## 2 Related Work
### GWO Algorithm  
The gray wolf optimizer (GWO) is a metaheuristic algorithm inspired by the social structure and hunting behaviors of gray wolves. In the wild, gray wolves have a hierarchical structure, with an alpha leader and lower-ranking beta and delta wolves. To effectively seek prey, these wolves collaborate as a team. Likewise, the GWO method is intended to tackle optimization problems by emulating the cooperative and communicative behaviors of wolves. The various solutions to the problem are modeled as a pack of wolves, and their placements in the solution space represent their fitness. The alpha wolf is currently the most excellent solution, although the beta and delta wolves are also viable options [10]. The description of the mathematical representation for the GWO (gray wolf optimization) algorithm is outlined below. _Encirling Prey:_ This phase involves the gray wolves encirling their prey. Mathematically, this behavior is represented by the following equations, Equations (4) and (5):  
\[\overset{\rightarrow}{D}=\overset{\rightarrow}{C}.\overset{\rightarrow}{X_{p }}(t)-\overset{\rightarrow}{X_{w}}(t) \tag{7}\]  
\[\overset{\rightarrow}{X_{w}}(t+1)=\overset{\rightarrow}{X_{p}}(t)-\overset{ \rightarrow}{A}.\overset{\rightarrow}{D} \tag{8}\]  
where \(t\) stands for the current iteration, \(\overset{\rightarrow}{A}\) and \(\overset{\rightarrow}{C}\) are the coefficient vectors, the prey's position vector is indicated by \(X_{p}\), and \(\overset{\rightarrow}{X_{w}}\) represents a gray wolf's position vector. In addition, \(\overset{\rightarrow}{A}\) and \(\overset{\rightarrow}{C}\) are calculated using the following formulas: Equations (9) and (10). \[\overset{\rightarrow}{A}=2\overset{\rightarrow}{a}.\overset{\rightarrow}{ r_{1}}-\overset{\rightarrow}{a} \tag{9}\]  
\[\overset{\rightarrow}{C}=2.\overset{\rightarrow}{r_{2}} \tag{10}\]  
where \(r_{1}\) and \(r_{2}\) depict a set of random vectors in \([0,1]\), and \(\overset{\rightarrow}{a}\) is linearly decreased from 2 to 0. _Hunting:_ During this stage, the alpha wolf, serving as the leader, and the beta and delta wolves, acting as consultants, possess ample knowledge about the prey's whereabouts. As a result, the other wolves must adjust their positions based on the location of the most skilled agent, represented by mathematical equations Equations (11)-(13):  
\[\overset{\rightarrow}{D_{a}}=\left|\overset{\rightarrow}{C_{1}}.\overset{ \rightarrow}{X_{a}}-\overset{\rightarrow}{X}\right|\hskip 14.226378 pt \overset{\rightarrow}{D_{\beta}}=\left|\overset{\rightarrow}{C_{1}}. \overset{\rightarrow}{X_{\beta}}-\overset{\rightarrow}{X}\right|\hskip 14.226378 pt \overset{\rightarrow}{D_{\delta}}=\left|\overset{\rightarrow}{  
\[\vec{X_{w}}(t+1)=\frac{X_{1}+X_{2}+X_{3}}{3} \tag{13}\]  
_Attacking Prey:_ Exploitation and exploration, which involve pursuing and searching for prey, are essential aspects of wolves' hunting behavior. When wolves chase and attack prey, it showcases their proficiency in capturing prey, which can be considered as their exploitation ability. This exploitation ability allows wolves to reach global optima, maximizing their success in hunting. The value of parameter A plays a vital role in this process. If the magnitude of \(|\)A\(|\)\(<\) 1, the gray wolves are compelled to pursue the current prey aggressively. However, if the magnitude of \(|\)A\(|\)\(>\) 1, the gray wolves are compelled to abandon the current prey and explore other potential targets. The pseudocode of the GWO algorithm [10] is depicted in Algorithm 1. _Equations Power Consumption Models:_ The energy usage of a server can be categorized into two components: idle and dynamic. Idle consumption refers to the power used when the server is inactive and not performing any tasks, while dynamic consumption represents the power utilized during active operations and computations. We can calculate the idle power consumption and dynamic power consumption given by Equations (14) and (15), respectively [29; 30]. ```
1. \"Initialize Population
2. Initialize a, A, and C
3.