## 6 Experimental Results and Simulations
### Results with Feature Selection
#### 6.3.3 Comparison of Top Variants WOA-S2 and WOA-V4  
Table 12 reports a compression between WOA-S2 and WOA-V4 based on Average and standard deviations for AUC, number of selected features, and fitness value. It is evident that for both datasets, WOA-V4 outperforms the WOA-S2 in all measurements. Moreover, the Wilcoxon test results show that both transfer functions have a \(p\)-value less than 0.05. Thus, from all the previous results, the performance of V-shape version 4 is more reliable with WOA for both datasets. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**WOA-V4 VERSUS**} & \multicolumn{2}{c}{**WOA-V4**} & \multicolumn{2}{c}{**WOA-V4**} \\ \cline{3-11}  & & **WOA-S1** & **WOA-S2** & **WOA-S3** & **WOA-S4** & **WAO-V1** & **WOA-V2** & **WO-V3** & **WOA-V4** \\ \hline \multirow{4}{*}{Data1} & AUC & 1.81E-04 & 1.81E-04 & 1.81E-04 & 1.81E-04 & 5.85E-02 & 3.06E-01 & 3.84E-01 & 1 \\  & Features & 1.28E-04 & 1.22E-04 & 1.25E-04 & 1.29E-04 & 3.87E-01 & 6.90E-01 & 5.92E-01 & 1 \\  & Fitness & 1.82E-04 & 1.82E-04 & 1.82E-04 & 1.82E-04 & 6.94E-02 & 4.05E-01 & 3.25E-01 & 1 \\ \hline \multirow{4}{*}{Data2} & AUC & 1.83E-04 & 1.83E-04 & 1.83E-04 & 1.83E-04 & 2.45E-04 & 9.70E-01 & 3.60E-03 & 1 \\  & Features & 6.29E-05 & 6.07E-05 & 6.16E-05 & 6.29E-05 & 3.68E-01 & NaN & NaN & 1 \\ \cline{1-1}  & Fitness & 1.83E-04 & 1.83E-04 & 1.83E-04 & 1.83E-04 & 2.45E-04 & 9.70E-01 & 3.60E-03 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: \(p\)-values of the Wilcoxon test for the AUC, number of features, and fitness results of the top variant WOA-V4 versus other variants (\(p\leq 0.05\) are presented in bold face, NaN: means Not Applicable). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**WOA-S1**} & \multicolumn{2}{c}{**WOA-S2**} & \multicolumn{2}{c}{**WOA-S3**} & \multicolumn{2}{c}{**WOA-S4**} \\  & & **Avg** & **Std** & **Avg** & **Std** & **Avg** & **Std** & **Avg** & **Std** \\ \hline \multirow{4}{*}{Data1} & AUC & 0.90613 & 0.00237 & 0.90695 & 0.00187 & 0.90512 & 0.00120 & 0.90578 & 0.00156 \\  & Features & 16.00 & 4.88 & 14.30 & 3.20 & 13.90 & 2.77 & 13.30 & 2.67 \\  & Fitness & 0.09793 & 0.00324 & 0.09659 & 0.00209 & 0.09828 & 0.00152 & 0.09743 & 0.00200 \\ \hline \multirow{4}{*}{Data2} & AUC & 0.64690 & 0.00125 & 0.64625 & 0.00155 & 0.64486 & 0.00098 & 0.64438 & 0.00243 \\  & Features & 24.00 & 2.67 & 19.50 & 2.63 & 19.10 & 2.28 & 18.20 & 2.57 \\  & Fitness & 0.35707 & 0.00148 & 0.35631 & 0.00115 & 0.35756 & 0.00102 & 0.35775 & 0.00260 \\ \hline Overall Rank (F-Test) & 2.67 & & **1.83** & & 3.00 & & 2.50 & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Evaluation results of WOA using four S-shaped TFs in terms of average and standard deviation of AUC, No. selected features, and fitness values. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**WOA-S1**} & \multicolumn{2}{c}{**WOA-S2**} & \multicolumn{2}{c}{**WOA-S3**} & \multicolumn{2}{c}{**WOA-S4**} \\  & & **Avg** & **Std** & **Avg** & **Std** & **Avg** & **Std** & **Avg** & **Std** \\ \hline \multirow{4}{*}{Data1} & AUC & 0.91305 & 0.00121 & 0.91370 & 0.00148 & 0.91403 & 0.00163 & 0.91445 & 0.00156 \\  & Features & 1.30 & 0.95 & 1.30 & 0.67 & 1.90 & 1.60 & 1.40 & 0.70 \\  & Fitness & 0.08649 & 0.00111 & 0.08584 & 0.00138 & 0.08570 & 0.00163 & 0.08513 & 0.00157 \\ \hline \multirow{4}{*}{Data2} & AUC & 0.65304 & 0.00283 & 0.65524 & 0.00054 & 0.65452 & 0.00062 & 0.65526 & 0.00050 \\  & Features & 4.10 & 3.48 & 3.00 & 0.00 & 3.00 & 0.00 & 3.00 & 0.00 \\ \cline{1-1}  & Fitness & 0.34477 & 0.00387 & 0.34225 & 0.00053 & 0.34296 & 0.00062 & 0.34223 & 0.00050 \\ \hline Overall Rank (F-Test) & 3.58 & & 2.25 & & 2.67 & & **1.50** & \\ \hline \hline \end{tabular}
\end{table}