On Some Properties of the lbest Topology in Particle Swarm Optimization

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 is mostly based on the gbest (global best) particle 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 paper presents a first step towards a probabilistic analysis of the lbest PSO with variable random neighborhood topology by addressing issues like inter-particle interaction and probabilities of selection based on particle ranks.