Decay rate andl2gain analysis for the particle swarm optimization algorithm
Yuji Wakasa, Kanya Tanaka, Takuya Akashi, Yûki Nishimura · Asian Journal of Control · 2010
Abstract The behavior of the particle swarm optimization (PSO) algorithm is analyzed by regarding its dynamics as a system with multiplicative noise and applying control‐theoretic analysis methods. In order to evaluate the convergence and diversity of the PSO algorithm, two new measures related to the decay rate andl2gain of the PSO dynamics are introduced. These measures are characterized by linear matrix inequalities and are therefore efficiently computed by convex optimization tools. Numerical experiments suggest that the measures are effective enough to evaluate the convergence and diversity of the PSO algorithm, which can lead to better understanding of the PSO algorithm from the viewpoints of exploitation and exploration abilities. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society