Stability analysis in consideration of random numbers for particle swarm optimization dynamics: The best parameter for sustainable search

Particle Swarm Optimization (PSO), which has attracted special interest as a global optimization method recently, has a drawback in that its sustainable search can not be executed until the end of computation. In order to endow global searching abilities to PSO, repetition of unstable and stable states of the particles is necessary. In this paper, based on stability analysis of PSO's model, with considering its random numbers, we realize sustainable search by choosing system parameters on boundary region between unstable and stable states, and then introduce an optimization model with global searching abilities as a revision of the conventional PSO.