Procedure GMP::Column::SetDecomposition(GMP, column, value)

GMP::Column::SetDecomposition

The procedure GMP::Column::SetDecomposition can be used to specify a decomposition to be used by a solver. It changes the decomposition value of a single column in the generated mathematical program.

This procedure can be used to specify a decomposition for the Benders algorithm in CPLEX by assigning the columns to the master problem or a subproblem. It can also be used to specify a decompostion for ODH-CPLEX. And it can be used to specify a partition for GUROBI to be used by its partition heuristic.

GMP::Column::SetDecomposition(
     GMP,            ! (input) a generated mathematical program
     column,         ! (input) a scalar reference or column number
     value           ! (input) a numerical expression
     )

Arguments

GMP

An element in AllGeneratedMathematicalPrograms.

column

A scalar reference to an existing column in the matrix or the number of that column in the range \(\{ 0 .. n-1 \}\) where \(n\) is the number of columns in the matrix.

value

The decomposition value assigned to the column.

Return Value

The procedure returns 1 on success, and 0 otherwise.

Note

  • Use GMP::Column::SetDecompositionMulti if the decomposition value of many columns corresponding to some variable have to be set, because that will be more efficient.

  • This procedure can be used to specify the decomposition in the Benders algorithm of CPLEX. See the CPLEX option Benders strategy for more information.

  • For CPLEX, use a value of 0 to assign a column to the master problem, and a value between 1 and \(N\) to assign a column to one of the \(N\) subproblems (\(N\) can be 1 if you only want to use one subproblem). A value of -1 indicates that the column is not assigned to the master problem or a subproblem.

  • This procedure can be used to specify model structure or a decomposition used by ODH-CPLEX.

  • For ODH-CPLEX, use a value between 1 and \(N\) to assign a column to one of the \(N\) subproblems. A value of 0 or lower indicates that the column is not assigned to any subproblem.

  • This procedure can be used to specify a partition used by the partition heuristic of GUROBI 8.0 or higher. See the GUROBI option Partition heuristic for more information.

  • For GUROBI, use a positive value to indicate that the column should be included when the correspondingly numbered sub-MIP is solved, a value of 0 to indicate that the column should be included in every sub-MIP, and a value of -1 to indicate that the column should not be included in any sub-MIP. (Variables that are not included in the sub-MIP are fixed to their values in the current incumbent solution.)

  • This procedure is not used by the Automatic Benders’ Decomposition module in AIMMS.

Example

The first example shows how to specify a decomposition for the Benders algorithm in CPLEX. The integer variable IntVar is assigned to the master problem while the continuous variable ContVar is assigned to the subproblem.

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

! Switch on CPLEX option for using Benders strategy with decomposition specified by user.
GMP::Instance::SetOptionValue( myGMP, 'benders strategy', 1 );

for (i) do
    GMP::Column::SetDecomposition( myGMP, IntVar(i), 0 );
endfor;

for (j) do
    GMP::Column::SetDecomposition( myGMP, ContVar(j), 1 );
endfor;

GMP::Instance::Solve( myGMP );

The second example shows how to specify model structure used by ODH-CPLEX. All columns X(i,j) and Y(i,j,k) with the same ‘i‘ are assigned to the same subproblem.

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

for (i,j) do
    GMP::Column::SetDecomposition( myGMP, X(i,j), Ord(i) );
endfor;

for (i,j,k) do
    GMP::Column::SetDecomposition( myGMP, Y(i,j,k), Ord(i) );
endfor;

GMP::Instance::Solve( myGMP );