Lévy Flight Distribution (LFD)

Lévy Flight Distribution: A new metaheuristic algorithm for solving engineering optimization problems

Abstract
In this paper, we propose a new optimization algorithm based on the L´evy flight called L´evy flight distribution (LFD) for solving real optimization problems. The LFD algorithm is inspired by the L´evy flight random walk for exploring unknown large search spaces (e.g., wireless sensor networks (WSNs)). To assess the performance of the LFD algorithm, various optimization testbed problems are considered, namely the congress on evolutionary computation (CEC) 2017 suite and three engineering optimization problems: tension/compression spring, the welded beam, and pressure vessel. The statistical simulation results revealed that the LFD algorithm provides better results with superior performance in most tests compared to several well-known metaheuristic algorithms such as simulated annealing (SA), differential evolution (DE), particle swarm optimization (PSO), elephant herding optimization (EHO), the genetic algorithm (GA), moth-flame optimization algorithm (MFO), whale optimization algorithm (WOA), grasshopper optimization algorithm (GOA), and Harris Hawks Optimization (HHO) algorithm. Furthermore, the performance of the LFD algorithm is tested on other different optimization problems of unknown large search spaces such as the area coverage problem in WSNs. The LFD algorithm shows high performance in providing a good deployment schema than energy-efficient connected dominating set (EECDS), A3, and CDS-Rule K topology construction algorithms for solving the area coverage problem in WSNs. Eventually, the LFD algorithm performs successfully achieving a high coverage rate up to 43.16 %, while the A3, EECDS, and CDS-Rule K algorithms achieve low coverage rates up to 40 % based on network sizes used in the simulation experiments. Also, the LFD algorithm succeeded in providing a better deployment schema than A3, EECDS, and CDS-Rule K algorithms and enhancing the detection capability of WSNs by minimizing the overlap between sensor nodes and maximizing the coverage rate.