Empirical Study on the Benefits of Multiobjectivization for Solving Single-Objective Problems

Steinhoff Vera, Kerschke Pascal, Grimme Christian

Abstract
When dealing with continuous single-objective problems, multimodality poses one of the biggest difficulties for global optimization. Local optima are often preventing algorithms from making progress and thus pose a severe threat. In this paper we analyze how single-objective optimization can benefit from multiobjectivization by considering an additional objective. With the use of a sophisticated visualization technique based on the multi-objective gradients, the properties of the arising multi-objective landscapes are illustrated and examined. We will empirically show that the multi-objective optimizer MOGSA is able to exploit these properties to overcome local traps. The performance of MOGSA is assessed on a testbed of several functions provided by the COCO platform. The results are compared to the local optimizer Nelder-Mead.

Keywords
Single-Objective Optimization; Multimodality; Multiobjectivization; Continuous Optimization; Local Search