New clustering method and its applications in multimodal optimization

This paper presents a new cluster analysis algorithm combined with fitness sharing genetic algorithm for solving multimodal optimization problems. The new algorithm maximizes the square sum of the inter-cluster distances to determine the cluster centers and minimizes the square sum of the inner-cluster distances to classify the individuals. The fitness of all individuals is also taken into account in determining the cluster center and individual clustering. After clustering all individuals, the fitness sharing genetic method is employed to find multiple peaks for the problem. Several tests on benchmark problems show that the proposed algorithm is more efficient with better search ability and less computational time than some existing methods.