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...