Equal(100.0, x.Ub());

        Variable y = solver.MakeNumVar(0.0, 100.0, "y");
        Assert.Equal(0.0, y.Lb());
        Assert.Equal(100.0, y.Ub());

        Constraint ct1 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) >= 3);
        Assert.Equal(7.0, ct1.GetCoefficient(x));
        Assert.Equal(5.0, ct1.GetCoefficient(y));
        Assert.Equal(2.0, ct1.Lb());
        Assert.Equal(double.PositiveInfinity, ct1.Ub());

        Constraint ct2 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) <= 3);
        Assert.Equal(7.0, ct2.GetCoefficient(x));
        Assert.Equal(5.0, ct2.GetCoefficient(y));
        Assert.Equal(double.NegativeInfinity, ct2.Lb());
        Assert.Equal(2.0, ct2.Ub());

        Constraint ct3 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) >= 3 - x - y);
        Assert.Equal(8.0, ct3.GetCoefficient(x));
        Assert.Equal(6.0, ct3.GetCoefficient(y));
        Assert.Equal(2.0, ct3.Lb());
        Assert.Equal(double.PositiveInfinity, ct3.Ub());

        Constraint ct4 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) <= -x - y + 3);
        Assert.Equal(8.0, ct4.GetCoefficient(x));
        Assert.Equal(6.0, ct4.GetCoefficient(y));
        Assert.Equal(double.NegativeInfinity, ct4.Lb());
        Assert.Equal(2.0, ct4.Ub());
    }

    [Fact]
    public void SumArray()
    {
        Solver solver = Solver.CreateSolver("CLP");

        Variable[] x = solver.MakeBoolVarArray(10, "x");
        Constraint ct1 = solver.Add(x.Sum() == 3);
        Assert.Equal(1.0, ct1.GetCoefficient(x[0]));

        Constraint ct2 = solver.Add(-2 * x.Sum() == 3);
        Assert.Equal(-2.0, ct2.GetCoefficient(x[0]));

        LinearExpr[] array = new LinearExpr[] { x[0] + 2.0, x[0] + 3, x[0] + 4 };
        Constraint ct3 = solver.Add(array.Sum() == 1);
        Assert.Equal(3.0, ct3.GetCoefficient(x[0]));
        Assert.Equal(-8.0, ct3.Lb());
        Assert.Equal(-8.0, ct3.Ub());
    }

    [Fact]
    public void Objective()
    {
        Solver solver = Solver.CreateSolver("CLP");
        Variable x = solver.MakeNumVar(0.0, 100.0, "x");
        Assert.Equal(0.0, x.Lb());
        Assert.Equal(100.0, x.Ub());

        Variable y = solver.MakeNumVar(0.0, 100.0, "y");
        Assert.Equal(0.0, y.Lb());
        Assert.Equal(100.0, y.Ub());

        solver.Maximize(x);
        Assert.Equal(0.0, solver.Objective().Offset());
        Assert.Equal(1.0, solver.Objective().GetCoefficient(x));
        Assert.True(solver.Objective().Maximization());

        solver.Minimize(-x - 2 * y + 3);
        Assert.Equal(3.0, solver.Objective().Offset());
        Assert.Equal(-1.0, solver.Objective().GetCoefficient(x));
        Assert.Equal(-2.0, solver.Objective().GetCoefficient(y));
        Assert.True(solver.Objective().Minimization());
    }

    void SolveAndPrint(in Solver solver, in Variable[] variables, in Constraint[] constraints)
    {
        Console.WriteLine($"Number of variables = {solver.NumVariables()}");
        Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");

        Solver.ResultStatus resultStatus = solver.Solve();
        // Check that the problem has an optimal solution.
        if (resultStatus != Solver.ResultStatus.OPTIMAL)
        {
            Console.WriteLine("The problem does not have an optimal solution!");
        }
        else
        {
            Console.WriteLine("Solution:");
            foreach (Variable var in variables)
            {
                Console.WriteLine($"{var.Name()} = {var.SolutionValue()}");
            }
            Console.WriteLine($"Optimal objective value = {solver.Objective().Value()}");
            Console.WriteLine("");
            Console.WriteLine("Advanced usage:");
            Console.WriteLine($"Problem solved in {solver.WallTime()} milliseconds");
            Console.WriteLine($"Problem solved in {solver.Iterations()} iterations");
            foreach (Variable var in variables)
            {
                Console.WriteLine($"{var.Name()}: reduced cost {var.ReducedCost()}");
            }

            double[] activities = solver.ComputeConstraintActivities();
            foreach (Constraint ct in constraints)
            {
                Console.WriteLine($"{ct.Name()}: dual value = {ct.DualValue()}",
                                  $" activity = {activities[ct.Index()]}");
            }
        }
    }

    void RunLinearProgrammingExample(in String problemType)
    {
        Console.WriteLine($"------ Linear programming example with {problemType} ------");

        Solver solver = Solver.CreateSolver(problemType);
        if (solver == null)
            return;

        // x and y are continuous non-negative variables.
        Variable x = solver.MakeNumVar(0.0, double.PositiveInfinity, "x");
        Variable y = solver.MakeNumVar(0.0, double.PositiveInfinity, "y");

