Lévy flight PSO

The particle swarm optimization (abbr. PSO) is classified into one of meta-heuristics, it mimics the behavior of swarm intelligence of school of fish and flock of birds. Since the PSO is a simple algorithm, the implementation is easy. Also, the PSO does not require the gradient of the objective function. Therefore, the PSO can apply to various optimization applications. The PSO has two important control parameters: an inertia coefficient and an acceleration parameter. Especially, the inertia coefficient controls the convergence property. In order to improve the performance of the solution search ability, various kinds of control methods for the inertia coefficient are proposed. In this article, we propose a novel PSO that Lévy flight is applied to the inertia coefficient. The novel PSO is named Lévy flight PSO (abbr. Lévy-PSO). In order to confirm the performance of Lévy-PSO, we carry out some numerical simulations by using well-known benchmark function. The numerical simulation results indicate that the heavy-tailed of Lévy distribution is important to improve the search performance of Lévy-PSO.