Dispersion and velocity indices for observing dynamic behavior of particle swarm optimization

A better balance of exploitation and exploration of solution space by the swarm is often mentioned as the key to a good performance of Particle Swarm Optimization (PSO) algorithm. Traditionally, the balance of exploitation and exploration ability of a PSO algorithm is usually shown empirically by the final result of the algorithm over some benchmark functions and not by the dynamic behavior of the swarm during the iteration process. In order to observe the dynamic behavior of the swarm in a PSO algorithm in details, two measurement indices, Dispersion Index and Velocity Index, are proposed. In an empirical study, these indices are embedded in two PSO Algorithms and applied to six benchmark problems. The results of this study indicate that a good balance between exploration and exploitation does lead to a better PSO. This balance could be achieved by allowing enough time or iteration step for both exploration and exploitation processes to take place. Finally, the utilization of these indices to balance strategy for exploitation and exploration on the PSO is discussed. It is also suggested that the velocity index can be used as a basis for controlling the length of iteration step of PSO algorithm.