Analysis of dynamical characteristic of canonical deterministic PSO

A particle swarm optimization (PSO) system is one of the powerful systems for solving global optimization problems. The PSO algorithm can search an optimal value of a given evaluation function quickly compared with other proposed meta-heuristics algorithms. The conventional PSO system contains some random factors, therefore, the dynamics of the system can be regarded as stochastic dynamics. In order to analyze the dynamics rigorously, some papers pay attention to deterministic PSO systems which does not contain any stochastic factors. According to these results, the eigenvalues of the system impinge on the dynamics of the particles. Depending on the parameter, the searching ability of the deterministic PSO is decreased. Also, the eigenvalue is complex conjugate number, the system exhibits remarkable searching ability. In order to overcome this, we propose a canonical deterministic PSO which can control its eigenvalues easily, and can improve the searching ability. The dynamics of the system can characterize the damping factor and the rotation angle which can derive from its eigenvalue. We will confirm relation between these parameters and the searching ability of the optimal value from some numerical simulations.