        // Objectif function: Maximize 3x + 4y.
        Objective objective = solver.Objective();
        objective.SetCoefficient(x, 3);
        objective.SetCoefficient(y, 4);
        objective.SetMaximization();

        // x + 2y <= 14.
        Constraint c0 = solver.MakeConstraint(double.NegativeInfinity, 14.0, "c0");
        c0.SetCoefficient(x, 1);
        c0.SetCoefficient(y, 2);

        // 3x - y >= 0.
        Constraint c1 = solver.MakeConstraint(0.0, double.PositiveInfinity, "c1");
        c1.SetCoefficient(x, 3);
        c1.SetCoefficient(y, -1);

        // x - y <= 2.
        Constraint c2 = solver.MakeConstraint(double.NegativeInfinity, 2.0, "c2");
        c2.SetCoefficient(x, 1);
        c2.SetCoefficient(y, -1);

        SolveAndPrint(solver, new Variable[] { x, y }, new Constraint[] { c0, c1, c2 });
    }
    void RunMixedIntegerProgrammingExample(in String problemType)
    {
        Console.WriteLine($"------ Mixed integer programming example with {problemType} ------");

        Solver solver = Solver.CreateSolver(problemType);
        if (solver == null)
            return;

        // x and y are integers non-negative variables.
        Variable x = solver.MakeIntVar(0.0, double.PositiveInfinity, "x");
        Variable y = solver.MakeIntVar(0.0, double.PositiveInfinity, "y");

        // Objectif function: Maximize x + 10 * y.
        Objective objective = solver.Objective();
        objective.SetCoefficient(x, 1);
        objective.SetCoefficient(y, 10);
        objective.SetMaximization();

        // x + 7 * y <= 17.5.
        Constraint c0 = solver.MakeConstraint(double.NegativeInfinity, 17.5, "c0");
        c0.SetCoefficient(x, 1);
        c0.SetCoefficient(y, 7);

        // x <= 3.5.
        Constraint c1 = solver.MakeConstraint(double.NegativeInfinity, 3.5, "c1");
        c1.SetCoefficient(x, 1);
        c1.SetCoefficient(y, 0);

        SolveAndPrint(solver, new Variable[] { x, y }, new Constraint[] { c0, c1 });
    }
    void RunBooleanProgrammingExample(in String problemType)
    {
        Console.WriteLine($"------ Boolean programming example with {problemType} ------");

        Solver solver = Solver.CreateSolver(problemType);
        if (solver == null)
            return;

        // x and y are boolean variables.
        Variable x = solver.MakeBoolVar("x");
        Variable y = solver.MakeBoolVar("y");

        // Objectif function: Maximize 2 * x + y.
        Objective objective = solver.Objective();
        objective.SetCoefficient(x, 2);
        objective.SetCoefficient(y, 1);
        objective.SetMinimization();

        // 1 <= x + 2 * y <= 3.
        Constraint c0 = solver.MakeConstraint(1, 3, "c0");
        c0.SetCoefficient(x, 1);
        c0.SetCoefficient(y, 2);

        SolveAndPrint(solver, new Variable[] { x, y }, new Constraint[] { c0 });
    }

    [Fact]
    public void OptimizationProblemType()
    {
        RunLinearProgrammingExample("GLOP");
        RunLinearProgrammingExample("GLPK_LP");
        RunLinearProgrammingExample("CLP");
        RunLinearProgrammingExample("GUROBI_LP");

        RunMixedIntegerProgrammingExample("GLPK");
        RunMixedIntegerProgrammingExample("CBC");
        RunMixedIntegerProgrammingExample("SCIP");
        RunMixedIntegerProgrammingExample("SAT");

        RunBooleanProgrammingExample("SAT");
        RunBooleanProgrammingExample("BOP");
    }

    [Fact]
    static void testSetHintAndSolverGetters()
    {
        Console.WriteLine("testSetHintAndSolverGetters");
        Solver solver = Solver.CreateSolver("glop");
        // x and y are continuous non-negative variables.
        Variable x = solver.MakeIntVar(0.0, double.PositiveInfinity, "x");
        Variable y = solver.MakeIntVar(0.0, double.PositiveInfinity, "y");

        // Objectif function: Maximize x + 10 * y.
        Objective objective = solver.Objective();
        objective.SetCoefficient(x, 1);
        objective.SetCoefficient(y, 10);
        objective.SetMaximization();

        // x + 7 * y <= 17.5.
        Constraint c0 = solver.MakeConstraint(double.NegativeInfinity, 17.5, "c0");
        c0.SetCoefficient(x, 1);
        c0.SetCoefficient(y, 7);

        // x <= 3.5.
        Constraint c1 = solver.MakeConstraint(double.NegativeInfinity, 3.5, "c1");
        c1.SetCoefficient(x, 1);
        c1.SetCoefficient(y, 0);

        Constraint[] constraints = solver.constraints();
        Assert.Equal(constraints.Length, 2);
        Variable[] variables = solver.variables();
        Assert.Equal(variables.Length, 2);

        solver.SetHint(new Variable[] { x, y }, new double[] { 2.0, 3.0 });
    }
}
} // namespace Google.OrTools.Tests