Adaptive particle swarm optimization

The Particle Swarm Optimization (PSO) method is one of the most powerful methods for solving unconstrained and constrained global optimization problems. Little is, however, known about how the PSO method works or finds a globally optimal solution of a global optimization problem when the method is applied to global optimization problems. This paper deals with the analysis of the dynamics of PSO in order to obtain an understanding about how it searches a globally optimal solution and a strategy about how to tune its parameters. While a generalized reduced model of PSO is proposed in order to analyze the dynamics of PSO, the stability analysis is carried out on the basis of both the eigenvalue analysis and some numerical simulations on a typical global optimization problem.