Particle Swarm Optimization and L´evy Flight integration

Abstract

Particle Swarm Optimization (PSO) is a well-known and popular stochastic optimization method. The Lévy Flight (LF) properties were used to improve the canonical PSO known as premature convergence. The Lévy Flight was applied to change each particle walk on the fitness landscape. We analyze the literature modifications that concluded that Levy flight improved the PSO providing better search space exploration. Based on this conclusion, we propose new approaches to integrate Lévy Flight with PSO by changing initial points in the search space and learning strategies as inertia and constriction coefficients. We use seven standard test functions for an experimental evaluation and scores based on ranking to compare PSO variants. The ranked benchmarks were average performance, standard deviation, and best and worst found solutions obtained from multiple trials. The main contributions are a systematic overview of LF modifications applied in PSO and three new LF applications in canonical PSO procedure. The new approaches are swarm initialization based on LF, lower dimension LF inertia coefficient, and LF-based constriction factor. Another contribution is numerical evaluations on various benchmark functions with diverse characteristics. Two of the proposed modifications performed better or equal, and the third was only 2% worse than the best canonical PSO from the trial.