Stochastic approximation driven Particle Swarm Optimization

Particle Swarm Optimization (PSO) is attracting an ever-growing attention and more than ever it has found many application areas for many challenging optimization problems. In this paper, we draw the focus on a major drawback of the PSO algorithm: the poor gbest update. This can be a severe problem, which causes pre-mature convergence to local optima since gbest as the common term in the update equation of all particles, is the primary guide of the swarm. Therefore, we basically seek a solution for the social problem in PSO, i.e. “Who will guide the guide?” which resembles the rhetoric question posed by Plato in his famous work on government: “Who will guard the guards?” (Quis custodiet ipsos custodes?). Stochastic approximation (SA) is purposefully adapted into two approaches to guide (or drive) the gbest particle (with simultaneous perturbation) towards the right direction with the gradient estimate of the underlying surface (or function) whilst avoiding local traps due to its stochastic nature. We purposefully used simultaneous perturbation SA (SPSA) for its low cost and since SPSA is applied only to the gbest (not the entire swarm), both approaches have thus a negligible overhead cost over the entire PSO process. Yet we have shown over a wide range of non-linear functions that both approaches significantly improve the performance of PSO especially if the parameters of SPSA suits to the problem in hand.