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

TL;DR

This paper investigates how multiobjectivization can improve the optimization of single-objective problems by analyzing multi-objective landscapes and demonstrating the effectiveness of the MOGSA algorithm in overcoming local optima.

Contribution

It introduces a visualization technique for multi-objective landscapes and empirically shows that MOGSA outperforms Nelder-Mead on several benchmark functions.

Findings

MOGSA exploits multi-objective landscape properties to escape local traps.

Multi-objectivization enhances global optimization performance.

MOGSA outperforms Nelder-Mead on COCO benchmark functions.

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.