Double-layer-clustering differential evolution multimodal optimization by speciation and self-adaptive strategies

Multimodal optimization aims to find and maintain as many global and local optima of a function as possible. Niching techniques based on multi-populations and clustering proved to be efficient for tackling multimodal optimization problems. The main focus of this work is to enhance the diversity of the population and improve the global search ability to locate more optima. A Double-Layer-Clustering Speciation Differential Evolution (DLCSDE) algorithm for multimodal optimization is proposed. We also show how the DLCSDE can be improved by integrating with a self-adaptive strategy to form the Self-adaptive DLCSDE (SDLCSDE). Based on speciation, first layer clustering divides the entire population into multiple subpopulations to locate global and local optima. The seeds from each species then form a sub-population to search globally during the second layer clustering to find peaks missed during the first layer clustering search process. To test the performance, both DLCSDE and SDLCSDE are compared with 17 state-of-art niching algorithms on 29 multimodal problems with different dimensions. The experiment results demonstrate that both the proposed algorithms outperform or perform comparably to the 17 niching algorithms on all the test functions.