## 2 The Proposed DLSODC-GWM Technique
### AOA-Based Hyperparameter Tuning Module  
Usually, as another MH technique, the AOA contains two search stages [19], namely, exploration and exploitation, which are simulated as mathematics functions such as \(-,+,\;*\), and \(/\). Initial, the AOA makes a group of \(N\) solution (agent). All but one demonstrates the agent to the tested problems. Therefore, the solution/agent signifies the \(X\) population, as follows:  
\[X=[x_{N-1,1}x_{N,1}x_{2,1}x_{1,1}\;x_{N-1,j}x_{N,j}x_{2,j}x_{1,j}\;x_{N,n-1}x_ {1,n-1}\;x_{N-1,n}x_{N,n}x_{2,n}x_{1,n}] \tag{4}\]  
\[X=\left[\begin{array}{cccc}x_{1,1}&\cdots&x_{1,j}&x_{1,n-1}&x_{1,n}\\ x_{2,1}&\cdots&x_{2,j}&\cdots&x_{2,n}\\ \cdots&\cdots&\cdots&\cdots&\cdots\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ x_{N-1,1}&\cdots&x_{N-1,j}&\cdots&x_{N-1,n}\\ x_{N,1}&\cdots&x_{N,j}&x_{N,n-1}&x_{N,n}\end{array}\right] \tag{5}\]  
Afterward, the FF of all solutions is calculated to detect the optimum one \(X_{b}\). Next, based on the Math Optimizer Accelerated (MOA) value, the AOA executes exploration or exploitation procedures. At that time, \(MOA\) was upgraded as the following subsequent formula:  
\[MOA(t)=\;\text{Min}\;+t\times\left(\frac{\text{Max}_{MOA}-\text{Min}_{MOA}}{ M_{t}}\right) \tag{6}\]  
where \(M_{t}\) denotes the entire number of iterations. \(\text{Min}_{MOA}\) and signifies the minimal and maximal values of accelerated functions, correspondingly. In particular, multiplication (M) and division (D) were used from the exploration stage of AOA as obtainable from the following subsequent formula:  
\[X_{ij}(t+1)=\left\{\begin{array}{ll}X_{bj}\div(M_{OP}+\in)\times\left(\left( UB_{j}-LB_{j}\right)\times\mu+LB_{j}\right),&r_{2}<0.5\\ X_{bj}\times M_{OP}\times\left(\left(UB_{j}-LB_{j}\right)\times\mu+LB_{j} \right),&\text{otherwise}\end{array}\right. \tag{7}\]where \(e\) implies the smaller integer values, \(UB_{j}\) and \(LB_{j}\) stands for the lower and upper boundaries of the searching region at \(j^{th}\) dimensional. \(\mu=0.5\) refers the control functions. In addition, the Math Optimizer \((M_{\text{OP}})\) was explained as follows:  
\[M_{\text{OP}}(t)=1-\frac{t^{1/\alpha}}{M_{t}^{1/\alpha}} \tag{8}\]  
\(\alpha=5\) defines the dynamic parameter that resolves the precision of the exploitation stage throughout iterations.  
Moreover, addition (A) and subtracting (D) functions were utilized for implementing the AOA exploitation stage utilizing the subsequent formula.  
\[x_{i,j}(t+1)=\left\{\begin{array}{l}X_{bj}-M_{\text{OP}}\times\left(\left(UB _{j}-LB_{j}\right)\times\mu+LB_{j}\right),\;r_{3}<0.5\\ X_{bj}+M_{\text{OP}}\times\left(\left(UB_{j}-LB_{j}\right)\times\mu+LB_{j} \right),\;otherwise\end{array}\right. \tag{9}\]  
where \(r_{3}\) implies the arbitrary number generated between zero and one. Then, the solution's upgrade method was executed utilizing the AOA operator. In summary, Algorithm 1 defines the important stages of the AOA.  
```
Input: The parameter of AOA-like dynamic exploitation parameters (\(\alpha\)), control function amount of solutions (N), and entire amount of iterations \(M_{t}\). Create the primary value to solutions \(X_{i}i=1,\ldots\;N/\). while (\(t<M_{t}\)) do  Calculate the FF to all the solutions.  Define the optimum solutions \(X_{b}\)  Upgrade the \(M\)OA and \(M_{\text{OP}}\) utilizing in Equations (3) and (5) correspondingly for \(i=1\) to \(N\) do  for \(j=1\) to \(Dim\) do  Upgrade the value of \(r_{1}\), \(r_{2}\) and \(r_{3}\).  if \(r_{1}>MOA\) then  Exploration stage  Utilize Equation (4) for updating the \(X_{i}\)  else  Exploitation stage  Utilize Equation (6) for updating the \(X_{i}\)  end if  end for  end for \(t=t+1\) end while Output the optimum solution (feature subset) (\(X_{b}\))
```  
**Algorithm 1** Steps involved in AOA