Chaotic particle swarm optimization and analysis

A single particle structure of the classical particle swarm optimization was analyzed which was found to have some properties of a Chaos-Hopfield neural network. A new model of the particle swarm optimization was proposed. The model is a deterministic Chaos-Hopfield neural network swarm which is different from the existing one with stochastic parameters. Its search orbits show an evolution process of inverse period bifurcation from chaos to periodic orbits then to sink. In this evolution process, the initial chaos-like search expands the optimal scope, and inverse period bifurcation determines the stability and convergence of the search. Moreover, the convergence is theoretically analyzed. Finally, the numerical simulation shows the difference between the chaotic particle swarm optimization and the classical particle swarm optimization; and it also demonstrates the efficiency of the presented technique.