Hot off the Press: Finding e-locally Optimal Solutions for Multi-objective Multimodal Optimization

Rodriguez-Fernandez, Angel E.; Schäpermeier, Lennart; Hernández, Carlos; Kerschke, Pascal; Trautmann, Heike; Schütze, Oliver

Abstract

Here we briefly summarize the main findings of the above men-tioned paper by Rodriguez-Fernandez et al., 2024 [4]. In this work, the authors address the problem of computing all locally optimal solutions of a given multi-objective problem whose images are suffi-ciently close to the Pareto front. Such e-locally optimal solutions are particularly interesting in the context of multi-objective multimodal optimization (MMO). To this end, first a new set of interest, LQϵ, epsilon, is defined. Second, a new unbounded archiver, Archive UpdateLQϵ , epsilon is proposed that aims to capture this set in the limit. Third, several MOEAs are equipped with ArchiveUpdate LQϵ epsilon as external archiver and compared to their archive-free counterparts on selected bench-mark problems. Finally, in order to make a fair comparison of the outcomes in particular for MOPs with a larger number of decision variables, a new performance indicator, I EDR is proposed and used.