Adaptive memetic differential evolution with niching competition and supporting archive strategies for multimodal optimization

Multimodal optimization, which aims at locating multiple optimal solutions within the search space, is inherently a difficult problem. This work proposes an adaptive memetic differential evolution algorithm with niching competition and supporting archive strategies to tackle the problem. In the proposed algorithm, a niching competition strategy is designed to competitively employ niches according to their potentials by encouraging high potential niches for exploitation while low potential niches for exploration, thus appropriately searching the space to identify multiple optima. Further, a supporting archive strategy is devised and implemented at the niche level with a dual purpose of helping maintain potential optima as well as facilitate the evolution of population. In this strategy, the writing and reading of archive is implicitly implemented during evolution rather than requiring external rules. Additionally, an adaptive Cauchy-based local search scheme, which considers the possible locations of optima to implement the local search, is developed and incorporated into the proposed method to efficiently and properly improve niching seeds. The resulting algorithm has been evaluated with extensive experiments on benchmark functions as well as a robot kinematics problem and compared with related methods. The results show that our method is able to consistently and accurately locate multiple optima in the solution space, and outperform related methods.This work was supported in part by the National Natural Science Foundation of China under Grant 61873082, Grant 62003121 and Zhejiang Provincial Natural Science Foundation of China under Grant LQ20F030014