Analysis of particle trajectories and monitoring velocity behavior in particle swarm optimization

Particle swarm optimization (PSO) is motivated by the social behavior of individual in a group. The trajectory of the particles in PSO show that a particle catches a wave during the search. This paper analyzes the trajectory of a particle in PSO with and without construction coefficient. The particles follow the path defined by sinusoidal wave while amplitude and frequency are random. The paper considers multidimensional and multi particle swarm. The paper provides a derivation of the closed from of PSO with constriction coefficient.