Particle swarm optimization: surfing the waves

Abstract

A new optimization method has been proposed by Kennedy et. al. in [7, 8], called Particle Swarm Optimization (PSO). This approach combines social psychology principles in socio-cognition of human,(and artificial) agents and evolutionary computation. It has been successfully applied to nonlinear function optimization and neural network training. Preliminary formal analyses for a simple PSO system show that a particle in a simple PSO system follows a path defined by a sinusoidal wave, randomly deciding on both its amplitude and frequency [12]. This paper takes the next step, generalizing to obtain closed form equations for trajectories of particles in a multi-dimensional search space.