Multimodal optimization by particle swarm optimization with graph-based speciation using \(\beta\)-relaxed relative neighborhood graph and seed-centered mutation

Multimodal optimization is a very difficult task to search for all optimal solutions at once in optimization problems with multiple optimal solutions. Speciation using a proximity graph has been proposed to solve multimodal optimization problems. Gabriel graph (GG) and relative neighborhood graph (RNG) are often used as the proximity graph. The search efficiency is good when GG is used, but the discovery rate of the optimal solutions is lower than when RNG is used. In this study, we propose a new proximity graph with a parameter \(\beta\) named “\(\beta\) relaxed relative neighborhood graph” (\(\beta\)RNG) that can be generated relatively fast and has intermediate properties between GG (\(\beta\)=1) and RNG (\(\beta\)=2). \(\beta\)RNG is adopted in speciation-based particle swarm optimization using graphs (SPSO-G) for graph-based speciation. Also, seed-centered mutation is introduced. The performance of the proposed method is shown by optimizing well-known benchmark problems for “CEC’2013 special session and competition on niching methods for multimodal function optimization”.