Solving multiple objective problems

Explains how to solve a multiple objective problem.

The CPLEX multiobjective optimization algorithm sorts the objectives by decreasing priority value. If several objectives have the same priority, they are blended in a single objective using the weight attributes provided. As a result, CPLEX constructs a sorted list of objectives (or blended objectives), each with a unique priority. CPLEX can then proceed to find the lexicographically minimal (or maximal) solution for this order.

To obtain this solution, each objective is optimized in turn by decreasing order of the priority value in a hierarchical manner. Whenever the optimal solution for an objective (or blended objective) is found, CPLEX imposes that, for the remaining (lower priority) objectives, the only solutions considered are those that are also optimal for the previously (higher priority) optimized objectives.

The two attributes AbsTol and RelTol relax the requirement that in each step the objective is optimized among the solutions that are optimal to the previous optimization problems. More precisely, for each objective AbsTol and RelTol specify, in absolute and relative terms, the maximum deviations allowed from the optimal value of that objective.