## 2 Material and Methods
### Grasshopper Optimization Algorithm (GO)
\begin{table}
\begin{tabular}{p{14.2 pt} p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline
**1 st STEP** & \(A_{i}=\sum\limits_{j=1,j\
eq i}^{N}a\Big{(}f_{ij}\Big{)}\cdot f_{ij}\) & \(\bullet\) & \(f_{ij}\) is a space, which divides the \(i\)th and \(j\)th grasshoppers, \(f_{ij}=|a_{j}-a_{i}|\) \\
**1 st STEP** & \(A_{i}=\sum\limits_{j=1,j\
eq i}^{N}a\Big{(}f_{ij}\Big{)}\cdot f_{ij}\) & \(\bullet\) & \(f_{ij}=(a_{i}-a_{j})/f_{ij}\) means the unit vector between the \(i\)th and \(j\)th grasshoppers \\ \cline{2-3}  & \(a(m)=z\cdot e^{-m_{d}}-e^{-m}\) & \(\bullet\) & \(z\) is the attraction intensity \(d\) signifies the attractive length scale \(\bullet\) & (8) \\  & \(\bullet\) & \(m=|d_{ij}|\) & \\ \hline
**2 nd STEP** & \(B_{i}=-b\cdot e_{b}\) & \(\bullet\) & \(b\) is gravitational constant \(e_{b}\) stands for the unit vector heading to the globe center & (9) \\ \hline
**3 rd STEP** & \(C_{i}=x\cdot e_{\omega}\) & \(\bullet\) & \(x\) is a constant drift \(e_{\omega}\) refers to a unity vector in the wind direction \(N\) signifies the grasshoppers’ number \\ \cline{2-3}  & \(Y_{i}=\sum\limits_{j=1,j\
eq i}^{N}b\Big{(}\Big{|}a_{j}-a_{i}\Big{|}\Big{)} \cdot\frac{a_{j}-a_{i}}{f_{ij}}-t\cdot e_{t}+x\cdot e_{\omega}\) & & (11) \\ \cline{2-3}  & \(Y_{i}^{f}=c\Big{(}\sum\limits_{j=1,j\
eq i}^{N}c\,\frac{wb_{i}-db_{j}}{2}\cdot a \Big{(}\Big{|}d_{j}^{d}-a_{i}^{d}\Big{|}\Big{)}\cdot\frac{a_{j}-a_{j}}{f_{ij}} \Big{)}+O_{f}\) & \(\bullet\) & \(dy_{j}\) and \(ub_{d}\) are lower and upper boundaries in the \(F\)th dimension \(O_{f}\) is the location of the optimum solution it has found yet \\ \cline{2-3}  & \(c=c_{max}-d\cdot\frac{c_{max}-c_{min}}{D}\) & \(\bullet\) & \(c_{min}\) and \(c_{max}\) refers to the minimum and the maximum values of the coefficient \(c\) \(d\) implies the existing iteration \(D\) represents the greatest iterations \\ \hline \end{tabular}
\end{table} 
Table 2: Implementation steps of GO algorithm. formed. Typically, the grasshoppers reach their pleasure areas rapidly, and the group does not gather in particular spots. Thus, Equation (11) is unable to deal with the optimization queries immediately. This equation was amended to solve the optimization issue mentioned above, and Equation (12) was created. As shown in Equation (12), \"\(c\)\" is a lessening coefficient which is utilized on the way to decrease the comfort, attraction, and repulsion areas. In this Equation, the \"\(c\)\" enters double because of the following reasons:  
* By expanding the abundance of iterations, the motion of marked grasshoppers is decreased by the initial \"\(c\)\". This parameter equilibrates the whole exploration and exploitation of the target. * The following \"\(c\)\" decreases the repulsion, attraction, and comfort areas amongst grasshoppers. The aforementioned decline is proportionate to the iterations' abundance. GO needs to be avoided by becoming stuck in the local optimum. Alternatively, it attempts to acquire a precise calculation of the global optima. Grasshoppers achieve progressive equilibrium between exploration and exploitation because of the diverse pleasure area parameter \"\(c\)\". In each iteration, the \"\(c\)\" can be calculated by Equation (13). In this study, the authors employed great rates of repulsion since this is a crucial method in the GO to circumvent local solutions. The outcomes reveal that great repulsion rates limit grasshoppers to staying at a local optimum. To summarize, Algorithm 1 depicts the processes involved in executing the GO.