public void TestMILPSolver1()
{
var solver = new Z3MILPSolver();
int goal;
solver.AddRow("goal", out goal);
int x1, x2, z;
// 0 <= x1 <= 2
solver.AddVariable("x1", out x1);
solver.SetBounds(x1, 0, 2);
// 0 <= x2 <= 2
solver.AddVariable("x2", out x2);
solver.SetBounds(x2, 0, 2);
// z is an integer in [0,1]
solver.AddVariable("z", out z);
solver.SetIntegrality(z, true);
solver.SetBounds(z, 0, 1);
//max x1 + x2
solver.SetCoefficient(goal, x1, 1);
solver.SetCoefficient(goal, x2, 1);
solver.AddGoal(goal, 1, false);
// 0 <= x1 -z <= 1
int row1;
solver.AddRow("rowI1", out row1);
solver.SetBounds(row1, 0, 1);
solver.SetCoefficient(row1, x1, 1);
solver.SetCoefficient(row1, z, -1);
// 0 <= x2 + z <= 2
int row2;
solver.AddRow("rowI2", out row2);
solver.SetBounds(row2, 0, 2);
solver.SetCoefficient(row2, x2, 1);
solver.SetCoefficient(row2, z, 1);
var p = new Z3MILPParams();
solver.Solve(p);
Assert.IsTrue(solver.Result == LinearResult.Optimal);
Assert.AreEqual(solver.GetValue(x1), 2 * Rational.One);
Assert.AreEqual(solver.GetValue(x2), Rational.One);
Assert.AreEqual(solver.GetValue(z), Rational.One);
Assert.AreEqual(solver.GetValue(goal), 3 * Rational.One);
}
public void TestMILPSolver2()
{
var solver = new Z3MILPSolver();
int goal, extraGoal;
Rational M = 100;
solver.AddRow("goal", out goal);
int x1, x2, z;
// 0 <= x1 <= 100
solver.AddVariable("x1", out x1);
solver.SetBounds(x1, 0, M);
// 0 <= x2 <= 100
solver.AddVariable("x2", out x2);
solver.SetBounds(x2, 0, M);
// z is an integer in [0,1]
solver.AddVariable("z", out z);
solver.SetIntegrality(z, true);
solver.SetBounds(z, 0, 1);
solver.SetCoefficient(goal, x1, 1);
solver.SetCoefficient(goal, x2, 2);
solver.AddGoal(goal, 1, false);
solver.AddRow("extraGoal", out extraGoal);
solver.SetCoefficient(extraGoal, x1, 2);
solver.SetCoefficient(extraGoal, x2, 1);
solver.AddGoal(extraGoal, 2, false);
// x1 + x2 >= 1
int row;
solver.AddRow("row", out row);
solver.SetBounds(row, 1, Rational.PositiveInfinity);
solver.SetCoefficient(row, x1, 1);
solver.SetCoefficient(row, x2, 1);
// x1 - M*z <= 0
int row1;
solver.AddRow("rowI1", out row1);
solver.SetBounds(row1, Rational.NegativeInfinity, 0);
solver.SetCoefficient(row1, x1, 1);
solver.SetCoefficient(row1, z, -M);
// x2 - M* (1-z) <= 0
int row2;
solver.AddRow("rowI2", out row2);
solver.SetBounds(row2, Rational.NegativeInfinity, M);
solver.SetCoefficient(row2, x2, 1);
solver.SetCoefficient(row2, z, M);
var p = new Z3MILPParams();
p.OptKind = OptimizationKind.BoundingBox;
solver.Solve(p);
Assert.IsTrue(solver.Result == LinearResult.Optimal);
Assert.AreEqual(solver.GetValue(goal), 200 * Rational.One);
Assert.AreEqual(solver.GetValue(extraGoal), 200 * Rational.One);
}
