/// <summary>
/// Dùng phương pháp tuyến tính tối ưu 3x + y với yêu cầu sau:
/// 0 ≤ x ≤ 1
/// 0 ≤ y ≤ 2
/// x + y ≤ 2
///
/// Kết quả:
/// - Giá trị: 4
/// - x = 1
/// - y = 1
///
/// Main steps in solving the problem
/// - Create the variables
/// - Define the constraints
/// - Define the objective function
/// - Declare the solver—the method that implements an algorithm for finding the optimal solution
/// - Invoke the solver and display the results
/// </summary>
/// <param name="args"></param>
static void Main(string[] args)
{
// Create the linear solver with the GLOP backend.
var solver = new Google.OrTools.LinearSolver.Solver("SimpleLpProgram", Google.OrTools.LinearSolver.Solver.GLOP_LINEAR_PROGRAMMING);
// Create the variables x and y.
var x = solver.MakeNumVar(0.0, 1.0, "x");
var y = solver.MakeNumVar(0.0, 2.0, "y");
Console.WriteLine("Number of variables = " + solver.NumVariables());
// Create a linear constraint, 0 <= x + y <= 2.
var ct = solver.MakeConstraint(0.0, 2.0, "ct");
ct.SetCoefficient(x, 1);
ct.SetCoefficient(y, 1);
Console.WriteLine("Number of constraints = " + solver.NumConstraints());
// Create the objective function, 3 * x + y.
var objective = solver.Objective();
objective.SetCoefficient(x, 3);
objective.SetCoefficient(y, 1);
objective.SetMaximization();
solver.Solve();
Console.WriteLine("Solution:");
Console.WriteLine("Objective value = " + objective.Value());
Console.WriteLine("x = " + x.SolutionValue());
Console.WriteLine("y = " + y.SolutionValue());
Console.ReadLine();
}
/// <summary>
/// feasible_region.png
/// Dùng phương pháp tuyến tính Glop tối ưu 3x + 4y với yêu cầu sau:
/// x + 2y ≤ 14
/// 3x – y ≥ 0
/// x – y ≤ 2
///
/// Kết quả:
/// x = 6.0
/// y = 4.0
/// Giá trị = 34.0
///
/// </summary>
/// <param name="args"></param>
static void Main(string[] args)
{
var solver = new Google.OrTools.LinearSolver.Solver("LinearProgrammingExample", Google.OrTools.LinearSolver.Solver.GLOP_LINEAR_PROGRAMMING);
// x and y are continuous non-negative variables.
var x = solver.MakeNumVar(0.0, double.PositiveInfinity, "x");
var y = solver.MakeNumVar(0.0, double.PositiveInfinity, "y");
// x + 2y <= 14.
var c0 = solver.MakeConstraint(double.NegativeInfinity, 14.0);
c0.SetCoefficient(x, 1);
c0.SetCoefficient(y, 2);
// 3x - y >= 0.
var c1 = solver.MakeConstraint(0.0, double.PositiveInfinity);
c1.SetCoefficient(x, 3);
c1.SetCoefficient(y, -1);
// x - y <= 2.
var c2 = solver.MakeConstraint(double.NegativeInfinity, 2.0);
c2.SetCoefficient(x, 1);
c2.SetCoefficient(y, -1);
// Objective function: 3x + 4y.
var objective = solver.Objective();
objective.SetCoefficient(x, 3);
objective.SetCoefficient(y, 4);
objective.SetMaximization();
solver.Solve();
Console.WriteLine("Number of variables = " + solver.NumVariables());
Console.WriteLine("Number of constraints = " + solver.NumConstraints());
// The value of each variable in the solution.
Console.WriteLine("Solution:");
Console.WriteLine("x = " + x.SolutionValue());
Console.WriteLine("y = " + y.SolutionValue());
// The objective value of the solution.
Console.WriteLine("Optimal objective value = " + solver.Objective().Value());
Console.ReadLine();
}
