Specifying multiple objective problems
Explains how to specify multiple objective problems.
Multiple objectives can be specified, both through LP and MPS input files, and
through the various APIs. Together with the linear form describing the objective function, each
objective has four attributes: priority, weight, absolute tolerance (AbsTol) and
relative tolerance (RelTol).
The attribute priority is used to order objectives by priority.
The weight is a scalar by which the objective coefficients are multiplied when forming a blended objective.
For a purely blended objective, each objective receives the same priority, and a (not necessarily unique) weight value. For a purely lexicographic objective, each objective receives a different priority that specifies the hierarchy of objective. Weights are not required, but a weight other than 1.0 can be used to rescale a particular objective. For a combination of blended and lexicographic objectives, the blending weights are applied separately to objectives with the same priority.
The absolute tolerance, AbsTol, is an amount by which the final returned
solution may deviate from the optimal value for this objective in absolute terms.
The relative tolerance, RelTol, is an amount by which the final returned
solution may deviate from the optimal value for this objective in relative terms.
AbsTol or RelTol
depends on whether the multiobjective problem is an LP or MIP, as will be explained in the section
Solving multiple objective problems.For more information, see Multiobjective optimization in LP file format and Multiobjective optimization in MPS files.