Whale optimization algorithm based on nonlinear convergence factor and chaotic inertial weight

Abstract

The whale optimization algorithm (WOA) is a new biological meta-heuristic algorithm based on the social hunting behaviors of humpback whales. However, it can easily fall into a local optimum when solving complex problems and exhibits slow convergence speed and poor exploration. This study proposed three improved versions of the WOA based on the concepts of chaos initialization, nonlinear convergence factor, and chaotic inertial weight to enhance its exploration abilities. These properties were employed to improve the population diversity and maintain the balance between exploration and exploitation. The performance of the best version was compared with those of moth-flame optimization, firefly algorithm, particle swarm optimization, gray wolf optimizer, flower pollination algorithm, original WOA, and two recently proposed hybrid WOA through 19 benchmark functions. Experimental results indicated that the proposed algorithms exhibit better performance in terms of complexity and convergence speed. INDEX TERMS chaotic inertial weightconvergence factorcube mappingmeta-heuristic algorithmwhale optimization algorithm (WOA) 1 INTRODUCTION Meta-heuristic algorithms have the advantages of simplicity and easy implementation. They can effectively avoid falling into a local optima entrapment. They were developed to quickly solve large-scale and complex problems to obtain satisfactory solutions. 1 These algorithms are widely used in production scheduling, 2,3 signal processing, 4 image processing, 5 and dynamic optimization. 6 The idea of meta-heuristic algorithms originated from various biological mechanisms and physical laws. As an important concept of meta-heuristic algorithms, swarm intelligence algorithms obtain optimal solutions by iteratively updating the population. Representative swarm intelligence algorithms include particle swarm optimization (PSO) 7 which simulates the predatory behaviors of bird flocks; genetic algorithm (GA), 8 which simulate the natural evolution of Darwin's biological evolution theory and the genetic mechanism of biological evolution; ant colony optimization (ACO) algorithm, 9 which simulates ant foraging behaviors; artificial bee colony, 10 which simulates the bee collecting behavior; firefly algorithm (FA), 11 which simulates the glowing behavior of fireflies; and the bat algorithm, 12 which simulates the bat hunting behavior via ultrasound. The whale optimization algorithm (WOA) 13 is a new swarm intelligence algorithm proposed by an Australian scholar Mirjalili, inspired by the social behavior of humpback whales. The WOA determines the global optimum by encircling, searching, and attacking the preys. It has a simple principle, few parameter settings, and strong optimization ability; moreover, it successfully solved 29 mathematical and six structural optimization problems. 13 This algorithm has been successfully applied to tasks such as image segmentation, 14 optimized location, 15 and neural network training. 16 However, like other meta-heuristic optimization algorithms, the traditional WOA...

Chaos in metaheuristic based artificial intelligence algorithms: a short review

“…Of the studies with WO algorithm on Table 4: the study by Ding et al [46] using cubic map observes the highest success rate result, in comparison with Rosenbrock benchmark function; the study by Kaur and Arora [45] using logistic, tent and sine map observes the highest success rate result, in comparison with Rastrigin benchmark function; the studies by Kaur and Arora [45] using logistic, tent and sine map and Ding et al [46] using cubic map observe the highest success rate results, in comparison with Griewank benchmark function.…”

“…It was also compared with two recently proposed hybrid WOAs. Experimental results proved the proposed algorithms to perform better with regard to complexity and convergence speed [46]. Table 4 shows the comparison of two different WO algorithms including chaotic maps in common features.…”

“…Rastrigin Griewank Chaotic maps [45] mean ± std [46] mean ± std [45] mean ± std [46] mean ± std [45] mean ± std [46] mean ± std Three benchmark functions were used to measure the performance of WDO-modified cuckoo search (WDO-MCS) algorithm and to make comparisons between algorithms [48].…”

An Improved Gorilla Troops Optimizer Based on Lens Opposition-Based Learning and Adaptive β-Hill Climbing for Global Optimization

“…Jia et al [48] introduced the dynamic control parameter and mutation strategies into the Harris Hawks Optimization, and then proposed a novel method called DHHO/M to segment satellite images. Ding et al [49] constructed an improved Whale Optimization Algorithm (LNAWOA) for continuous optimization, in which the nonlinear convergence factor is utilized to speed up the convergence. Besides, authors in [50] employed Lévy flight and crossover operation to further promote the robust and global exploration capability of the native Salp Swarm Algorithm.…”

An advanced hybrid algorithm for nonlinear function optimization with real world applications

“…1 Presently, a bunch of optimization methods known as meta-heuristics algorithms (MAs) has been introduced to solve COPs, to overcome drawbacks of traditional optimization methods. According to mechanical differences the MAs can be categorized into four groups as follows: swarm intelligence algorithms (SIAs): inspired from behavior of social insects or animals like particle swarm optimization (PSO), 2 artificial bee colony (ABC), 3,4 animal migration optimization (AMO), 5 whale optimization algorithm (WOA), 6,7 social spider optimization (SSO), 8 chicken swarm optimization (CSO), 9 wind driven dragonfly algorithm (WDDA), 10 firefly algorithm (FA), 11 and so forth; evolutionary algorithms (EAs)-inspired from biology such as differential evolution (DE), 12 genetic algorithm (GA), 13 and so forth; physics based algorithms (PBAs): inspired by the rules governing a natural phenomenon like harmony search (HS), 14 gravitational search algorithm (GSA), 15 and so forth and human behavior based algorithms (HBAs): inspired from the human being like teaching-learning-based optimization (TLBO), 16 gaining sharing knowledge based Algorithm (GSK), 17 and so forth.…”