NMath Reference Guide

## Mixed |

Class MixedIntegerLinearProgrammingProblem encapsulates a Linear programming problem
which may contain integral constraints.

Inheritance Hierarchy

SystemObject

CenterSpace.NMath.CoreBoundedVariableProblem

CenterSpace.NMath.CoreLinearConstrainedProblem

CenterSpace.NMath.CoreLinearProgrammingProblem

CenterSpace.NMath.CoreMixedIntegerLinearProgrammingProblem

CenterSpace.NMath.CoreBoundedVariableProblem

CenterSpace.NMath.CoreLinearConstrainedProblem

CenterSpace.NMath.CoreLinearProgrammingProblem

CenterSpace.NMath.CoreMixedIntegerLinearProgrammingProblem

Syntax

The MixedIntegerLinearProgrammingProblem type exposes the following members.

Constructors

Name | Description | |
---|---|---|

MixedIntegerLinearProgrammingProblem | Default constructor. Behavior of resulting object is undefined. | |

MixedIntegerLinearProgrammingProblem(DoubleVector) | Constructs a MixedIntegerLinearProgrammingProblem object for minimizing objective function dot(objectiveCoefficients, x), where x is the vector of variables. |

Properties

Name | Description | |
---|---|---|

Constraints |
Gets and sets the linear constraints for the problem.
(Inherited from LinearConstrainedProblem) | |

IntegralVariableIndices | Gets the zero based indices of variables with integral constraints. | |

NumVariables |
Gets the number of variables.
(Inherited from LinearProgrammingProblem) | |

ObjectiveCoefficients |
Gets and sets the coefficients for the objective function.
(Inherited from LinearProgrammingProblem) | |

VariableBounds |
Gets and sets variable bounds for the problem.
(Inherited from BoundedVariableProblem) |

Methods

Name | Description | |
---|---|---|

AddBinaryConstraint(Int32) | Adds a binary constraint to the variable at the given index. A binary constraint restricts the variable to a value of zero or one. | |

AddBinaryConstraint(Int32) | Adds a binary constraint to the variables at the given indices. A binary constraint restricts the variable to a value of zero or one. | |

AddBounds(Int32, Double, Double) |
Adds upper and lower bound constraints to a variable.
(Inherited from BoundedVariableProblem) | |

AddBounds(Int32, Double, Double, Double) |
Adds upper and lower bound constraints to a variable.
(Inherited from BoundedVariableProblem) | |

AddConstraint(LinearConstraint) |
Adds the given constraint to the problem.
(Inherited from LinearConstrainedProblem) | |

AddConstraint(DoubleVector, Double, Double) |
Adds a linear inequality constraint of the form
lowerBound <= coefficients'x < upperBound
(Inherited from LinearConstrainedProblem) | |

AddConstraint(ILinearConstraintCoefficients, Double, Double) |
Adds a linear inequality constraint of the form
lowerBound <= coefficients'x < upperBound
(Inherited from LinearConstrainedProblem) | |

AddConstraint(DoubleVector, Double, Double, Double) |
Adds a linear inequality constraint of the form
lowerBound <= coefficients'x < upperBound
(Inherited from LinearConstrainedProblem) | |

AddConstraint(ILinearConstraintCoefficients, Double, Double, Double) |
Adds a linear inequality constraint of the form
lowerBound <= coefficients'x < upperBound
(Inherited from LinearConstrainedProblem) | |

AddEqualityConstraint(DoubleVector, Double) |
Adds an equality constraint of the form
coefficients'x = rightHandSide
(Inherited from LinearConstrainedProblem) | |

AddEqualityConstraint(ILinearConstraintCoefficients, Double) |
Adds an equality constraint of the form
coefficients'x = rightHandSide
(Inherited from LinearConstrainedProblem) | |

AddIntegralConstraint | Adds in integral constraint to the variable at the given zero based index. The index must be between zero and number of variables minus one, inclusive. | |

AddLowerBound(Int32, Double) |
Adds an lower bound constraint on the variable at the given index.
(Inherited from BoundedVariableProblem) | |

AddLowerBound(Int32, Double, Double) |
Adds an lower bound constraint on the variable at the given index.
(Inherited from BoundedVariableProblem) | |

AddLowerBoundConstraint(DoubleVector, Double) |
Adds a linear inequality constraint of the form
coefficients'x >= lowerBound
(Inherited from LinearConstrainedProblem) | |

AddLowerBoundConstraint(ILinearConstraintCoefficients, Double) |
Adds a linear inequality constraint of the form
coefficients'x >= lowerBound
(Inherited from LinearConstrainedProblem) | |

AddLowerBoundConstraint(DoubleVector, Double, Double) |
Adds a linear inequality constraint of the form
coefficients'x >= lowerBound
(Inherited from LinearConstrainedProblem) | |

AddLowerBoundConstraint(ILinearConstraintCoefficients, Double, Double) |
Adds a linear inequality constraint of the form
coefficients'x >= lowerBound
(Inherited from LinearConstrainedProblem) | |

AddUpperBound(Int32, Double) |
Adds an upper bound constraint on the variable at the given index.
(Inherited from BoundedVariableProblem) | |

AddUpperBound(Int32, Double, Double) |
Adds an upper bound constraint on the variable at the given index.
(Inherited from BoundedVariableProblem) | |

AddUpperBoundConstraint(DoubleVector, Double) |
Adds a linear inequality constraint of the form
coefficients'x <= upperBound
(Inherited from LinearConstrainedProblem) | |

AddUpperBoundConstraint(ILinearConstraintCoefficients, Double) |
Adds a linear inequality constraint of the form
coefficients'x <= upperBound
(Inherited from LinearConstrainedProblem) | |

AddUpperBoundConstraint(DoubleVector, Double, Double) |
Adds a linear inequality constraint of the form
coefficients'x <= upperBound
(Inherited from LinearConstrainedProblem) | |

AddUpperBoundConstraint(ILinearConstraintCoefficients, Double, Double) |
Adds a linear inequality constraint of the form
coefficients'x <= upperBound
(Inherited from LinearConstrainedProblem) | |

CheckVariableIndex |
Checks that the given variable array index is valid.
(Inherited from LinearProgrammingProblem) | |

Clone | Returns a deep copy of self. | |

EvaluateConstraints |
Evaluates each of the constraints at the specified point and
returns the results.
(Inherited from LinearConstrainedProblem) | |

GetIntegrality | Gets the integral constraint state of the variable at the given zero based index. | |

PointIsFeasible(DoubleVector) |
Function for determining the feasibility of a give point. A point
x is feasible if it satisfies all variable bounds, linear
and integral constraints.
(Overrides LinearConstrainedProblemPointIsFeasible(DoubleVector)) | |

PointIsFeasible(DoubleVector, Double) |
Function for determining the feasibility of a give point. A point
x is feasible if it satisfies all variable bounds, linear
and integral constraints.
(Overrides LinearConstrainedProblemPointIsFeasible(DoubleVector, Double)) | |

SetIntegrality | Sets an integrality constraint for the variable with the given zero based index. | |

ToString |
Creates a string representation of the problem.
(Overrides LinearProgrammingProblemToString) |

Fields

Name | Description | |
---|---|---|

constraints_ |
Problem constraints.
(Inherited from LinearConstrainedProblem) | |

variableBounds_ |
Map containing variable bounds. Key is the variable ID, the value is the bounds.
(Inherited from BoundedVariableProblem) |

Remarks

A mixed integer linear programming (LP) problem optimizes a linear objective function subject to
a set of linear constraints, and optionally subject to a set of variable bounds.
Some or all of the variables may further be constrained to have integral values.
For example:

See Also