Directional mutation and crossover for immature performance of whale algorithm with application to engineering optimization

Abstract

In recent years, a range of novel and pseudonovel optimization algorithms has been proposed for solving engineering problems. Swarm intelligence optimization algorithms (SIAs) have become popular methods, and the whale optimization algorithm (WOA) is one of the highly discussed SIAs. However, regardless of novelty concerns about this method, the basic WOA is a weak method compared to top differential evolutions and particle swarm variants, and it suffers from the problem of poor initial population quality and slow convergence speed. Accordingly, in this paper, to increase the diversity of WOA versions and enhance the performance of WOA, a new WOA variant, named LXMWOA, is proposed, and based on the Lévy initialization strategy, the directional crossover mechanism, and the directional mutation mechanism. Specifically, the introduction of the Lévy initialization strategy allows initial populations to be dynamically distributed in the search space and enhances the global search capability of the WOA. Meanwhile, the directional crossover mechanism and the directional mutation mechanism can improve the local exploitation capability of the WOA. To evaluate its performance, using a series of functions and three models of engineering optimization problems, the LXMWOA was compared with a broad array of competitive optimizers. The experimental results demonstrate that the LXMWOA is significantly superior to its exploration and exploitation capability peers. Therefore, the proposed LXMWOA has great potential to be used for solving engineering problems.