Procedure GMP::Benders::UpdateSubProblem(GMP1, GMP2, solution, round)

GMP::Benders::UpdateSubProblem

The procedure GMP::Benders::UpdateSubProblem updates a Benders’ subproblem (or the corresponding feasibility problem) using the solution of a Benders’ master problem. This procedure is typically used in a Benders’ decomposition algorithm.

GMP::Benders::UpdateSubProblem(
     GMP1,             ! (input) a generated mathematical program
     GMP2,             ! (input) a generated mathematical program
     solution,         ! (input) a solution
     [round]           ! (optional, default 0) a scalar value
)

Arguments

GMP1

An element in the set AllGeneratedMathematicalPrograms representing a Benders’ subproblem.

GMP2

An element in the set AllGeneratedMathematicalPrograms representing a Benders’ master problem.

solution

An integer scalar reference to a solution of GMP2.

round

A binary scalar indicating whether the level values of the integer variables (if any) should be rounded to the nearest integer value in the solution used to update the subproblem.

Return Value

The procedure returns 1 on success, or 0 otherwise.

Note

• The GMP1 should have been created using the function GMP::Benders::CreateSubProblem or the function GMP::Instance::CreateFeasibility.

• The GMP2 should have been created using the function GMP::Benders::CreateMasterProblem.

• The solution of the Benders’ master problem (represented by GMP2) is used to update the Benders’ subproblem (represented by GMP1). That is, the right-hand-side values of the constraints in the subproblem are reevaluated using the level values of the variables in the solution of the Benders’ master problem.

Example

Before solving the subproblem it should be updated using a solution of the master problem. In the example below we use the solution at position 1 in the solution repository of the GMP belonging to the master problem.

myGMP := GMP::Instance::Generated( MP );

gmpM := GMP::Benders::CreateMasterProblem( myGMP, AllIntegerVariables,
                                           'BendersMasterProblem', 0, 0 );

gmpS := GMP::Benders::CreateSubProblem( myGMP, masterGMP, 'BendersSubProblem',
                                        0, 0 );

GMP::Instance::Solve( gmpM );

GMP::Benders::UpdateSubProblem( gmpS, gmpM, 1, round : 1 );

GMP::Instance::Solve( gmpS );

See also

The functions GMP::Benders::CreateMasterProblem, GMP::Benders::CreateSubProblem and GMP::Instance::CreateFeasibility.