Search Dynamics on Multimodal Multi-Objective Problems

Kerschke Pascal, Wang Hao, Preuss Mike, Grimme Christian, Deutz André, Trautmann Heike, Emmerich Michael

Abstract
We continue recent work on the definition of multimodality in multi-objective optimization (MO) and the introduction of a test-bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations for Exploratory Landscape Analysis (ELA) in MO.

Keywords
Multi-Objective Optimization; Multimodality; Landscape Analysis; Hypervolume Gradient Ascent; Set Based Optimization