Niching particle swarm optimization based on Euclidean distance and hierarchical clustering for multimodal optimization

Multimodal optimization is still one of the most challenging tasks in the evolutionary computation field, when multiple global and local optima need to be effectively and efficiently located. In this paper, a niching particle swarm optimization (PSO)-based Euclidean distance and hierarchical clustering (EDHC) for multimodal optimization is proposed. This technique first uses the Euclidean distance-based PSO algorithm to perform preliminarily search. In this phase, the particles are rapidly clustered around peaks. Secondly, hierarchical clustering is applied to identify and concentrate the particles distributed around each peak to finely search as a whole. Finally, a small-world network topology is adopted in each niche to improve the exploitation ability of the algorithm. At the end of this paper, the proposed EDHC-PSO algorithm is applied to the traveling salesman problems (TSP) after being discretized. The experiments demonstrate that the proposed method outperforms existing niching techniques on benchmark problems and is effective for TSP.