387 lines
14 KiB
C#
387 lines
14 KiB
C#
using System;
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using Google.OrTools.LinearSolver;
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using Xunit;
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namespace Google.OrTools.Tests {
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public class LinearSolverTest {
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[Fact]
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public void VarOperator() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable x = solver.MakeNumVar(0.0, 100.0, "x");
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Assert.Equal(0.0, x.Lb());
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Assert.Equal(100.0, x.Ub());
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Constraint ct1 = solver.Add(x >= 1);
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Assert.Equal(1.0, ct1.GetCoefficient(x));
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Assert.Equal(1.0, ct1.Lb());
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Assert.Equal(double.PositiveInfinity, ct1.Ub());
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Constraint ct2 = solver.Add(x <= 1);
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Assert.Equal(1.0, ct2.GetCoefficient(x));
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Assert.Equal(double.NegativeInfinity, ct2.Lb());
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Assert.Equal(1.0, ct2.Ub());
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Constraint ct3 = solver.Add(x == 1);
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Assert.Equal(1.0, ct3.GetCoefficient(x));
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Assert.Equal(1.0, ct3.Lb());
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Assert.Equal(1.0, ct3.Ub());
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Constraint ct4 = solver.Add(1 >= x);
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Assert.Equal(1.0, ct4.GetCoefficient(x));
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Assert.Equal(double.NegativeInfinity, ct4.Lb());
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Assert.Equal(1.0, ct4.Ub());
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Constraint ct5 = solver.Add(1 <= x);
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Assert.Equal(1.0, ct5.GetCoefficient(x));
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Assert.Equal(1.0, ct5.Lb());
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Assert.Equal(double.PositiveInfinity, ct5.Ub());
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Constraint ct6 = solver.Add(1 == x);
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Assert.Equal(1.0, ct6.GetCoefficient(x));
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Assert.Equal(1.0, ct6.Lb());
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Assert.Equal(1.0, ct6.Ub());
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}
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[Fact]
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public void VarAddition() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable x = solver.MakeNumVar(0.0, 100.0, "x");
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Assert.Equal(0.0, x.Lb());
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Assert.Equal(100.0, x.Ub());
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Variable y = solver.MakeNumVar(0.0, 100.0, "y");
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Assert.Equal(0.0, y.Lb());
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Assert.Equal(100.0, y.Ub());
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Constraint ct1 = solver.Add(x + y == 1);
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Assert.Equal(1.0, ct1.GetCoefficient(x));
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Assert.Equal(1.0, ct1.GetCoefficient(y));
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Constraint ct2 = solver.Add(x + x == 1);
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Assert.Equal(2.0, ct2.GetCoefficient(x));
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Constraint ct3 = solver.Add(x + (y + x) == 1);
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Assert.Equal(2.0, ct3.GetCoefficient(x));
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Assert.Equal(1.0, ct3.GetCoefficient(y));
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Constraint ct4 = solver.Add(x + (y + x + 3) == 1);
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Assert.Equal(2.0, ct4.GetCoefficient(x));
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Assert.Equal(1.0, ct4.GetCoefficient(y));
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Assert.Equal(-2.0, ct4.Lb());
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Assert.Equal(-2.0, ct4.Ub());
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}
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[Fact]
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public void VarMultiplication() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable x = solver.MakeNumVar(0.0, 100.0, "x");
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Assert.Equal(0.0, x.Lb());
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Assert.Equal(100.0, x.Ub());
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Variable y = solver.MakeNumVar(0.0, 100.0, "y");
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Assert.Equal(0.0, y.Lb());
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Assert.Equal(100.0, y.Ub());
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Constraint ct1 = solver.Add(3 * x == 1);
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Assert.Equal(3.0, ct1.GetCoefficient(x));
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Constraint ct2 = solver.Add(x * 3 == 1);
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Assert.Equal(3.0, ct2.GetCoefficient(x));
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Constraint ct3 = solver.Add(x + (2 * y + 3 * x) == 1);
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Assert.Equal(4.0, ct3.GetCoefficient(x));
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Assert.Equal(2.0, ct3.GetCoefficient(y));
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Constraint ct4 = solver.Add(x + 5 * (y + x + 3) == 1);
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Assert.Equal(6.0, ct4.GetCoefficient(x));
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Assert.Equal(5.0, ct4.GetCoefficient(y));
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Assert.Equal(-14.0, ct4.Lb());
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Assert.Equal(-14.0, ct4.Ub());
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Constraint ct5 = solver.Add(x + (2 * y + x + 3) * 3 == 1);
