## 2 Materials and Methods
### Overview of ESRO-SRO Algorithm  
In the SRO approach, the human position is equal to the resolution of the optimization issues, and the clue quantity accomplished in the location characterizes the objective function. The group members gather clue information in the search. Few clues are absent in the event of gaining optimal clues in another position, but the dataset is exploited for optimizing the searching technique [19]. Here, the position of the left clue can be stored in the (\(M\) memory matrix), where the position of the human is stored in the (\(X\) position matrix). The \(M\) matrix dimension is the same as \(X\). They are \(N\times D\) matrices, whereas \(D\) symbolizes problem dimension and \(N\) embodies human count. The clue matrixes have the attained clue position. The \(M\) and \(C\) matrixes are upgraded in all human searching processes [19]:  
\[C=\left\{ \begin{array}{c}X\\ M\end{array} \right\}=\left\{ \begin{array}{ccc}X_{11}&\cdots&X_{1D}\\ \vdots&\ddots&\vdots\\ X_{N1}&\cdots&X_{ND}\\ M_{11}&\cdots&M_{1D}\\ \vdots&\ddots&\vdots\\ M_{N1}&\cdots&M_{ND}\end{array} \right\}, \tag{1}\]  
In Equation (1), \(X\) and \(M\) represent the position of human and memory matrixes; correspondingly, \(X_{N1}\) embodies the position of initialized dimension for \(N^{\text{th}}\) human, and \(M_{1D}\) characterizes \(D^{\text{th}}\) dimensional position for the preliminary memory. Given the description presented in the previous section, in addition to an arbitrary clue amid accomplished clues, the search path is described as follows:  
\[\text{SD}_{i}=\left(X_{i}-C_{k}\right)\,,\;k\
eq i, \tag{2}\]  
In Equation (2), \(X_{i}\), \(C_{k}\), and \(\text{SD}_{i}\) correspondingly symbolize \(j^{\text{th}}\) human location, the \(k^{\text{th}}\) clue location, and \(j^{\text{th}}\) human searching direction; \(k\) suggests arbitrary numbers within 1 and \(2N\) and appropriately chosen \(k\
eq i\). It is important to emphasize that human usually seeks accordingly, and some repetitious positions could not be searched another time. Henceforth, the search should be generated if the group member is restrained. Therefore, \(X_{j}\) dimension could not be rehabilitated. For applying this constraint, the binomial crossover operator has been exploited when the clue is larger than that of the clue associated with the present position, an \(\text{SD}_{j}\) direction and the position of that search clue; next, the searching method undergoes the present location beside the \(\text{SD}_{i}\) direction [16]. \[X^{\prime}_{i,j=}\left\{\begin{array}{ccc}C_{k,j}+r1\times\left(X_{i,j}-C_{k, j}\right),if\;f(C_{k})>,f(X_{i})&\\ X_{i,j}+r1\times\left(X_{i,j}-C_{k,j}\right),otherwise,&\;\;\;\;\;\;\  
permitted solution region, they should be altered. If the novel place of a human is farther from the solution region, the succeeding equation is exploited for altering the novel place:  
\[X_{i,j}^{\prime}=\left\{ \begin{array}{l}\frac{\left(x_{i,j}+X_{j}^{\prime max} \right)}{2},if\ X_{i,j}^{\prime}>x_{j}^{\prime max},\\ \frac{\left(x_{i,j}+X_{j}^{\prime min}\right)}{2},if\ X_{i,j}^{\prime}<x_{j}^{ \prime min},\end{array} \right.\left( \begin{array}{c}j\\ =1,\ldots,\ D\end{array} \right) \tag{5}\]  
The process involved in the SRO algorithm is given in Algorithm 1. Next, in all iterations, the member of the group searched according to the two phases, and after each stage, once the value of the main function is in position, \(X_{i}^{\prime}(f(X_{i}^{\prime}))\) is greater than that of the preceding one (\(f\left(X_{i}\right)\)), thus the earlier position \(\left(X_{i}\right)\) would be stored in an arbitrary place of the M memory matrix and it would be adopted as a novel place. If not, the position is left and memory is not improved:  
\[M_{n}=\left\{ \begin{array}{l}X_{i},if\ f\left(X_{i}^{\prime}\right)>,f(X_{i} )\\ M_{n},\ \text{otherwise}\end{array} \right. \tag{6}\]  
\[X_{i}=\left\{ \begin{array}{l}X_{i}^{\prime},if\ f\left(X_{i}^{\prime}\right)>,f(X_{i})\\ X_{i},\ \text{otherwise},\end{array} \right.