Inter-particle communication and search-dynamics of lbest particle swarm optimizers: An analysis

Particle Swarm Optimization (PSO) is arguably one of the most popular nature-inspired algorithms for real parameter optimization at present. The existing theoretical research on PSO focuses on the issues like stability, convergence, and explosion of the swarm. However, all of them are based on the gbest (global best) communication topology, which usually is susceptible to false or premature convergence over multi-modal fitness landscapes. The present standard PSO (SPSO 2007) uses an lbest (local best) topology, where a particle is stochastically attracted not towards the best position found in the entire swarm, but towards the best position found by any particle in its topological neighborhood. This article presents a first step towards a probabilistic analysis of the particle interaction and information exchange in an lbest PSO with variable random neighborhood topology (as found in SPSO 2007). It addresses issues like the distribution of particles over neighborhoods, the probability distributions of the social and cognitive terms in lbest model, and the explorative power of the lbest PSO. It also presents a state-space model of the lbest PSO and draws important conclusions regarding the stability and convergence of the particle dynamics in the light of control theory.