Parameter selection in particle swarm optimisation from stochastic stability analysis

Abstract

Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical systems (RDS) which, due to the quasi-linear swarm dynamics, yields exact analytical results for the stability properties in the single particle case. The calculated stability region in the parameter space extends beyond the region determined by earlier approximations. This is also evidenced by simulations which indicate that the algorithm performs best in the asymptotic case if parameterised near the margin of instability predicted by the RDS approach.