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QuickStart Samples

# Linear Programming QuickStart Sample (Visual Basic)

Illustrates solving linear programming (LP) problems using classes in the Extreme.Mathematics.Optimization.LinearProgramming namespace in Visual Basic.

Option Infer On

' The linear programming classes reside in their own namespace.
Imports Extreme.Mathematics.Optimization
' Vectors and matrices are in the Extreme.Mathematics.LinearAlgebra
' namespace
Imports Extreme.Mathematics

Namespace Extreme.Numerics.QuickStart.VB
' Illustrates solving linear programming problems
' using the classes in the Extreme.Mathematics.Optimization
' namespace of the Extreme Optimization Numerical Libraries for .NET.
Module LinearProgramming

Sub Main()
' This QuickStart illustrates the three ways to create a Linear Program.

' The first is in terms of matrices. The coefficients
' are supplied as a matrix. The cost vector, right-hand side
' and constraints on the variables are supplied as a vector.

' The cost vector:
Dim c = Vector.Create(-1.0, -3.0, 0.0, 0.0, 0.0, 0.0)
' The coefficients of the constraints:
Dim A = Matrix.Create(4, 6, New Double() _
{ _
1, 1, 1, 0, 0, 0, _
1, 1, 0, -1, 0, 0, _
1, 0, 0, 0, 1, 0, _
0, 1, 0, 0, 0, 1 _
}, MatrixElementOrder.RowMajor)
' The right-hand sides of the constraints:
Dim b = Vector.Create(1.5, 0.5, 1.0, 1.0)

' We're now ready to call the constructor.
' The last parameter specifies the number of equality
' constraints.
Dim lp1 As New LinearProgram(c, A, b, 4)

' Now we can call the Solve method to run the Revised
' Simplex algorithm:
Dim x = lp1.Solve()
' The GetDualSolution method returns the dual solution:
Dim y = lp1.GetDualSolution()
Console.WriteLine("Primal: {0:F1}", x)
Console.WriteLine("Dual:   {0:F1}", y)
' The optimal value is returned by the Extremum property:
Console.WriteLine("Optimal value:   {0:F1}", lp1.OptimalValue)

' The second way to create a Linear Program is by constructing
Dim lp2 As New LinearProgram()

' Next, we add two variables: we specify the name, the cost,
' and optionally the lower and upper bound.

' Next, we add constraints. Constraints also have a name.
' We also specify the coefficients of the variables,
' the lower bound and the upper bound.
' If a constraint is a simple equality or inequality constraint,
' you can supply a LinearProgramConstraintType value and the
' right-hand side of the constraint.

' We can now solve the linear program:
x = lp2.Solve()
y = lp2.GetDualSolution()
Console.WriteLine("Primal: {0:F1}", x)
Console.WriteLine("Dual:   {0:F1}", y)
Console.WriteLine("Optimal value:   {0:F1}", lp2.OptimalValue)

' Finally, we can create a linear program from an MPS file.
' The MPS format is a standard format.
' We can go straight to solving the linear program:
x = lp3.Solve()
y = lp3.GetDualSolution()
Console.WriteLine("Primal: {0:F1}", x)
Console.WriteLine("Dual:   {0:F1}", y)
Console.WriteLine("Optimal value:   {0:F1}", lp3.OptimalValue)

Console.Write("Press Enter key to exit...")