An Investigation on Particle Trajectories of PSO

Particle swarm optimization (PSO) is an effective robust and simple method to solve many problems proposed in science and engineering. How does the particle motion and how the particles in a swarm find the optimal solutions are an open problem. This paper investigates the particle trajectories for the standard PSO based on difference equations theories. Equilibrium point and asymptotically stable are used to study the particle trajectories. The theoretical analysis shows that the particle will just stop at the stable point with the proper PSO parameters.