INTRODUCTION

The whale optimization algorithm (WOA) was proposed by Mirjalili and Lewis in 2016. It is a new swarm intelligence optimization algorithm that simulates humpback whale hunting behavior. The main idea of the algorithm is to solve the target problem by imitating the whale’s predatory behavior. Since its introduction, the WOA has been favored by many scholars, and it has been widely used in optimal allocation of water resources , optimal control , and feature selection. But as a swarm intelligence optimization algorithm, like DE, PSO, ACO, and other algorithms, they all have the shortcomings of slow convergence and easy to fall into local optimum. *erefore, in practical applications, various improvements have been made to the standard algorithms, such as. Terefore, for the WOA algorithm, in recent years, many scholars have made a lot of improvements in improving algorithm convergence speed and optimization accuracy. For example, Abdel-Basset et al. used Levy flight and logical chaos ´ mapping to replace and determine the coefficient vector C and switching probability P in the WOA, proposed an improved whale optimization algorithm (IWOA), and verified the effectiveness of the proposed algorithm through experiments.

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Related Research Work

Constrained optimization problems (Cops) are a type of nonlinear programming problems that often occur in the fields of daily life and engineering applications. *ere are usually two ways to solve this problem: deterministic algorithm and random algorithm. Deterministic algorithms generally have high initial requirements, and they are generally unable to solve some problems that are not derivable, the feasible region is not connected, or there is no obvious mathematical expression. Even if some problems can be solved, the solutions obtained are mostly local optimal solutions. The random algorithm is a swarm intelligence optimization algorithm that has emerged in recent years; it has obtained a lot of research in solving constrained optimization problems. Chen and Huo proposed to use an improved GA to solve the Cops; this method used floating-point encoding; they also improved the genetic mutation operator and termination criterion. Long and Zhang proposed an improved bat algorithm for solving Cops. This method used the good point set method to construct the initial population to maintain population diversity and also used inertial weights to improve the performance of the algorithm. An improved particle swarm optimization algorithm for solving Cops was proposed by Mi Yong and Gao. This method used the penalty function method to treat constrained optimization problems as unconstrained optimization problems and used feasible basis rules to update individual and global extreme values. Lei et al. proposed a new empire competition algorithm to solve the Cops and used the lexicographic method to simultaneously optimize the objective function of the problem and the degree of constraint violation. Long et al. proposed the firefly algorithm to solve the constrained optimization problem. The algorithm used chaotic sequences to initialize the firefly position and introduced a dynamic random local search to speed up the convergence of the algorithm.

Inspiration of the algorithm:

Whale optimization algorithm (WOA): A nature inspired meta-heuristic optimization algorithm which mimics the hunting behaviour of humpback whales. The algorithm is inspired by the bubble-net hunting strategy

Foraging behavior of Humpback whales is called bubble-net feeding method. Humpback whales prefer to hunt school of krill or small fishes close to the surface. It has been observed that this foraging is done by creating distinctive bubbles along a circle or ‘9’-shaped path as shown in Fig.

Two maneuvers associated with bubble net feeding are ‘upward-spirals’ and ‘double-loops’.

In ‘upward-spirals’ maneuver humpback whales dive around 12 m down and then start to create bubble in a spiral shape around the prey and swim up toward the surface.
‘double-loops’ maneuver includes three different stages: coral loop, lobtail, and capture loop