Clustering and differential evolution for multimodal optimization

Abstract

This paper presents a new differential evolution algorithm for multimodal optimization that uses self-adaptive parameter control, clustering and crowding methods. The algorithm includes a new clustering mechanism that is based on small subpopulations with the best strategy and, as such, improves the algorithm's efficiency. Each subpopulation is generated according to the best individual from a population that is not added to any other subpopulation. These small subpopulations are also used to determine population size and to replace ‘bad’ individuals. Because of the small subpopulation size and crowding mechanism, bad individuals prevent the best individuals from converging to the optimum. Therefore, the algorithm is trying to replace bad individuals with the individuals that are close to the best individuals. The population size expansion is used within the algorithm according to the number of generated subpopulations and located optima. The proposed algorithm was tested on benchmark functions for CEC'2013 special session and competition on niching methods for multimodal function optimization. The performance of the proposed algorithm was comparable with the state-of-the-art algorithms.