Hybridizing Niching, Particle Swarm Optimization, and Evolution Strategy for Multimodal Optimization

Multimodal optimization problems (MMOPs) are common problems with multiple optimal solutions. In this article, a novel method of population division, called nearest-better-neighbor clustering (NBNC), is proposed, which can reduce the risk of more than one species locating the same peak. The key idea of NBNC is to construct the raw species by linking each individual to the better individual within the neighborhood, and the final species of the population is formulated by merging the dominated raw species. Furthermore, a novel algorithm is proposed called NBNC-PSO-ES, which combines the advantages of better exploration in particle swarm optimization (PSO) and stronger exploitation in the covariance matrix adaption evolution strategy (CMA-ES). For the purpose of demonstrating the performance of NBNC-PSO-ES, several state-of-the-art algorithms are adopted for comparisons and tested using typical benchmark problems. The experimental results show that NBNC-PSO-ES performs better than other algorithms.