## 3 Results and Discussion
### Hyperparameter Tuning and Metrics for Training, Testing, and Validation
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Train \(MAE\)** & **Test \(MAE\)** & **Train \(R^{2}\)** & **Test \(R^{2}\)** & **Train \(RMSE\)** & **Test RMSE** \\ \hline GA-DT (20) & 0.3015 & 0.3499 & 0.7579 & 0.6369 & 0.4920 & 0.6202 \\ AGA-DT (35) & 0.3015 & 0.3499 & 0.7579 & 0.6369 & 0.4920 & 0.6202 \\ GA-RF (50) & 0.2832 & 0.3598 & 0.8449 & 0.5492 & 0.3938 & 0.6911 \\ AGA-RF (80) & 0.2515 & 0.3408 & 0.8810 & 0.6334 & 0.3448 & 0.6232 \\ GA-XGB (20) & 0.0396 & 0.4082 & 0.9321 & 0.5730 & 0.0576 & 0.6726 \\ AGA-XGB (50) & 0.0441 & 0.4354 & 0.9198 & 0.5170 & 0.0626 & 0.7153 \\ GA-SVR (35) & 0.2667 & 0.3346 & 0.8405 & 0.6244 & 0.3994 & 0.6308 \\ AGA-SVR (20) & 0.2685 & 0.3307 & 0.8371 & 0.6375 & 0.4036 & 0.6197 \\ GA-ANN-1(20) & 0.3426 & 0.2510 & 0.8017 & 0.8529 & 0.4454 & 0.3948 \\ AGA-ANN-1 (20) & 0.2986 & 0.1882 & 0.8457 & 0.9508 & 0.3928 & 0.2283 \\ GA-ANN-2 (50) & 0.2868 & 0.2282 & 0.8698 & 0.9059 & 0.3609 & 0.3158 \\ AGA-ANN-2 (50) & 0.2760 & 0.2437 & 0.8711 & 0.8327 & 0.3590 & 0.4210 \\ GA-ELM-3 (65) & 0.3143 & 0.1941 & 0.8262 & 0.9544 & 0.4168 & 0.2198 \\ AGA-ELM-3 (20) & 0.3145 & 0.1940 & 0.8262 & 0.9544 & 0.4169 & 0.2197 \\ GA-ELM-4 (50) & 0.3145 & 0.1940 & 0.8262 & 0.9544 & 0.4169 & 0.2197 \\ AGA-ELM-4 (20) & 0.3055 & 0.2765 & 0.8308 & 0.8504 & 0.4113 & 0.3981 \\ \hline \hline \end{tabular} The hatched cells represent the model that presented the best result for the adopted criteria.  
\end{table} 
Table 3: Training and testing metrics for the best set of hyperparameters determined for each machine learning model. With respect to tree-based models, their validation performance was significantly lower than that of the SVR and neural network-based models. Among the tree-based approaches evaluated, the random forest (RF) models consistently outperformed both decision tree (DT) and extreme gradient boosting (XGB) variants across the three validation metrics considered (\(MAE\), \(R^{2}\), and \(RMSE\)). In contrast, DT models exhibited the weakest performance during validation, highlighting their limited generalization capacity in this context. Interestingly, this outcome diverges from the results observed during testing, where DT models outperformed other tree-based models and even surpassed the SVR in terms of the \(R^{2}\) metric. This inconsistency suggests that DT models may have benefited from favorable data characteristics in the specific testing split, and therefore lack the robustness and consistency required to generalize well across different data partitions. Such variability underscores the importance of rigorous cross-validation in performance assessment. Neural network models, including both artificial neural networks and extreme learning machines, demonstrated consistently high performance across training, testing, and validation. In addition to their robustness, the ELM models were particularly efficient, requiring only 0.5% of the total computational time, while achieving top-tier accuracy. Considering the experiments using the testing dataset, the best overall model for predicting equivalent linear overbreak along was AGA-ANN-1 with 20 individuals, which provided a balance between accuracy, stability, and robustness. The stacking approach, discussed in the following sections, aims to further enhance predictions by integrating the strengths of multiple high-performing models.