Particle Swarm Optimization: dynamic system analysis for parameter selection in global optimization frameworks

In this paper we consider the evolutionary Particle Swarm Optimization (PSO) algorithm, for the minimization of a computationally costly nonlinear function, in global optimization frameworks. We study a reformulation of the standard iteration of PSO [KE95, CK02] into a linear dynamic system. Then, the latter is partially investigated in order to provide indications for the parameters selection in PSO. We carry out our analysis on a generalized PSO iteration, which includes the standard one proposed in the literature. In our scheme the path of any particle is possibly affected by the trajectories of all the other particles in the swarm. Then, for any particle we give indications on both the starting point and the trajectory, in terms of the PSO coefficients. We analyze the scheme assuming either deterministic and uniformly randomly distributed coefficients. Convergence analysis is partially provided.