The whale optimization algorithm (WOA) is a nature-inspired metaheuristic optimization algorithm, which was proposed by Mirjalili and Lewis in 2016. This algorithm has shown its ability to solve many problems. Comprehensive surveys have been conducted about some other nature-inspired algorithms, such as ABC and PSO. Nonetheless, no survey search work has been conducted on WOA. Therefore, in this paper, a systematic and meta-analysis survey of WOA is conducted to help researchers to use it in different areas or hybridize it with other common algorithms. Thus, WOA is presented in depth in terms of algorithmic backgrounds, its characteristics, limitations, modifications, hybridizations, and applications. Next, WOA performances are presented to solve different problems. Then, the statistical results of WOA modifications and hybridizations are established and compared with the most common optimization algorithms and WOA. The survey’s results indicate that WOA performs better than other common algorithms in terms of convergence speed and balancing between exploration and exploitation. WOA modifications and hybridizations also perform well compared to WOA. In addition, our investigation paves a way to present a new technique by hybridizing both WOA and BAT algorithms. The BAT algorithm is used for the exploration phase, whereas the WOA algorithm is used for the exploitation phase. Finally, statistical results obtained from WOA-BAT are very competitive and better than WOA in 16 benchmarks functions. WOA-BAT also outperforms well in 13 functions from CEC2005 and 7 functions from CEC2019.

<p>Note: This paper has been accepted by the journal of neural computing and applications.</p><p><br></p><p>A recent metaheuristic algorithm, such as Whale Optimization Algorithm (WOA), was proposed. The idea of proposing this algorithm belongs to the hunting behavior of the humpback whale. However, WOA suffers from poor performance in the exploitation phase and stagnates in the local best solution. Grey Wolf Optimization (GWO) is a very competitive algorithm comparing to other common metaheuristic algorithms as it has a super performance in the exploitation phase while it is tested on unimodal benchmark functions. Therefore, the aim of this paper is to hybridize GWO with WOA to overcome the problems. GWO can perform well in exploiting optimal solutions. In this paper, a hybridized WOA with GWO which is called WOAGWO is presented. The proposed hybridized model consists of two steps. Firstly, the hunting mechanism of GWO is embedded into the WOA exploitation phase with a new condition which is related to GWO. Secondly, a new technique is added to the exploration phase to improve the solution after each iteration. Experimentations are tested on three different standard test functions which are called benchmark functions: 23 common functions, 25 CEC2005 functions and 10 CEC2019 functions. The proposed WOAGWO is also evaluated against original WOA, GWO and three other commonly used algorithms. Results show that WOAGWO outperforms other algorithms depending on the Wilcoxon rank-sum test. Finally, WOAGWO is likewise applied to solve an engineering problem such as pressure vessel design. Then the results prove that WOAGWO achieves optimum solution which is better than WOA and Fitness Dependent Optimizer (FDO).</p>

This paper proposes a novel nature-inspired optimization algorithm called the Fox optimizer (FOX) which mimics the foraging behavior of foxes in nature when hunting prey. The algorithm is based on techniques for measuring the distance between the fox and its prey to execute an efficient jump. After presenting the mathematical models and the algorithm of FOX, five classical benchmark functions and CEC2019 benchmark test functions are used to evaluate its performance. The FOX algorithm is also compared against the Dragonfly optimization Algorithm (DA), Particle Swarm Optimization (PSO), Fitness Dependent Optimizer (FDO), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Chimp Optimization Algorithm (ChOA), Butterfly Optimization Algorithm (BOA) and Genetic Algorithm (GA). The results indicate that FOX outperforms the above-mentioned algorithms. Subsequently, the Wilcoxon rank-sum test is used to ensure that FOX is better than the comparative algorithms in s statistically significant manner. Additionally, parameter sensitivity analysis is conducted to show different exploratory and exploitative behaviors in FOX. The paper also employs FOX to solve engineering problems, such as pressure vessel design, and it is also used to solve electrical power generation: economic load dispatch problems. The FOX has achieved better results in terms of optimizing the problems against GWO, PSO, WOA, and FDO.

Fitness Dependent Optimizer (FDO) is a recent metaheuristic algorithm that mimics the reproduction behavior of the bee swarm in finding better hives. This algorithm is similar to Particle Swarm Optimization (PSO) but it works differently. The algorithm is very powerful and has better results compared to other common metaheuristic algorithms. This paper aims at improving the performance of FDO, thus, the chaotic theory is used inside FDO to propose Chaotic FDO (CFDO). Ten chaotic maps are used in the CFDO to consider which of them are performing well to avoid local optima and finding global optima. New technic is used to conduct population in specific limitation since FDO technic has a problem to amend population. The proposed CFDO is evaluated by using 10 benchmark functions from CEC2019. Finally, the results show that the ability of CFDO is improved. Singer map has a great impact on improving CFDO while the Tent map is the worst. Results show that CFDO is superior to GA, FDO, and CSO. Both CEC2013 and CEC2005 are used to evaluate CFDO.Finally, the proposed CFDO is applied to classical engineering problems, such as pressure vessel design and the result shows that CFDO can handle the problem better than WOA, GWO, FDO, and CGWO. Besides, CFDO is applied to solve the task assignment problem and then compared to the original FDO. The results prove that CFDO has better capability to solve the problem.

A recent metaheuristic algorithm, such as Whale Optimization Algorithm (WOA), was proposed. The idea of proposing this algorithm belongs to the hunting behavior of the humpback whale. However, WOA suffers from poor performance in the exploitation phase and stagnates in the local best solution. Grey Wolf Optimization (GWO) is a very competitive algorithm comparing to other common metaheuristic algorithms as it has a super performance in the exploitation phase while it is tested on unimodal benchmark functions. Therefore, the aim of this paper is to hybridize GWO with WOA to overcome the problems. GWO can perform well in exploiting optimal solutions. In this paper, a hybridized WOA with GWO which is called WOAGWO is presented. The proposed hybridized model consists of two steps. Firstly, the hunting mechanism of GWO is embedded into the WOA exploitation phase with a new condition which is related to GWO. Secondly, a new technique is added to the exploration phase to improve the solution after each iteration. Experimentations are tested on three different standard test functions which are called benchmark functions: 23 common functions, 25 CEC2005 functions and 10 CEC2019 functions. The proposed WOAGWO is also evaluated against original WOA, GWO and three other commonly used algorithms. Results show that WOAGWO outperforms other algorithms depending on the Wilcoxon rank-sum test. Finally, WOAGWO is likewise applied to solve an engineering problem such as pressure vessel design. Then the results prove that WOAGWO achieves optimum solution which is better than WOA and Fitness Dependent Optimizer (FDO).