Clustering and pattern search for enhancing particle swarm optimization with Euclidean spatial neighborhood search

There are many well-known particle swarm optimization (PSO) algorithms which consider ring/star/von Neumann et al. topological neighborhood and scarcely aim at Euclidean spatial neighborhood structure. k-Nearest Neighbors (k-NN) is a kind of clustering method to find the necessary representatives among a group of objects efficiently. Pattern search (PS) is a successful derivative-free coordinate search method for global optimization. All these observations inspire the innovative ideas to propose an enhanced particle swarm optimization algorithm (pkPSO). Particles efficiently explore for the promising areas and solutions with clustering on the Euclidean spatial neighborhood structure. Particle swarm continuously exploits at the just found promising areas with PS strategy at the latter stage of optimization. The cooperative effect of k-NN and PS strategies is firstly verified. Based on classical, rotated and shifted benchmarks, extensive experimental comparisons indicate that pkPSO has a competitive performance when comparing with the well-known PSO variants and other evolutionary algorithms.