BSO-CMA-ES: Brain Storm Optimization Based Covariance Matrix Adaptation Evolution Strategy for Multimodal Optimization

Abstract

Recently, covariance matrix adaption evolution strategy (CMA-ES) and its variants have achieved great success in the continuous unimodal optimization tasks owing to its strong local search capabilities. However, it is precisely this capability that reduces the population diversity, which makes it unable to obtain the good performance on the multimodal optimization problems (MMOPs) aiming at locating all global optimal solutions during a single algorithm run. To address this problem, we first propose a swarm learning framework which is capable of collaboratively training multiple optimization algorithms (e.g., CMA-ES in this paper). Specifically, it introduces two objectives including individual objective and neighbor objective to balance the exploitation and exploration. The former guides each algorithm to locate at least one global optimal solution (exploitation), and the latter aims at maintaining the diversity of the different algorithms (exploration). Based on this framework, the brain storm optimization (BSO) is incorporated with multiple CMA-ES models, called BSO-CMA-ES, which makes the multiple CMA-ESs be collaboratively trained. To validate the effectiveness of the proposed method, several comparison algorithms are adopted and tested on typical MMOPs benchmark functions. Experimental results show that BSO-CMA-ES could obtain promising performance.