Multimodal LaF-CMA-ES algorithm based on homotopic convex transformation
Huan Liu, Jun Zhang · IET conference proceedings. · 2023
Multimodal optimization is a difficult problem in the field of evolutionary computation due to multiple attraction basins. The balance of exploration and exploitation is important to the performance of the algorithm in multimodal problems. In this paper, a novel algorithm, named KbP-LaF-CMAES, is proposed based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to cope with the multimodal optimization problem. Two strategies, the leader and follower (LaF) mechanism and the homotopic convex transformation mechanism, are introduced in the algorithm. In the first stage of the proposed algorithm, the LaF strategy is conducted to explore the search space in a vast domain. Two co-evolutionary populations, leaders and followers evolve synergistically. When the solutions are stalled in the first stage, the KbP strategy is performed to improve the ability of exploration. In the second stage of the proposed KbP-LaF-CMAES, two variants of the CMA-ES algorithm are adopted to exploit the specific domain-containing local optimum domain, which has a potential global optimum of the problem. Finally, the experimental results on the CEC benchmark show significant improvements in the performance of KbP-LaF-CMAES than other CMA-ES variants and SPSRDEMMS. The performance of the proposed KbP-LaF-CMAES is comparable with the EBO with CMAR.