Multimodal Optimization by Speciation-Based Differential Evolution using Graphs with Stochastic Global and Local Searches and Crossover

Multimodal optimization is a very difficult task to search for all optimal solutions at once in optimization problems with multiple optimal solutions. Speciation using proximity graphs has been proposed for multimodal optimization. In multimodal optimization, it is necessary to first discover many candidates of optimal solutions by global search, and then to converge to optimal solutions using local search. In this study, the speciation-based differential evolution using graphs (SDE- G) is improved by introducing βRNG, a stochastic change from global search to local search, and a crossover operation. By using βRN G, it is possible to first discover many candidates of optimal solutions using the coarse graph, and to gradually narrow down the candidates using the dense graph. Since it is difficult to decide when to switch from global to local search, we propose a stochastic switch as the search progresses. Also, the crossover operation with adaptive crossover rate is proposed to generate new solutions by combining elements of good candidates. 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”.