## 6 Experimental Results and Simulations
### Results with Feature Selection  
To examine the performance of WOA, we performed a sensitivity analysis on WOA with S2 (WOA-S2) as a transfer function using a different number of agents (whales). Table 8 explores the obtained results LDA classifier with different number of agents (i.e., 5, 10, 20, 30, 40, and 50). It is evident that the performance of LDA is not stable with a different number of agents. For example, the best performance is obtained when the number of agents equals 30 for both datasets. Choosing the correct number of agents that fit wither with the problem itself and classifier is important.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Classifier**} & \multicolumn{5}{c}{**Ovarsampling Ratio**} \\ \cline{3-8}  & & **0 * & **0.2** & **0.4** & **0.7** & **1** \\ \hline \multirow{4}{*}{Data1} & KNN & 0.8236 & 0.8521 & 0.8600 & 0.8590 & 0.8558 \\  & DT & 0.8303 & 0.8384 & 0.8360 & 0.8379 & 0.8407 \\  & LDA & 0.8223 & 0.8672 & 0.8720 & 0.8818 & 0.8794 \\  & LB & 0.8463 & 0.8450 & 0.8479 & 0.8499 & 0.8502 \\  & NB & 0.7262 & 0.8629 & 0.8503 & 0.8015 & 0.7746 \\ \hline \multirow{4}{*}{Data2} & KNN & 0.5842 & 0.6210 & 0.6307 & 0.6305 & 0.6332 \\  & DT & 0.5914 & 0.5968 & 0.6003 & 0.6031 & 0.6045 \\ \cline{1-1}  & LDA & 0.5105 & 0.5378 & 0.5946 & 0.6314 & 0.6352 \\ \cline{1-1}  & LB & 0.5982 & 0.6066 & 0.6113 & 0.6168 & 0.6187 \\ \cline{1-1}  & NB & 0.5197 & 0.5215 & 0.5344 & 0.5716 & 0.5685 \\ \hline \multicolumn{2}{c}{Rank (F-Test)} & 4.9 & 3.6 & 2.7 & 2.1 & **1.7** \\ \hline \hline \end{tabular}  
*balancing ratio of 0 indicates data without re-sampling.  
\end{table}
Table 6: The AUC results obtained by classification algorithms with different balancing ratios (without FS).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Metric**} & \multicolumn{5}{c}{**KNN**} & \multicolumn{2}{c}{**DT**} & \multicolumn{2}{c}{**LDA**} & \multicolumn{2}{c}{**LB**} & \multicolumn{2}{c}{**NB**} \\ \cline{3-10}  & & **without** & **with** & **without** & **with** & **without** & **with** & **without** & **with** & **without** & **with** \\ \hline \multirow{4}{*}{Data1} & TPR & 0.9649 & 0.7990 & 0.9329 & 0.9313 & 0.9625 & 0.8347 & 0.9482 & 0.9470 & 0.9846 & 0.5548 \\  & TNR & 0.6824 & 0.9126 & 0.7276 & 0.7500 & 0.6822 & 0.9241 & 0.7443 & 0.7535 & 0.4678 & 0.9943 \\  & AUC & 0.8236 & 0.8558 & 0.8303 & 0.8407 & 0.8223 & 0.8794 & 0.8463 & 0.8502 & 0.7262 & 0.7746 \\ \hline \multirow{4}{*}{Data2} & TPR & 0.2380 & 0.5486 & 0.2812 & 0.3438 & 0.0280 & 0.6395 & 0.2471 & 0.3088 & 0.0570 & 0.4640 \\  & TNR & 0.9303 & 0.7179 & 0.9017 & 0.8652 & 0.9930 & 0.6309 & 0.9493 & 0.9286 & 0.9824 & 0.6730 \\ \cline{1-1}  & AUC & 0.5842 & 0.6332 & 0.5914 & 0.6045 & 0.5105 & 0.6352 & 0.5982 & 0.6187 & 0.5197 & 0.5685 \\ \hline \hline \end{tabular}  
*balancing ratio of 0 indicates data without re-sampling.  
\end{table}
Table 7: Comparison results of classification methods without oversampling and with oversampling in terms of TPR, TNR, and AUC.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Metric**} & \multicolumn{5}{c}{**No. Search Agents**} \\ \cline{3-8}  & & **5** & **10** & **20** & **30** & **40** & **50** \\ \hline \multirow{4}{*}{Data1} & AUC & 0.9023 & 0.9030 & 0.9053 & 0.9069 & 0.9060 & 0.9048 \\  & Features & 16.9 & 16.5 & 14.5 & 14.3 & 12.3 & 14.1 \\  & Fitness & 0.1020 & 0.1012 & 0.0983 & 0.0966 & 0.0969 & 0.0987 \\ \hline \multirow{4}{*}{Data2} & AUC & 0.6436 & 0.6444 & 0.6454 & 0.6462 & 0.6460 & 0.6458 \\  & Features & 20.1 & 19.8 & 19.7 & 19.5 & 19.1 & 19.3 \\ \cline{1-1}  & Fitness & 0.3592 & 0.3582 & 0.3572 & 0.3563 & 0.3564 & 0.3566 \\ \hline \multicolumn{2}{c}{Overall Rank} & 6.00 & 5.00 & 3.67 & 1.67 & 1.67 & 3.00 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Evaluation results of WOA-S2 with different number of search agents for the re-balanced datasets.