## 3 Proposed RBAVO-DE for GS
### The Complete RBAVO-DE Algorithm
It is determined in the following way: \[Mean_{AC}=\sum_{k=1}^{30}\sum_{r=1}^{m}match(PL_{r},AL_{r})\] (23) In this formula, \(m\) denotes the number of samples in the test dataset, while \(PL_{r}\) and \(AL_{r}\) denote the predicted labels from the classifier and the actual class labels for sample \(r\), respectively. The function \(match(PL_{r},AL_{r})\) serves as a comparison mechanism, where if \(PL_{r}\) is equal to \(AL_{r}\), then \(match(PL_{r},AL_{r})\) is assigned a value of 1; if they do not match, it is assigned a value of 0. \begin{table}
\begin{tabular}{l l} \hline
**Optimizer** & **Parameters** \\ \hline \hline \multirow{8}{*}{Proposed RBAVO-DE} & Dimensionality \(D=\) The count of genes \\  & in the employed datasets \\  & Upper boundaries \(UB\) \\  & Lower boundaries \(LB\) \\  & Parameter \(L_{1}=0.7\) \\  & Parameter \(L_{2}=0.2\) \\  & Parameter \(w=2\) \\  & Parameter \(P_{1}=0.6\) \\  & Parameter \(P_{2}=0.6\) \\  & Parameter \(P_{3}=0.5\) \\ BSSA & Count of scroungers \(SD=0.1\times N\) \\  & Count of producers \(PD=0.2\times N\) \\  & Safety threshold \(ST=0.8\) \\ BABC & Count of employed bees \(=16\) \\  & Count of scout bees \(=3\) \\  & Count of omokoc bees \(=4\) \\ BPSO & Inertia weight (\(\omega max=0.9\omega min=0.4\)) \\  & Acceleration coefficients (\(c_{2}=c_{1}=1.2\)) \\ BBA & Loudness \(A=0.8\) \\  & Pulse emission rate \(r=0.95\) \\  & Lower and upper pulse frequencies \(=0,10\) \\ BWOA & \(a\) is linearly decreased from 2 to 0 \\  & \(p=0.5\) \\  & \(b=1.0\) \\ BHHO & Rabbit energy \(E\in[-1,1]\) \\ BGWO & \(a\) is linearly decreased from 2 to 0 \\ BGOA & \(C_{\min}=0.00004\) and \(C_{\max}=1\) \\ BBSA & Frequency of flight \(ff=10\) \\  & Effect on birds’ vigilance \\  & Followed coefficient \(fl=0.5\) \\  & Probability of foraging for food \(p=0.8\) \\  & Acceleration coefficients (\(c_{1}=c_{2}=1.5\)) \\  & behaviors (\(a_{1}=a_{2}=1.0\)) \\ BASO & Depth weight \(\alpha=50\) \\  & Multiplier weight \(\beta=0.2\) \\ BHGSO & Count of clusters \(=2\) \\  & \(\alpha=\beta=0.1\)\(K=1.0\), and \(l_{3}=1E-02\) \\  & \(l_{1}=5E-03,l_{2}=1E+02\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._* **Mean fitness \((Mean_{Fi})\)**: This measure calculates the average \(meanFi\), achieved by running the proposed approach thirty times independently. It gauges the balance between lowering the classification error rate and minimizing the number of genes selected. A lower value indicates a superior solution, assessed based on fitness: \[MeanFi=\frac{1}{30}\sum_{k=1}^{30}f_{*}^{k}\] (24) where \(f_{*}^{k}\) shows the optimum fitness value achieved in the \(k-th\) execution. * **Mean number of chosen genes \((MeanGe)\)**: This metric calculates the average number of genes chosen (or GS ratio) by running the proposed approach thirty times independently, and it is defined as follows: \[MeanFe=\frac{1}{30}\sum_{k=1}^{30}\frac{|d_{*}^{k}|}{|D|}\] (25) Here, \(|d_{*}^{k}|\) denotes the total count of genes chosen in the optimal solution for the \(k^{th}\) execution, and \(|D|\) represents the total number of genes present in the initial benchmark. * **Standard Deviation \((STDE)\)**: Based on the outcomes above, the overall average results derived from thirty separate executions of each optimizer on every benchmark were assessed for stability in the following manner: \[STDE=\sqrt{\frac{1}{29}\sum_{k=1}^{30}(Y_{*}^{k}-Mean_{Y})^{2}}\] (26) where \(Y\) shows the measure to be utilized, \(Y*k\) denotes the measure value \(Y\) in the \(k_{t}h\) run, and \(Mean_{Y}\) is the mean of the measure from thirty independent executions. The data in the subsequent tables represent the mean values obtained from thirty independent executions, focusing on classification accuracy, the number of chosen genes, average fitness, precision, recall, and F1-score. The ensuing subsections thoroughly examine and discuss these experimental findings, with bold figures highlighting the optimal results.