Averaged Hausdorff Approximations of Pareto Fronts based on Multiobjective Estimation of Distribution Algorithms

TL;DR

This paper introduces a postprocessing method that uses the averaged Hausdorff indicator to select a uniformly distributed subset of solutions from the archive of multiobjective estimation of distribution algorithms, improving Pareto front approximation.

Contribution

It proposes a novel postprocessing strategy applying the averaged Hausdorff indicator to enhance the uniformity of Pareto front approximations in MEDAs.

Findings

Improved uniformity in Pareto front approximations.

Effective selection of nondominated solutions from archives.

Enhanced quality of multiobjective optimization results.

Abstract

In the a posteriori approach of multiobjective optimization the Pareto front is approximated by a finite set of solutions in the objective space. The quality of the approximation can be measured by different indicators that take into account the approximation's closeness to the Pareto front and its distribution along the Pareto front. In particular, the averaged Hausdorff indicator prefers an almost uniform distribution. An observed drawback of multiobjective estimation of distribution algorithms (MEDAs) is that - as common for randomized metaheuristics - the final population usually is not uniformly distributed along the Pareto front. Therefore, we propose a postprocessing strategy which consists of applying the averaged Hausdorff indicator to the complete archive of generated solutions after optimization in order to select a uniformly distributed subset of nondominated solutions from the archive. In this paper, we put forward a strategy for extracting the above described subset. The effectiveness of the proposal is contrasted in a series of experiments that involve different MEDAs and filtering techniques.