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Assert.Equal(4.0, ct5.GetCoefficient(x));
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Assert.Equal(6.0, ct5.GetCoefficient(y));
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Assert.Equal(-8.0, ct5.Lb());
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Assert.Equal(-8.0, ct5.Ub());
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}
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[Fact]
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public void BinaryOperator() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable x = solver.MakeNumVar(0.0, 100.0, "x");
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Assert.Equal(0.0, x.Lb());
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Assert.Equal(100.0, x.Ub());
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Variable y = solver.MakeNumVar(0.0, 100.0, "y");
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Assert.Equal(0.0, y.Lb());
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Assert.Equal(100.0, y.Ub());
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Constraint ct1 = solver.Add(x == y);
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Assert.Equal(1.0, ct1.GetCoefficient(x));
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Assert.Equal(-1.0, ct1.GetCoefficient(y));
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Constraint ct2 = solver.Add(x == 3 * y + 5);
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Assert.Equal(1.0, ct2.GetCoefficient(x));
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Assert.Equal(-3.0, ct2.GetCoefficient(y));
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Assert.Equal(5.0, ct2.Lb());
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Assert.Equal(5.0, ct2.Ub());
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Constraint ct3 = solver.Add(2 * x - 9 == y);
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Assert.Equal(2.0, ct3.GetCoefficient(x));
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Assert.Equal(-1.0, ct3.GetCoefficient(y));
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Assert.Equal(9.0, ct3.Lb());
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Assert.Equal(9.0, ct3.Ub());
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Assert.True(x == x);
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Assert.True(!(x != x));
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Assert.True((x != y));
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Assert.True(!(x == y));
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}
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[Fact]
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public void Inequalities() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable x = solver.MakeNumVar(0.0, 100.0, "x");
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Assert.Equal(0.0, x.Lb());
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Assert.Equal(100.0, x.Ub());
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Variable y = solver.MakeNumVar(0.0, 100.0, "y");
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Assert.Equal(0.0, y.Lb());
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Assert.Equal(100.0, y.Ub());
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Constraint ct1 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) >= 3);
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Assert.Equal(7.0, ct1.GetCoefficient(x));
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Assert.Equal(5.0, ct1.GetCoefficient(y));
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Assert.Equal(2.0, ct1.Lb());
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Assert.Equal(double.PositiveInfinity, ct1.Ub());
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Constraint ct2 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) <= 3);
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Assert.Equal(7.0, ct2.GetCoefficient(x));
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Assert.Equal(5.0, ct2.GetCoefficient(y));
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Assert.Equal(double.NegativeInfinity, ct2.Lb());
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Assert.Equal(2.0, ct2.Ub());
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Constraint ct3 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) >= 3 - x - y);
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Assert.Equal(8.0, ct3.GetCoefficient(x));
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Assert.Equal(6.0, ct3.GetCoefficient(y));
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Assert.Equal(2.0, ct3.Lb());
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Assert.Equal(double.PositiveInfinity, ct3.Ub());
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Constraint ct4 = solver.Add(2 * (x + 3) + 5 * (y + x - 1) <= -x - y + 3);
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Assert.Equal(8.0, ct4.GetCoefficient(x));
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Assert.Equal(6.0, ct4.GetCoefficient(y));
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Assert.Equal(double.NegativeInfinity, ct4.Lb());
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Assert.Equal(2.0, ct4.Ub());
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}
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[Fact]
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public void SumArray() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable[] x = solver.MakeBoolVarArray(10, "x");
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Constraint ct1 = solver.Add(x.Sum() == 3);
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Assert.Equal(1.0, ct1.GetCoefficient(x[0]));
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Constraint ct2 = solver.Add(-2 * x.Sum() == 3);
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Assert.Equal(-2.0, ct2.GetCoefficient(x[0]));
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LinearExpr[] array = new LinearExpr[] { x[0] + 2.0, x[0] + 3, x[0] + 4 };
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Constraint ct3 = solver.Add(array.Sum() == 1);
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Assert.Equal(3.0, ct3.GetCoefficient(x[0]));
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Assert.Equal(-8.0, ct3.Lb());
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Assert.Equal(-8.0, ct3.Ub());
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}
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[Fact]
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public void Objective() {
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Solver solver = new Solver(
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"Solver",
