## 3 The Proposed System
### Energy Model
#### 3.2.4 The Aquila Optimizer Algorithm (AO)  
Aquila Optimizer (AO) is a novel optimization method, which results from Aquila's behaviors in the environment pending prey being caught. The AO algorithm's optimization procedures are divided into four categories: selecting the search area by high flying with a vertical stoop, discovering within a separate search space by contour flying with a short glide attack, utilizing within a converged search area by low flying with a slow descent attack, and pouncing by walking and grabbing prey [27]. AO can swap shooting strategies for varied prey and then attack prey with its fast speed combined with strong feet and claws. [PERSON] et al. [30]. The next is a summary of the mathematical model.  
There are two methods, exploration and exploitation [8].  
**Firstly**, In the expanded exploration.  
**In the exploration \(ag1\)**, the Aquila flies above the ground and discovers the search space, followed by a vertical dive just after the Aquila has determined the prey location.  
**The narrowed exploration \(ag2\)**: contour flight with short glide attack is the most common way for Aquila to hunt; it attacks the prey with short gliding after descending within the selected area and flying around the prey.  
The mathematical formula for the exploration and narrowed exploration is represented, respectively, as the following:  
\[ag_{1}(t+1)=ag_{b}(t)*\left[\left(\frac{1-t}{mn}\right)-r_{1}\right]+ag_{m}(t) \tag{11}\]  
\[ag_{m}(t+1)=\frac{1}{N}\ \sum_{N}^{1}ag_{i}(t)\]  
The average value of the current position of all agents. \(1-t\)  
During the exploration phase, the search is directed by \(\left(\frac{1-t}{mn}\right)\) Equation (11)  
* \(t\) and \(mn\): the current iterations and the maximum number of iterations. \[ag_{2}(t+1)=ag_{b}(t)*\left(LEVY(D)+ag_{R}(t)-(y-r)*r_{2}\right.\] (12)  
\[LEVY(D)=0.01*u*\left.\sigma*\left|V\right|^{\frac{-1}{p}}\]  
\[\left.\sigma=2^{\frac{(1-\beta)}{2}}\ sin\left(\frac{\pi\beta}{2}\right)* \ \left(\frac{\Gamma(1+\beta)}{\beta*\ \Gamma\left(\frac{1+\beta}{2}\right)}\right)\right.\]  
\[x=r*sin\left(\frac{300\pi-D_{1}}{200}\right)\,\ y=r*cos\left(\frac{300\pi-D_{1}}{200 }\right)\,\ r=r_{3}+\ 0.0057D_{1} \tag{13}\]  
The exploitation adjustment parameters fixed to 0.1.  
* \(ub\) and \(lb\): the upper and lower bound of the problem.
* \(D\): the dimension size \(LEVY\) (\(D\)) represents the Levy flight function.
* \(r_{1}\). \(r_{2}\). \(r_{3}\). \(r_{4}\). \(r_{5}\). \(r_{6}\). \(r_{7}\). \(r_{8}\): random numbers in the range [0, 1].
* \(D_{1}\): an integer number in the range [1, \(D\)].
* \(r\): the number of search cycles in the range [1, 20].  
**Secondly: Expanded exploitation \(qg_{3}\):** low-flying with a slow descent offensive.  
After determining the approximate location of the prey and descending vertically to launch a preliminary attack, Aquila uses the chosen area to get close to the prey and attack it. This behaviour is illustrated as follows:  
\[qg_{3}(t+1)=\alpha(ag_{b}(t)-ag_{m}(t))+\delta*(lb(1-r_{s})+r_{sub})-r_{4} \tag{14}\]  
**The narrowed exploitation:** walking and snatching prey.  
The Aquila hunts the victim and attacks it on the ground in this fashion. The next is a mathematical depiction of this behaviour:  
\[qg_{4}(t+1)=q(t)*qg_{b}(t)+(2r_{8}-1)\bigg{(}r_{7}-r*x(t)-2 LEVY(D)\bigg{(}1- \frac{t}{mn}\bigg{)}\bigg{)} \tag{15}\]  
\(q(t)\): The quality function is used to equilibrate the search strategy.