Niching Diversity Estimation for Multi-modal Multi-objective Optimization

TL;DR

This paper introduces a niching mechanism to improve diversity estimation in multi-modal multi-objective optimization, enhancing the performance of algorithms like SPEA2 and NSGA-II on complex problems.

Contribution

A novel niching diversity estimation method tailored for MMOPs, integrated into existing algorithms to better handle equivalent solutions in decision space.

Findings

Enhanced diversity preservation in MMOPs

Improved performance of SPEA2 and NSGA-II with the proposed method

Significant performance gains demonstrated in experiments

Abstract

Niching is an important and widely used technique in evolutionary multi-objective optimization. Its applications mainly focus on maintaining diversity and avoiding early convergence to local optimum. Recently, a special class of multi-objective optimization problems, namely, multi-modal multi-objective optimization problems (MMOPs), started to receive increasing attention. In MMOPs, a solution in the objective space may have multiple inverse images in the decision space, which are termed as equivalent solutions. Since equivalent solutions are overlapping (i.e., occupying the same position) in the objective space, standard diversity estimators such as crowding distance are likely to select one of them and discard the others, which may cause diversity loss in the decision space. In this study, a general niching mechanism is proposed to make standard diversity estimators more efficient when handling MMOPs. In our experiments, we integrate our proposed niching diversity estimation method into SPEA2 and NSGA-II and evaluate their performance on several MMOPs. Experimental results show that the proposed niching mechanism notably enhances the performance of SPEA2 and NSGA-II on various MMOPs.