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Solver.OptimizationProblemType.CLP_LINEAR_PROGRAMMING);
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Variable x = solver.MakeNumVar(0.0, 100.0, "x");
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Assert.Equal(0.0, x.Lb());
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Assert.Equal(100.0, x.Ub());
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Variable y = solver.MakeNumVar(0.0, 100.0, "y");
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Assert.Equal(0.0, y.Lb());
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Assert.Equal(100.0, y.Ub());
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solver.Maximize(x);
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Assert.Equal(0.0, solver.Objective().Offset());
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Assert.Equal(1.0, solver.Objective().GetCoefficient(x));
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Assert.True(solver.Objective().Maximization());
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solver.Minimize(-x - 2 * y + 3);
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Assert.Equal(3.0, solver.Objective().Offset());
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Assert.Equal(-1.0, solver.Objective().GetCoefficient(x));
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Assert.Equal(-2.0, solver.Objective().GetCoefficient(y));
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Assert.True(solver.Objective().Minimization());
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}
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void SolveAndPrint(in Solver solver, in Variable[] variables, in Constraint[] constraints) {
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Console.WriteLine($"Number of variables = {solver.NumVariables()}");
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Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");
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Solver.ResultStatus resultStatus = solver.Solve();
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// Check that the problem has an optimal solution.
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if (resultStatus != Solver.ResultStatus.OPTIMAL) {
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Console.WriteLine("The problem does not have an optimal solution!");
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}
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Console.WriteLine("Solution:");
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foreach (Variable var in variables) {
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Console.WriteLine($"{var.Name()} = {var.SolutionValue()}");
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}
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Console.WriteLine($"Optimal objective value = {solver.Objective().Value()}");
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Console.WriteLine("");
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Console.WriteLine("Advanced usage:");
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Console.WriteLine($"Problem solved in {solver.WallTime()} milliseconds");
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Console.WriteLine($"Problem solved in {solver.Iterations()} iterations");
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foreach (Variable var in variables) {
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Console.WriteLine($"{var.Name()}: reduced cost {var.ReducedCost()}");
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}
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double[] activities = solver.ComputeConstraintActivities();
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foreach (Constraint ct in constraints) {
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Console.WriteLine(
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$"{ct.Name()}: dual value = {ct.DualValue()}",
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$" activity = {activities[ct.Index()]}");
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}
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}
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void RunLinearProgrammingExample(in Solver.OptimizationProblemType problemType) {
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Solver solver = new Solver("LinearProgrammingExample", problemType);
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// x and y are continuous non-negative variables.
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Variable x = solver.MakeNumVar(0.0, double.PositiveInfinity, "x");
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Variable y = solver.MakeNumVar(0.0, double.PositiveInfinity, "y");
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// Objectif function: Maximize 3x + 4y.
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Objective objective = solver.Objective();
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objective.SetCoefficient(x, 3);
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objective.SetCoefficient(y, 4);
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objective.SetMaximization();
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// x + 2y <= 14.
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Constraint c0 = solver.MakeConstraint(double.NegativeInfinity, 14.0, "c0");
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c0.SetCoefficient(x, 1);
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c0.SetCoefficient(y, 2);
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// 3x - y >= 0.
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Constraint c1 = solver.MakeConstraint(0.0, double.PositiveInfinity, "c1");
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c1.SetCoefficient(x, 3);
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c1.SetCoefficient(y, -1);
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// x - y <= 2.
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Constraint c2 = solver.MakeConstraint(double.NegativeInfinity, 2.0, "c2");
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c2.SetCoefficient(x, 1);
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c2.SetCoefficient(y, -1);
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SolveAndPrint(solver, new Variable[] { x, y }, new Constraint[] { c0, c1, c2 });
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}
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void RunMixedIntegerProgrammingExample(in Solver.OptimizationProblemType problemType) {
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Solver solver = new Solver("MixedIntegerProgrammingExample", problemType);
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// x and y are integers non-negative variables.
