# Pressure Vessel Design Problem Using Improved Gray Wolf Optimizer Based on Cauchy Distribution
###### Abstract
[22] proposed a nonlinear convergence factor and search mechanism so that, when hunting, the update of the wolf pack is not only affected by the three leading wolves but also by the position of the surrounding wolves. The optimization ability of the above improved GWO algorithm has been enhanced to some extent, but there are still some limitations. For example, [PERSON] [23] proposed an improved convergence factor, which improved the accuracy of the algorithm; however, the problem of insufficient diversity in the later stage remained. [PERSON] and [PERSON] [24] adopted Levi flight and greedy strategies, which can improve the ability of the GWO algorithm to jump out of the local optimum when solving many multimodal problems but did not accelerate the convergence speed. Based on the above shortcomings, this paper proposes a series of strategies to improve GWO based on the long tail property of Cauchy distribution. First, an initialization strategy that follows a Cauchy distribution is used to increase the diversity of the initial population. Secondly, a dynamic nonlinear inertia weighting strategy based on Cauchy distribution and logarithmic function is proposed to further improve the search performance of the algorithm. Finally, in the late iteration of the algorithm, the inertia weight is taken as the key index to measure mutation probability, and a Cauchy mutation operator is introduced to update the position to improve the population diversity and greatly improve the ability of the algorithm to jump out of the local optimum. The Cauchy distribution's introduction to GWO enhances the algorithm's global search ability, maintains diversity within the population, and provides a dynamic balance between exploration and exploitation, which, collectively, solve the issues of premature convergence and limited late-stage search diversity. Simulation results show that CGWO has great advantages in terms of solution accuracy, convergence speed, and stability. The quest for optimal solutions in diverse engineering design scenarios has long stood as a pivotal challenge in the realm of industrial production. With the ongoing evolution of optimization technology, significant advancements have been achieved in addressingcomplex, real-world engineering conundrums [25]. Furthermore, a plethora of novel optimization methodologies have been effectively integrated into a myriad of engineering design processes [26]. Among these, the design of pressure vessels is recognized as a quintessential problem [27], with the primary objective of minimizing overall design costs. In this context, selecting an optimization technique that aptly balances exploratory and developmental aspects, while, concurrently, circumventing local optima, is of paramount importance. This paper introduces the application of the newly proposed Cauchy Gray Wolf Optimizer (CGWO) algorithm to this specific design challenge. The results pertaining to pressure vessel design underscore the formidable potential of CGWO in navigating the complexities inherent in practical engineering issues, thereby heralding a novel avenue for resolving intricate challenges in engineering design optimization. The rest of the paper is structured as follows: Section 2 describes the related work. Section 3 describes the details of the proposed CGWO algorithm and the algorithm flow. Section 4 shows the results and analysis of the simulation experiments on 23 standard test functions. Section 5 implements CGWO to a fundamental engineering task: the design of pressure vessels. Section 6 provides the conclusions.