Impact of Lèvy Flight on Modern Meta-heuristic Optimizers

Research Abstract

In this paper, a variant based on Lèvy flight was proposed to enhance the performance of two recently proposed optimizers. The first optimizer used in the study is Sine-Cosine Algorithm (SCA) while the second is Whale Optimization Algorithm (WOA). Both optimizers are composed of two phases of random walks in each optimization iteration and both have stagnation and premature convergence problems. Lèvy flight is used to replace the walk based on cosine function in the SCA and the spiral motion in the WOA as well. The Lèvy-based search guarantees a fraction of solutions to be generated apart from the current best solution and hence tolerates for optimizer stagnation, premature convergence, and allows for local optima avoidance. A smooth control of the scale of the Lèvy random walk is also proposed to ensure a smooth adaptation of exploration to exploitation switching. The proposed variants, as well as the original algorithms, were benchmarked using a set of unimodal, multimodal, fixed-dimension multimodal and composite benchmark functions. The evaluation is performed using a set of assessment indicators and results prove the capability of the proposed variants to outperform the original optimizers.

Research Keywords

Whale optimization algorithm; Sine-cosine algorithm; Lèvy flight; Lèvy whale optimization algorithm; Lèvy sine-cosine algorithm