- Procedure GMP::SolverSession::AddBendersFeasibilityCut(solverSession, GMP, solution, local, purgeable, tighten)
GMP::SolverSession::AddBendersFeasibilityCutgenerates a feasibility cut for a Benders’ master problem using the solution of a Benders’ subproblem (or the corresponding feasibility problem). The Benders’ master problem must be a MIP problem.
GMP::SolverSession::AddBendersFeasibilityCut( solverSession, ! (input) a solver session GMP, ! (input) a generated mathematical program solution, ! (input) a solution [local], ! (optional, default 0) a scalar binary expression [purgeable], ! (optional, default 0) a scalar binary expression [tighten] ! (optional, default 0) a scalar binary expression )
An element in the set
AllSolverSessionsrepresenting a solver session for the Benders’ master problem.
An element in the set
AllGeneratedMathematicalProgramsrepresenting a Benders’ subproblem.
An integer scalar reference to a solution of GMP2.
A scalar binary value to indicate whether the cut is valid for the local problem (i.e. the problem corresponding to the current node in the solution process and all its descendant nodes) only (value 1) or for the global problem (value 0).
A scalar binary value to indicate whether the solver is allowed to purge the cut if it deems it ineffective. If the value is 1, then it is allowed.
A scalar binary value to indicate whether the feasibility cut should be tightened. If the value is 1, tightening is attempted.
The procedure returns 1 on success, or 0 otherwise.
The generated mathematical program corresponding to the solverSession should have been created using the function
If the function
GMP::Benders::CreateSubProblemwas used to create a GMP representing the dual of the Benders’ subproblem then this GMP should be used as argument GMP2. If it represents the primal of the Benders’ subproblem then first the feasibility problem should be created which then should be used as argument GMP2.
The solution of the GMP is used to generate an optimality cut for the Benders’ master problem (represented by solverSession).
A feasibility cut \(a^T x \geq b\) can be tightened to \(1^T x \geq 1\) if \(x\) is a vector of binary variables and \(a_i \geq b > 0\) for all \(i\).
GMP::Benders::AddFeasibilityCutis called depends on whether the primal or dual of the Benders’ subproblem was generated. In the example below we use the dual. In that case an unbounded extreme ray is used to create a feasibility cut. In this example we solve only one Benders’ master problem (which is a MIP). During the solve, whenever the solver finds an integer (incumbent) solution we want to run a callback for lazy constraints. Therefore we install a callback for it.myGMP := GMP::Instance::Generated( MP ); gmpM := GMP::Benders::CreateMasterProblem( myGMP, AllIntegerVariables, 'BendersMasterProblem', 0, 0 ); gmpS := GMP::Benders::CreateSubProblem( myGMP, masterGMP, 'BendersSubProblem', useDual : 1, normalizationType : 0 ); GMP::Instance::SetCallbackAddLazyConstraint( gmpM, 'LazyCallback' ); ! Switch on solver option for calculating unbounded extreme ray. GMP::Instance::SetOptionValue( gmpS, 'unbounded ray', 1 ); GMP::Instance::Solve( gmpM );
The callback procedure
LazyCallbackhas one argument, namely
ThisSessionwhich is an element parameter with range
AllSolverSessions. Inside the callback procedure we solve the Benders’ subproblem. We assume that the Benders’ subproblem is always unbounded. The program status of the subproblem is stored in the element parameter
AllSolutionStates. Note that the subproblem is updated before it is solved.! Get MIP incumbent solution. GMP::Solution::RetrieveFromSolverSession( ThisSession, 1 ); GMP::Solution::SendToModel( gmpM, 1 ); GMP::Benders::UpdateSubProblem( gmpS, gmpM, 1, round : 1 ); GMP::Instance::Solve( gmpS ); ProgramStatus := GMP::Solution::GetProgramStatus( gmpS, 1 ) ; if ( ProgramStatus = 'Unbounded' ) then GMP::SolverSession::AddBendersFeasibilityCut( ThisSession, gmpF, 1 ); endif;
In this example we skipped the check for optimality of the Benders’ decomposition algorithm.