## 2 Methodology
### Proposed GSLEO-AEFA  
#### 2.2.1 Population Initialization Using Gaussian Mutation Specular Reflection Learning (GS)  
The variety of the starting agents has a major influence on the convergence rate and solution precision of metaheuristic algorithms [40]. However, AEFA frequently uses random initialization to generate the starting population. This initialization strategy lacks prior information of the search space, which might impact the updating method of the search agents. The population has the possibility of moving away from the ideal solution if the optimal solution is situated in the opposite location from where the randomly produced individuals are positioned. Solutions generated by the specular reflection learning (SRL) technique has been shown to outperform those produced only by random approaches [41]. This study introduces the application of specular reflection learning for the initialization of population and will produce an opposing population of the initial population. Afterwards, the Gaussian mutation (GM) process will be applied to the newly generated population to improve population variety from the generated agents. It is decided which individuals should be retained by comparing their fitness values with that of the original individuals. Due to its superior performance, opposition-based learning (OBL) is frequently employed to enhance metaheuristic algorithms [42]. OBL uses simultaneous examination of potential solution and its opposing solution to promote rapid convergence. Within the range \([lb,ub]\), the opposing value of \(p\) is defined as follows:  
\[p^{*}=lb+ub-p \tag{12}\]  
[PERSON] introduced the specular reflection learning (SRL) which was motivated by the specular reflection in physics and illustrated in Figure 2. Figure 2a shows the clear correlation between the incident light and the reflected light [35]. Based on this concept, it is possible to compute a solution and its reverse solution in the manner depicted in Figure 2b. Based on the aforementioned occurrence, it may be concluded that a solution and its opposing solution corresponds to some extent. A superior solution could be discovered, if both solutions are compared. The superiority of the SRL method over OBL has been established [43; 44]. Therefore, SRL is introduced during the initialization of the population of GSLEO-AEFA. The incorporation of GM allows for further mutation to be carried out on the population. Consider point \(P=(a,0)\) in the horizontal plane and its opposite point \(P^{\prime}=(b,0)\), \(\forall P,P^{\prime}\in[P_{l},P_{u}]\). The incidence angle is denoted by \(\alpha\) and the reflection angle is symbolized by \(\beta\). \(O=(p_{0},0)\) represents the midpoint of \([P_{l},P_{u}]\). From Figure 2b, the following equation can be deduced. \[\tan(\alpha)=\frac{p_{0}-a}{A_{0}} \tag{13}\]  
\[\tan(\beta)=\frac{b-p_{0}}{B_{0}} \tag{14}\]  
According to the reflection law \(\alpha\) and \(\beta\) are equal and the Equations (13) and (14) are represented as,  
\[\frac{p_{0}-a}{A_{0}}=\frac{b-p_{0}}{B_{0}} \tag{15}\]  
From Equation (15), \(b\) is equal to either (16)-(18). \[b=\frac{B_{0}(p_{0}-a)}{A_{0}}+p_{0} \tag{16}\]  
Figure 2: Specular reflection learning illustration; (a) The phenomenon of specular reflection and (b) The model of specular reflection. If \(B_{0}=\mu A_{0}\) then  
\[b=\mu(p_{0}-a)+p_{0} \tag{17}\]  
\[b=(\mu+1)p_{0}-\mu a=(0.5\mu+0.5)*(P_{l}+P_{u})-\mu a \tag{18}\]  
where \(\mu\) denoted a preset factor for scaling and when it changes, \(b\) can be computed as given as follows. \[b= \begin{cases}b_{1},&\mu\in(0,1),\\ 2p_{0}-a,&\mu=1\\ b_{2},&\mu\in(1,+\infty)\end{cases}  \tag{19}\]  
When \(\mu\) changes, \(b\) can explore all values of \([P_{l},P_{u}]\). Hence, it may be used to initialize the population and improve its variety and exploration. Let \(P=(p_{1},p_{2},\ldots,p_{n})\) represent an individual in a \(n\)-dimensional space.