WSAR with Levy Flight for Constrained Optimization

Abstract

The Lévy distribution, which represents a form of random walk (Lévy flight) consisting of a series of consecutive random steps, has recently been demonstrated to improve the performance of metaheuristic algorithms. Through consecutive random steps, Lévy flight is particularly beneficial for undertaking massive “jump” operations that allow the search to escape from a local optimum and restart in a different region of the search space. We examine this concept in this work by applying Lévy flight to weighted superposition attraction–repulsion algorithm (WSAR), a basic but effective swarm intelligence optimization method that was recently introduced in the literature. The experiments are performed on several constrained design optimization problems. The performance of the proposed Levy flight WSAR algorithm is compared with several metaheuristics including harmony search algorithm (HS) and plain WSAR. The computational results revealed that Levy flight WSAR (LF-WSAR) is able to outperform the other algorithms. HS and WSAR show competitive performance with each other. In addition, performance of the LF-WSAR is statistically compared with other algorithms through nonparametric statistical tests. According to the statistical results, the difference between LF-WSAR and other algorithm is statistically significant.