Towards Swarm Diversity: Random Sampling in Variable Neighborhoods Procedure Using a Lévy Distribution

Abstract

Particle Swarm Optimization (PSO) is a non-direct search method for numerical optimization. The key advantages of this metaheuristic are principally associated to its simplicity, few parameters and high convergence rate. In the canonical PSO using a fully connected topology, a particle adjusts its position by using two attractors: the best record stored for the current agent, and the best point discovered for the entire swarm. It leads to a high convergence rate, but also progressively deteriorates the swarm diversity. As a result, the particle swarm frequently gets attracted by sub-optimal points. Once the particles have been attracted to a local optimum, they continue the search process within a small region of the solution space, thus reducing the algorithm exploration. To deal with this issue, this paper presents a variant of the Random Sampling in Variable Neighborhoods (RSVN) procedure using a Lévy distribution, which is able to notably improve the PSO search ability in multimodal problems.