Particle swarm optimization: surfing the waves

A new optimization method has been proposed by J. Kennedy and R.C. Eberhart (1997; 1995), called Particle Swarm Optimization (PSO). This approach combines social psychology principles and evolutionary computation. It has been applied successfully to nonlinear function optimization and neural network training. Preliminary formal analyses showed that a particle in a simple one-dimensional PSO system follows a path defined by a sinusoidal wave, randomly deciding on both its amplitude and frequency (Y. Shi and R. Eberhart, 1998). The paper takes the next step, generalizing to obtain closed form equations for trajectories of particles in a multi-dimensional search space.