## 3 Results and Discussion
### Building the Stacking Models  
To evaluate whether combining different models would enhance prediction robustness, four stacking models were designed based on the best-performing models according to \(MAE\), \(R^{2}\), and \(RMSE\) metrics for the testing dataset. Following the methodology, the top models in descending order were AGA-ANN-1 (20), AGA-ELM-3 (20), GA-ELM-4 (50), GA-ANN-2 (50), AGA-SVR (20), GA-DT (20), GA-RF (50), and GA-XGB (20). Since ELM-3 and ELM-4 yielded identical results for both training and testing, only ELM-3 was considered for the stacking models to avoid redundancy in the metamodel. The four stacking configurations were defined as follows: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Validation \(MAE\)** & **Validation \(R^{2}\)** & **Validation \(RMSE\)** \\ \hline GA-DT (20) & 0.4570 \(\pm\) 0.1479 & 0.4853 \(\pm\) 0.4181 & 0.6227 \(\pm\) 0.1966 \\ AGA-DT (35) & 0.4578 \(\pm\) 0.1484 & 0.4850 \(\pm\) 0.4184 & 0.6233 \(\pm\) 0.1968 \\ GA-RF (50) & 0.4196 \(\pm\) 0.1246 & 0.6167 \(\pm\) 0.2257 & 0.5574 \(\pm\) 0.1609 \\ AGA-RF (80) & 0.4194 \(\pm\) 0.1227 & 0.6183 \(\pm\) 0.2213 & 0.5563 \(\pm\) 0.1577 \\ GA-XGB (20) & 0.4315 \(\pm\) 0.1202 & 0.6098 \(\pm\) 0.2263 & 0.5619 \(\pm\) 0.1582 \\ AGA-XGB (50) & 0.4623 \(\pm\) 0.1249 & 0.5638 \(\pm\) 0.2400 & 0.5954 \(\pm\) 0.1606 \\ GA-SVR (35) & 0.3566 \(\pm\) 0.1010 & 0.7125 \(\pm\) 0.1705 & 0.3954 \(\pm\) 0.0150 \\ AGA-SVR (20) & 0.3537 \(\pm\) 0.1006 & 0.7158 \(\pm\) 0.1689 & 0.4738 \(\pm\) 0.1385 \\ GA-ANN-1(20) & 0.3779 \(\pm\) 0.1004 & 0.7182 \(\pm\) 0.1357 & 0.4825 \(\pm\) 0.1213 \\ AGA-ANN-1 (20) & 0.3579 \(\pm\) 0.1036 & 0.7215 \(\pm\) 0.1749 & 0.4688 \(\pm\) 0.1348 \\ GA-ANN-2 (50) & 0.3648 \(\pm\) 0.0913 & 0.7270 \(\pm\) 0.1543 & 0.4659 \(\pm\) 0.1203 \\ AGA-ANN-2 (50) & 0.3544 \(\pm\) 0.0932 & 0.7436 \(\pm\) 0.1459 & 0.4531 \(\pm\) 0.1190 \\ GA-ELM-3 (65) & 0.3544 \(\pm\) 0.0902 & 0.7440 \(\pm\) 0.1536 & 0.4484 \(\pm\) 0.1165 \\ AGA-ELM-3 (20) & 0.3535 \(\pm\) 0.0908 & 0.7450 \(\pm\) 0.1496 & 0.4494 \(\pm\) 0.1160 \\ GA-ELM-4 (50) & 0.3534 \(\pm\) 0.0914 & 0.7466 \(\pm\) 0.1468 & 0.4479 \(\pm\) 0.1177 \\ AGA-ELM-4 (20) & 0.3568 \(\pm\) 0.0946 & 0.7411 \(\pm\) 0.1559 & 0.4532 \(\pm\) 0.1245 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean validation metrics for the best set of hyperparameters determined for each machine learning model. * Stacking 1: AGA-ANN-1 (20) and AGA-ELM-3 (20). * Stacking 2: AGA-ANN-1 (20), AGA-ELM-3 (20), and GA-ANN-2 (50). * Stacking 3: AGA-ANN-1 (20), AGA-ELM-3 (20), GA-ANN-2 (50), and AGA-SVR (20). * Stacking 4: AGA-ANN-1 (20), AGA-ELM-3 (20), GA-ANN-2 (50), AGA-SVR (20), and GA-DT (20). Table 5 presents the training and testing metrics for both the best machine learning models and the stacking models. Table 6 displays the mean validation metrics obtained through a 10-fold cross-validation procedure, with 30 repetitions. The results in Table 5 indicate that the stacking models achieved strong performance. For the training dataset, \(MAE\) ranged from 0.2881 to 0.3023, \(R^{2}\) varied between 0.8435 and 0.8582, and \(RMSE\) was between 0.3766 and 0.3956. For the testing dataset, \(MAE\) was between 0.2177 and 0.2437, \(R^{2}\) varied between 0.8924 and 0.9356, and \(RMSE\) ranged from 0.2613 to 0.3376. However, the stacking models generally underperformed compared to the individual neural networks (ANNs and ELMs) for the testing dataset. This suggests that increasing the number of base models in a metamodel did not necessarily improve \(ELOS\) prediction for the given dataset split. The validation experiments summarized in Table 6 further support this observation. The stacking models achieved mean \(MAE\) values between 0.3476 and 0.3583, mean \(R^{2}\) values between 0.7340 and 0.7454, and mean \(RMSE\) values between 0.4483 and 0.4593. These results closely matched those of the best neural networks and SVR models.