Multimodal Optimization Using a Biobjective Differential Evolution Algorithm Enhanced With Mean Distance-Based Selection

TLDR: Experimental results supported by nonparametric statistical tests suggest that MOBiDE is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.

Abstract: In contrast to the numerous research works that integrate a niching scheme with an existing single-objective evolutionary algorithm to perform multimodal optimization, a few approaches have recently been taken to recast multimodal optimization as a multiobjective optimization problem to be solved by modified multiobjective evolutionary algorithms. Following this promising avenue of research, we propose a novel biobjective formulation of the multimodal optimization problem and use differential evolution (DE) with nondominated sorting followed by hypervolume measure-based sorting to finally detect a set of solutions corresponding to multiple global and local optima of the function under test. Unlike the two earlier multiobjective approaches (biobjective multipopulation genetic algorithm and niching-based nondominated sorting genetic algorithm II), the proposed multimodal optimization with biobjective DE (MOBiDE) algorithm does not require the actual or estimated gradient of the multimodal function to form its second objective. Performance of MOBiDE is compared with eight state-of-the-art single-objective niching algorithms and two recently developed biobjective niching algorithms using a test suite of 14 basic and 15 composite multimodal problems. Experimental results supported by nonparametric statistical tests suggest that MOBiDE is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.