BBE: Basin-Based Evaluation of Multimodal Multi-objective Optimization Problems

Heins J, Rook J, Schäpermeier L, Kerschke P, Bossek J, Trautmann H

Abstract
In multimodal multi-objective optimization (MMMOO), the focus is not solely on convergence in objective space, but rather also on explicitly ensuring diversity in decision space. We illustrate why commonly used diversity measures are not entirely appropriate for this task and propose a sophisticated basin-based evaluation (BBE) method. Also, BBE variants are developed, capturing the anytime behavior of algorithms. The set of BBE measures is tested by means of an algorithm configuration study. We show that these new measures also transfer properties of the well-established hypervolume (HV) indicator to the domain of MMMOO, thus also accounting for objective space convergence. Moreover, we advance MMMOO research by providing insights into the multimodal performance of the considered algorithms. Specifically, algorithms exploiting local structures are shown to outperform classical evolutionary multi-objective optimizers regarding the BBE variants and respective trade-off with HV.

Keywords
Multi-objective optimization; Multimodality; Performance metric; Benchmarking; Continuous optimization; Anytime behavior