## 4 Result and Discussion
### Model Training
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Pop Size**} & \multicolumn{5}{c}{**Training**} \\ \cline{2-9}  & \multicolumn{2}{c}{**R\({}^{2}\) (Score)**} & \multicolumn{2}{c}{**MAE (Score)**} & \multicolumn{2}{c}{**VAF (Score)**} & \multicolumn{2}{c}{**RMSE (Score)**} \\ \cline{2-9}  & \(\theta\) & \(\pi_{h}\)/\(\tau\) & \(\theta\) & \(\pi_{h}\)/\(\tau\) & \(\theta\) & \(\pi_{h}\)/\(\tau\) & \(\theta\) & \(\pi_{h}\)/\(\tau\) \\ \hline
10 & 0.9906(5) & 0.9839(4) & 0.0095(5) & 0.0167(5) & 0.9803(5) & 0.9679(4) & 0.018(5) & 0.0284(4) \\ \hline
20 & 0.9885(4) & 0.9825(2) & 0.0107(4) & 0.0168(3) & 0.9766(4) & 0.9645(2) & 0.0195(4) & 0.0298(2) \\ \hline
40 & 0.9867(2) & 0.9828(3) & 0.0127(2) & 0.0175(2) & 0.9726(2) & 0.9651(3) & 0.0212(2) & 0.0296(3) \\ \hline
80 & 0.9874(3) & 0.9847(5) & 0.0113(3) & 0.0167(4) & 0.9742(3) & 0.969(5) & 0.0205(3) & 0.0279(5) \\ \hline
160 & 0.9834(1) & 0.9809(1) & 0.0132(1) & 0.0183(1) & 0.9662(1) & 0.9613(1) & 0.0235(1) & 0.0312(1) \\ \hline \multicolumn{9}{c}{Test} \\ \cline{2-9}  & \multicolumn{2}{c}{R\({}^{2}\) (score)} & \multicolumn{2}{c}{MAE (score)} & \multicolumn{2}{c}{VAF (score)} & \multicolumn{2}{c}{RMSE (score)} \\ \cline{2-9}  & \(\theta\) & \(\pi_{h}\)/\(\tau\) & \(\theta\) & \(\pi_{h}\)/\(\tau\) & \(\theta\) & \(\pi_{h}\)/\(\tau\) & \(\theta\) & \(\pi_{h}\)/\(\tau\) \\ \hline
10 & 0.9906(5) & 0.9839(4) & 0.0095(5) & 0.0167(5) & 0.9803(5) & 0.9679(4) & 0.018(5) & 0.0284(4) \\ \hline
20 & 0.9885(4) & 0.9825(2) & 0.0107(4) & 0.0168(3) & 0.9766(4) & 0.9645(2) & 0.0195(4) & 0.0298(2) \\ \hline
40 & 0.9867(2) & 0.9828(3) & 0.0127(2) & 0.0175(2) & 0.9726(2) & 0.9651(3) & 0.0212(2) & 0.0296(3) \\ \hline
80 & 0.9874(3) & 0.9847(5) & 0.0113(3) & 0.0167(4) & 0.9742(3) & 0.969(5) & 0.0205(3) & 0.0279(5) \\ \hline
160 & 0.9834(1) & 0.9809(1) & 0.0132(1) & 0.0183(1) & 0.9662(1) & 0.9613(1) & 0.0235(1) & 0.0312(1) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation metrics performance of different WAOA-ANN models. Figure 9: Comprehensive comparison of prediction performance of hybrid multi-output models: (**a**) WAOA-ANN; (**b**) WAOA-RF; (**c**) WAOA-XGBoost; (**d**) legend. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Training**} \\ \cline{2-10}
**Pop Size** & \multicolumn{2}{c}{**R\({}^{2}\) (Score)**} & \multicolumn{2}{c}{**MAE (Score)**} & \multicolumn{2}{c}{**VAF (Score)**} & \multicolumn{2}{c}{**RMSE (Score)**} \\ \cline{2-10}  & \(\theta\) & \(r_{b}/r\) & \(\theta\) & \(r_{b}/r\) & \(\theta\) & \(r_{b}/r\) & \(\theta\) & \(r_{b}/r\) \\ \hline
10 & 0.9999(5) & 0.9999(5) & 0.0009(5) & 0.0008(5) & 0.9999(5) & 0.9999(5) & 0.0013(5) & 0.0019(5) \\ \hline
20 & 0.9995(1) & 0.9996(2) & 0.0027(1) & 0.0029(2) & 0.999(1) & 0.9992(2) & 0.004(1) & 0.0044(2) \\ \hline
40 & 0.9997(3) & 0.9996(1) & 0.0023(4) & 0.003(1) & 0.9993(3) & 0.9992(1) & 0.0033(3) & 0.0045(1) \\ \hline
80 & 0.9995(2) & 0.9996(3) & 0.0026(2) & 0.0029(3) & 0.9991(2) & 0.9992(3) & 0.0039(2) & 0.0044(3) \\ \hline
160 & 0.9997(4) & 0.9997(4) & 0.0023(3) & 0.0025(4) & 0.9993(4) & 0.9995(4) & 0.0033(4) & 0.0037(4) \\ \hline \hline \multicolumn{10}{c}{Test} \\ \cline{2-10}  & \multicolumn{2}{c}{R\({}^{2}\) (score)} & \multicolumn{2}{c}{MAE (score)} & \multicolumn{2}{c}{VAF (score)} & \multicolumn{2}{c}{RMSE (score)} \\ \cline{2-10}  & \(\theta\) & \(r_{b}/r\) & \(\theta\) & \(r_{b}/r\) & \(\theta\) & \(r_{b}/r\) & \(\theta\) & \(r_{b}/r\) \\ \hline
10 & 0.9392(1) & 0.96(1) & 0.0261(1) & 0.0262(1) & 0.8819(1) & 0.9194(1) & 0.0435(1) & 0.045(1) \\ \hline
20 & 0.976(3) & 0.9816(5) & 0.0157(3) & 0.0164(5) & 0.9524(3) & 0.9628(5) & 0.0276(3) & 0.0305(5) \\ \hline
40 & 0.9796(5) & 0.9748(2) & 0.0151(4) & 0.0187(3) & 0.9594(5) & 0.949(2) & 0.0255(5) & 0.0358(2) \\ \hline
80 & 0.9776(4) & 0.9789(4) & 0.0149(5) & 0.0172(4) & 0.9555(4) & 0.9573(4) & 0.0267(4) & 0.0327(4) \\ \hline
160 & 0.973(2) & 0.9756(3) & 0.016(2) & 0.0195(2) & 0.9462(2) & 0.9501(3) & 0.0293(2) & 0.0354(3) \\ \hline \hline \end{tabular}
\end{table}