## 4 Grey Wolf Optimization in WSN  
### Definition and Algorithm  
Grey Wolf Optimization (GWO) is an innovative algorithm inspired by the social hierarchy and hunting behavior of grey wolves in nature. Developed by [PERSON] et al. in 2014 [40], GWO has gained significant attention due to its simplicity, flexibility, and effectiveness in solving complex optimization problems. GWO mimics the leadership structure of grey wolf packs, which includes alpha, beta, delta, and omega wolves. The alpha wolves represent the best solution, beta and delta wolves guide the search, and omega wolves explore new solutions. This hierarchy helps balance exploration and exploitation during the optimization process. The GWO algorithm (Algorithm 1) involves three main phases: searching for prey (exploration), encircling prey (exploitation), and attacking prey (convergence). Initially, wolves are randomly positioned in the search space. During the exploration phase, wolves update their positions relative to alpha, beta, and delta wolves, encouraging diverse search space exploration. In the exploitation phase, the algorithm fine-tunes solutions by encircling the best solutions found so far. Finally, the algorithm converges by simulating the wolves' attack on prey, refining the best solutions. GWO's ability to balance exploration and exploitation makes it highly effective across various applications, including engineering design, feature selection, and neural network training. Recent enhancements, such as hybridizing GWO with other optimization techniques like HC and SA, further improve its performance [41]. For instance, integrating GWO with HC and SA has shown superior performance in complex optimization tasks by enhancing solution quality and convergence speed. A significant advantage of GWO is its minimal parameter requirement, which simplifies implementation and reduces computational overhead. Moreover, GWO is derivative-free, making it suitable for problems with complex, non-differentiable objective functions. Its adaptability to different problem domains and its robustness in handling various optimization scenarios contributes to its growing popularity. Recent studies have focused on improving GWO's exploration capabilities and convergence rate. For example, researchers have proposed better exploration strategies and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Protocol/ Technique** & **Involved OSI Layers** & **MAC Technique** & **Parameters Used** & **Physical Layer Features** & **Data Link Layer Features** \\ \hline Markov Model [36] & Physical MAC & CSMA/CA & Duty Cycle, Sleep Mode, Active/Sleep Transitions & Energy-efficient transmission, minimized idle listening & Duty cycle optimization, sleep mode transitions \\ \hline OSTS, BSTS [38] & Physical MAC & CSMA/CA & Buffered Conditions, Channel Assessment, Sleep Scheduling & Optimized signal transmission, reduced interference & Buffer management, sleep scheduling \\ \hline Enhanced CCA [39] & Physical MAC & CSMA/CA & Signal Strength, Interference, Channel State & Improved channel sensing, interference handling & Enhanced CCA checks, adaptive strategies \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of different CSMA/CA-based routing protocols. adaptive mechanisms to maintain diversity in the population and prevent premature convergence. These improvements aim to enhance GWO's effectiveness in large-scale and high-dimensional optimization problems [42]. Experimental results have demonstrated GWO's superiority over other optimization algorithms in terms of solution quality and computational efficiency. By leveraging the natural behaviors of grey wolves, GWO provides a powerful and versatile tool for solving a wide range of optimization challenges [43]. 1. Initialize the grey wolf population \(X_{i}(i=1,2,\ldots,n)\), where \(n\) is the number of grey wolves;
2. Initialize the maximum number of iterations \(t_{max}\);
3. Initialize the parameters \(a\), \(A\), and \(C\);
4. Evaluate the fitness of each grey wolf;
5.