Evolutionary Multi - Modal Optimization Using Persistence-Based Clustering in Riemannian Manifolds

Xiang Meng, Yan Pei, Hideyuki Takagi

Abstract: This paper presents an innovative approach employing persistence-based clustering in Riemannian manifolds within evolutionary computation algorithms to address multi-modal optimization problems. The proposed framework is im-plemented and evaluated using the chaotic evolution algorithm. We introduce a novel algorithm named chaotic evolution with a clustering algorithm (CECA), which integrates the chaotic evolution characteristics from chaotic systems with the clustering method and Gaussian local search to solve multi-modal optimization problems. By leveraging chaotic dynamics, CECA enhances exploration and exploitation for efficient searching. Simultane-ously, it utilizes the clustering method to improve population diversity in the context of multi-modal optimization problems. The effectiveness and advantages of the proposed framework on the CECA algorithm are demonstrated through extensive experimental evaluations of various benchmark functions, in-cluding the Congress on Evolutionary Computation (CEC) con-ference functions. The experimental results indicate that the proposed framework exhibits distinct advantages in optimizing high-dimensional complex multi-modal functions. This study provides empirical evidence that persistence-based clustering in Riemannian manifolds constitutes an effective methodology for evolutionary multi-modal optimization.