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Variable x = solver.MakeIntVar(0.0, double.PositiveInfinity, "x");
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Variable y = solver.MakeIntVar(0.0, double.PositiveInfinity, "y");
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// Objectif function: Maximize x + 10 * y.
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Objective objective = solver.Objective();
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objective.SetCoefficient(x, 1);
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objective.SetCoefficient(y, 10);
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objective.SetMaximization();
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// x + 7 * y <= 17.5.
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Constraint c0 = solver.MakeConstraint(double.NegativeInfinity, 17.5, "c0");
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c0.SetCoefficient(x, 1);
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c0.SetCoefficient(y, 7);
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// x <= 3.5.
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Constraint c1 = solver.MakeConstraint(double.NegativeInfinity, 3.5, "c1");
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c1.SetCoefficient(x, 1);
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c1.SetCoefficient(y, 0);
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SolveAndPrint(solver, new Variable[] { x, y }, new Constraint[] { c0, c1 });
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}
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void RunBooleanProgrammingExample(in Solver.OptimizationProblemType problemType) {
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Solver solver = new Solver("BooleanProgrammingExample", problemType);
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// x and y are boolean variables.
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Variable x = solver.MakeBoolVar("x");
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Variable y = solver.MakeBoolVar("y");
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// Objectif function: Maximize 2 * x + y.
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Objective objective = solver.Objective();
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objective.SetCoefficient(x, 2);
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objective.SetCoefficient(y, 1);
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objective.SetMinimization();
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// 1 <= x + 2 * y <= 3.
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Constraint c0 = solver.MakeConstraint(1, 3, "c0");
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c0.SetCoefficient(x, 1);
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c0.SetCoefficient(y, 2);
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SolveAndPrint(solver, new Variable[] { x, y }, new Constraint[] { c0 });
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}
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[Fact]
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public void OptimizationProblemType() {
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Array problem_types = Enum.GetValues(typeof(Solver.OptimizationProblemType));
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foreach (Solver.OptimizationProblemType problem_type in problem_types) {
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if (problem_type.ToString().EndsWith("LINEAR_PROGRAMMING")) {
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Console.WriteLine($"------ Linear programming example with {problem_type} ------");
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RunLinearProgrammingExample(problem_type);
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} else if (problem_type.ToString().EndsWith("MIXED_INTEGER_PROGRAMMING")) {
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Console.WriteLine($"------ Mixed Integer programming example with {problem_type} ------");
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RunMixedIntegerProgrammingExample(problem_type);
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} else if (problem_type.ToString().EndsWith("INTEGER_PROGRAMMING")) {
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Console.WriteLine($"------ Boolean programming example with {problem_type} ------");
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RunBooleanProgrammingExample(problem_type);
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} else {
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Console.WriteLine($"Problem type {problem_type} unknow !");
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}
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}
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}
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[Fact]
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static void testSetHintAndSolverGetters() {
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Console.WriteLine("testSetHintAndSolverGetters");
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Solver solver = new Solver("testSetHintAndSolverGetters",
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Solver.OptimizationProblemType.GLOP_LINEAR_PROGRAMMING);
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// x and y are continuous non-negative variables.
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Variable x = solver.MakeIntVar(0.0, double.PositiveInfinity, "x");
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Variable y = solver.MakeIntVar(0.0, double.PositiveInfinity, "y");
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// Objectif function: Maximize x + 10 * y.
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Objective objective = solver.Objective();
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objective.SetCoefficient(x, 1);
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objective.SetCoefficient(y, 10);
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objective.SetMaximization();
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// x + 7 * y <= 17.5.
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Constraint c0 = solver.MakeConstraint(double.NegativeInfinity, 17.5, "c0");
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c0.SetCoefficient(x, 1);
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c0.SetCoefficient(y, 7);
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// x <= 3.5.
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Constraint c1 = solver.MakeConstraint(double.NegativeInfinity, 3.5, "c1");
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c1.SetCoefficient(x, 1);
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c1.SetCoefficient(y, 0);
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Constraint[] constraints = solver.constraints();
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Assert.Equal(constraints.Length, 2);
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Variable[] variables = solver.variables();
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Assert.Equal(variables.Length, 2);
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solver.SetHint(new Variable[] { x, y }, new double[] { 2.0, 3.0 });
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}
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}
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} // namespace Google.OrTools.Tests |