Partitioning methods for pruning the Pareto set with application to multiobjective allocation of a cross-trained workforce

- Allocation of a cross-trained workforce is posed as a multiobjective optimization problem.
- Variance-to-range normalization of the objective function is recommended.
- Four partitioning approaches for Pareto set reduction (PSR) are compared.
- p-median partitioning has several advantages as a method for PSR.
- Maximum split partitioning can effectively augment p-median partitioning for PSR.

The Pareto (or nondominated set) for a multiobjective optimization problem is often of nontrivial size, and the decision maker may have a difficult time establishing objective criterion weights to select a solution. In light of these issues, clustering or partitioning methods can be of considerable value for pruning the Pareto set and limiting the decision to a few choice exemplars. A three-stage approach is proposed. In stage one, a variance-to-range measure is used to normalize the criterion function values. In stage two, maximum split partitioning and p-median partitioning are each applied to the normalized measures, thus producing two partitions of the Pareto set and two sets of exemplars. Finally, in stage three, the union of the exemplars obtained by the two partitioning methods is accepted as the final set of exemplars. The partitioning methods are compared within the context of multiobjective allocation of a cross-trained workforce to achieve both operational and human resource objectives.