Convergence and Boundary Estimation of the Particle Dynamics in Generalized Particle Swarm Optimization

Concept of the particle swarms emerged from a simulation of the collective behavior of social creatures and gradually evolved into a powerful global optimization technique, now well-known as the Particle Swarm Optimization (PSO). A vast amount of analytical studies on various aspects of the PSO dynamics like stability, convergence, explorative power, sampling distribution and so on can be found in the literature. The boundary of the swarm is still as a challenging research interest. The upper boundary restricts the swarm members within a sub-region of the whole search space. Higher the upper boundary, higher is the diversity. This paper investigates mainly the diversity of the swarm in terms of the upper boundary of the swarm.