# Modified Grey Wolf Optimizer and Application in Parameter Optimization of PI Controller
## 1 Introduction  
Group-based metaheuristic solutions are widely recognized for their extensive applications in modern optimization tasks. Within these solutions, the search process is inherently collective. Algorithms are typically capped at a maximum number of iterations, beyond which they cease, having diligently sought the optimal solution for the group. Throughout these iterations, each participant within the group engages in ongoing searches, sharingpertinent information with peers to meet the defined objectives. This cooperative approach sets group-based metaheuristic solutions apart from their individual-based counterparts, as it facilitates a more effective search for optimal solutions. At present, several intelligent optimization algorithms have garnered significant attention in the field of computational intelligence. The popular intelligent optimization algorithms are the Grey Wolf Optimizer (GWO) [1], particle swarm optimization (PSO) [2] algorithm, Ant Lion optimization algorithm (ALO) [3], and Dragonfly algorithm (DA) [4]. These optimization algorithms have been integrated with a diverse array of problems, demonstrating their applicability across various domains. Among these algorithms, the Grey Wolf Optimization (GWO) algorithm, a member of the swarm intelligence optimization algorithms, has garnered substantial scholarly interest due to its rapid convergence and effective optimization capabilities. However, the traditional GWO is prone to converging prematurely at local minima, a limitation that has spurred significant advancements in its enhancement. Concurrently, these improvements have yielded innovative insights and approaches to address this challenge. In [5], GWO is integrated with SCA to improve global search capability by incorporating SCA into the position update of alpha wolves in GWO. GWO has been integrated with differential algorithm (DE) to obtain DE-GWO to solve the problem of gas emission localization [6]. In [7], Gaussian mutation and spiral function are introduced to help GWO skip local optima and improve the accuracy of the algorithm. In [8], random dynamic weight allocation is introduced to the first three wolves to accelerate the convergence in the later stage of optimization, which helps to find the global optimal solution. In [9], GWO is combined with WOA, and random control parameters and dynamic weighting strategies are added to improve the convergence accuracy and speed of the algorithm. In [10], the Contact List Mechanism (CLM) is utilized to update the population and improve its diversity and convergence accuracy. Scholars have introduced a chaos grouping mechanism into GWO to improve population diversity and utilized a dynamic sufficiency mechanism to balance exploration and development [11]. In [12], a new anti-learning strategy of following control was introduced into GWO to balance global optimization and local exploration. In [13], GWO is combined with the Cuckoo search (CS) algorithm to form a fractional order algorithm model to improve algorithm accuracy and optimize the management of wireless communication systems. In [14], the adaptive multi-objective particle swarm algorithm is integrated with GWO to improve the convergence accuracy of the algorithm for predicting and optimizing intelligent environmental control systems. In [15], the ReliefF algorithm and Coula entropy are introduced in the initialization process of GWO, and competitive guidance strategy and differential evolution-based leader wolf strategy are proposed to prevent the algorithm from becoming stuck in local optimal solutions. Nowadays, there are numerous solutions to engineering problems using metaheuristic algorithms. However, there is still limited research on optimizing the parameters of PI/PID controllers. The traditional method will bring huge computational burden to the optimization of PI/PID controller parameters. The strong optimization ability of metaheuristic algorithms has great application prospects in the optimization of PI/PID controller parameters.