## 3 Results and Discussion
### Hyperparameter Tuning and Metrics for Training, Testing, and Validation
As shown in Table 3, its performance on the training dataset was also satisfactory, with corresponding values of 0.2986, 0.8457, and 0.3928, indicating a consistent behavior across both data partitions and confirming the robustness of the model for the problem at hand. Figure 8: Training metrics for the best machine learning models. Figure 9: Testing metrics for the best machine learning models. Overall, all neural network models--both traditional artificial neural networks (ANNs) and extreme learning machines (ELMs)--exhibited excellent predictive capability across training and testing sets. Their \(MAE\) values ranged from 0.1882 to 0.2765, \(R^{2}\) values spanned from 0.8327 to 0.9544, and \(RMSE\) values varied from 0.2197 to 0.4210, further reinforcing the superior generalization ability of neural-based approaches for the dataset under investigation. A noteworthy observation concerns the moderate performance of the extreme gradient boosting (XGB) models for the testing dataset, despite their outstanding results for the training dataset--an indication of overfitting. Similarly, the random forest (RF) models exhibited a significant drop in predictive performance from training to testing, suggesting that they too may have been affected by overfitting. Conversely, among the tree-based models, the decision tree (DT) models--although presenting the weakest results during training--achieved the most favorable testing metrics, implying a more robust generalization under the specific conditions evaluated, in contrast to their more complex counterparts. Regarding the support vector regressor (SVR) models, their performance mirrored that of the RF models, with a notable reduction in accuracy from training to testing. Nevertheless, the gap in \(R^{2}\) between training and testing was smaller than that observed for the RF models, indicating relatively greater stability. A detailed comparison of the mean validation metrics for the best-performing models is provided in Table 4.  
In these experiments, the mean \(MAE\) values ranged from 0.3534 to 0.4623. The three best-performing models in this regard were GA-ELM-4 (50), AGA-ELM-3 (20), and AGA-SVR (20), once again highlighting the effectiveness of the ELM architecture, while also drawing attention to the solid performance of the SVR model, despite its less impressive results on the testing dataset. Regarding the \(R^{2}\) metric, values varied from 0.4850 to 0.7466, with the highest scores obtained by GA-ELM-4 (50), AGA-ELM-3 (20), and GA-ELM-3 (65), reaffirming the dominance of neural network-based models in capturing the variance of the target variable. As for \(RMSE\), the results fell between 0.3954 and 0.6233. Interestingly, the top three performers under this metric were GA-SVR (35), GA-ELM-4 (50), and GA-ELM-3 (65), with the SVR model outperforming its ELM counterparts in terms of error magnitude. Although artificial neural networks (ANNs) did not rank among the top three models for any of the evaluated metrics, they still delivered consistently strong and reliable performance, indicating their robustness across different validation scenarios.