Procedure GMP::Column::SetAsMultiObjective(GMP, column, priority, weight, abstol, reltol)

# GMP::Column::SetAsMultiObjective

The procedure GMP::Column::SetAsMultiObjective sets a column as one of the multi-objectives of a generated mathematical program, thereby creating a multi-objective optimization problem.

Lexicographic (or hierarchical) multi-objective optimization will optimize for the different objectives in the mathematical program one step at a time, in priority order.
GMP::Column::SetAsMultiObjective(
GMP,            ! (input) a generated mathematical program
column,         ! (input) a scalar reference or column number
priority,       ! (input) a numerical expression
weight,         ! (input) a numerical expression
[abstol],       ! (input/optional) a numerical expression
[reltol]        ! (input/optional) a numerical expression
)


## Arguments

GMP

An element in AllGeneratedMathematicalPrograms.

column

A scalar reference to an existing column in the matrix or an element in the set Integers in the range $$\{ 0 .. n-1 \}$$ where $$n$$ is the number of columns in the matrix.

priority

A scalar value specifying the priority of the objective. An objective with the highest priority is considered first.

weight

A scalar value specifying the weight of the objective. It defines the weight by which the objective coefficients are multiplied when forming a blended objective, i.e., if multiple objectives have the same priority.

abstol

A scalar value specifying the absolute tolerance. In subsequent steps (for objectives with a lower priority) the solution value of column may deviate from the optimized value of column, as calculated in this step, using this absolute tolerance. The default value is 0.0.

reltol

A scalar value specifying the relative tolerance. In subsequent steps (for objectives with a lower priority) the solution value of column may deviate from the optimized value of column, as calculated in this step, using this relative tolerance. The default value is 0.0.

## Return Value

The procedure returns 1 on success, and 0 otherwise.

Note

• The column should be linear and have at exactly one coefficient in the matrix.

• The column should be free, i.e., not have a lower or upper bound.

• If GMP::Column::SetAsMultiObjective is called twice for the same column then only the information from the second call is used (and the information from the first call is ignored).

• Use the procedure GMP::Instance::DeleteMultiObjectives to delete all multi-objectives.

• Multi-objective optimization is only supported by CPLEX and Gurobi.

• If you specify $$n$$ different priorities then CPLEX or Gurobi will optimize the mathematical program $$n$$ times using different objectives (in priority order).

• During the solution process, you may prefer that optimization problems with different priorities are solved with different option settings. CPLEX and Gurobi make this possible by using parameter files. See the option Read Parameter File in the CPLEX Help or the Gurobi Help for more information.

• Multi-objective optimization is not supported for generated mathematical programs created by one of the following functions:

• GMP::Instance::GenerateRobustCounterpart,

• GMP::Instance::GenerateStochasticProgram,

• GMP::Instance::CreatePresolved,

• GMP::Instance::CreateDual, or

• GMP::Instance::CreateMasterMIP.

• The meaning of the relaxation of the objective, which is controlled by the abstol and reltol arguments, depends on whether the multi-objective problem is an LP or MIP. See the Multi-Objective Optimization section in the CPLEX Help or the Gurobi Help for more information.

• The abstol and reltol arguments are meaningless for the objective(s) with the lowest priority.

## Example

In the example below two multi-objectives are specified:

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

GMP::Column::SetAsMultiObjective( myGMP, TotalDist, 2, 1.0, 0, 0.1 );
GMP::Column::SetAsMultiObjective( myGMP, TotalTime, 1, 1.0, 0, 0.0 );

GMP::Instance::Solve( myGMP );


We can now switch the priorities of the two objectives by adding:

GMP::Column::SetAsMultiObjective( myGMP, TotalDist, 1, 1.0, 0, 0.1 );
GMP::Column::SetAsMultiObjective( myGMP, TotalTime, 2, 1.0, 0, 0.0 );

GMP::Instance::Solve( myGMP );