NMath User's Guide

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29.1 Encapsulating LP Problems (.NET, C#, CSharp, VB, Visual Basic, F#)

Class LinearProgrammingProblem encapsulates an LP problem. Instances are constructed from a vector of coefficients representing the objective function.

Code Example – C# linear programming

// z = x1 + 4*x2 + 9*x3

var coeff = new DoubleVector( "[1 4 9]" );

var problem = new LinearProgrammingProblem( coeff );

MixedIntegerLinearProgrammingProblem encapsulates an LP problem which may contain integer or binary constraints.

Adding Bounds and Constraints

LinearProgrammingProblem instances maintain a list of LinearContraint objects, accessible via the Constraints property. A linear constraint on a set of variables is a constraint upon a linear combination of those variables. LinearConstraint supports to two such constraints: equality constraints and lower bound constraints. That is, given variables x0, x1,..., xn and constants b, a0, a1,..., an, two types of constraints may be formed




a0*x0 + a1*x1 + . . . + an*xn = b




and





a0*x0 + a1*x1 + . . . + an*xn >= b




NOTE—Upper
bound constraints are represented as negations of lower bound constraints.


Constraints may be added to a LinearProgrammingProblem
by working directly with the Constraints
list, or by using the AddConstraint() method.


LinearContraint
instances are constructed from a vector of coefficients, a right-hand
side, and a constraint type from the ConstraintType
enumeration.


Code Example – C# linear programming


// 0 <= x0 + 2*x1 + 2*x2




var coeff = new DoubleVector( 1.0, 2.0, 2.0 );




var constraint = new LinearConstraint( coeff, 0, 




  ConstraintType.GreaterThanOrEqualTo);




problem.AddConstraint( constraint );




A variety of convenience methods are also provided
on LinearProgrammingProblem for
adding constraints and variable bounds to an existing LP problem. These
methods create the required LinearConstraint
objects for you and add them to the Constraints
list.


Code Example – C# linear programming


// 0 <= x0 + 2*x1 + 2*x2 <= 72




var coeff = new DoubleVector( 1.0, 2.0, 2.0 );




problem.AddConstraint( coeff, 0, 72 );




MixedIntegerLinearProgrammingProblem
encapsulates an LP problem which may contain integer or binary constraints.
For example, in this code the first variable is constrained to be integer
valued.


Code Example – C# integer programming


problem.AddIntegralConstraint( 0 );




Here, the ith variable
in the solution must be binary.


Code Example – C# binary programming


problem.AddBinaryConstraint( i );




A binary constraint restricts the variable to a value
of zero or one.


Method GetIntegrality()
gets the integral constraint state of the variable at the given index.
IntegralVariableIndices returns the indices
of variables with integral constraints.





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