Hot off the Press: Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal Optimization

Here we briefly summarize the main findings of the above mentioned 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 sufficiently close to the Pareto front. Such ϵ-locally optimal solutions are particularly interesting in the context of multi-objective multimodal optimization (MMO). To this end, first a new set of interest, LQ,ϵ, is defined. Second, a new unbounded archiver, ArchiveUpdateLQ,ϵ, is proposed that aims to capture this set in the limit. Third, several MOEAs are equipped with ArchiveUpdateLQ,ϵ as external archiver and compared to their archive-free counterparts on selected benchmark 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, IEDR, is proposed and used.