## 3 Results and Discussion
### Hyperparameter Tuning and Metrics for Training, Testing, and Validation  
After completing the exploratory data analysis, various scaling techniques--standard, robust, and power scaling--were tested on the X_train and y_train datasets to improve model performance. It was found that applying the Yeo-Johnson [84] transformation significantly enhanced model accuracy, as this technique transforms data into a more Gaussian-like distribution, reduces high variance and skewness, and improves symmetry in variable distributions, making it easier for models to learn effectively. Following the data transformation, a random seed was fixed to ensure reproducibility before splitting the dataset. The next step involved optimizing the hyperparameters of the machine learning models using genetic algorithms. Table 2 compares the computational time required for hyperparameter tuning across different models. In total, 37,778 min were consumed in this stage. The least time-consuming models were DT (0.12%), ELM3 (0.20%), and ELM4(0.30%), while SVR (0.27%), ANN1 (7.78%), and ANN2(8.88%) consumed a moderate amount of time. The most time-consuming models were XGB (21.44%) and RF (61.02%), indicating a significantly higher computational burden. Figures 8 and 9 illustrate the performance of the best hyperparameter configurations for each machine learning model, while Table 3 summarizes their training and testing performance. As illustrated in Figure 8, the models demonstrated relatively consistent behavior for the training dataset with respect to the \(R^{2}\) metric, yielding values ranging from 0.7579 to 0.9321. In contrast, greater variability was observed for the \(MAE\) and \(RMSE\) metrics, which ranged from 0.0396 to 0.3426 and from 0.0576 to 0.4920, respectively. The GA-XGB model with a population of 20 individuals produced the most favorable training metrics overall. Conversely, the GA-ANN-1 model with 20 individuals exhibited the highest \(MAE\), while both decision tree-based models recorded the lowest \(R^{2}\) and highest \(RMSE\) values. Referring to Figure 9, the testing dataset results reveal a broader spread in model performance, particularly for the \(R^{2}\) metric, which ranged from 0.3981 to 0.9544. The \(MAE\) values ranged from 0.1882 to 0.4354, while the \(RMSE\) values ranged from 0.2197 to 0.7153. Notably, the AGA-ANN-1 model with 20 individuals yielded the lowest \(MAE\) on the testing dataset, at 0.1882. The highest \(R^{2}\) values were attained by three extreme learning machine-based models--GA-ELM-3 with 65 individuals, AGA-ELM-3 with 20 individuals, and GA-ELM-4 with 50 individuals. With respect to \(RMSE\), the best results were shared by \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **Pop 20 (min)** & **Pop 35 (min)** & **Pop 50 (min)** & **Pop 65 (min)** & **Pop 80 (min)** \\ \hline GA-DT & 2 & 2 & 3 & 4 & 8 \\ AGA-DT & 1 & 4 & 6 & 6 & 8 \\ GA-RF & 833 & 1277 & 1889 & 2696 & 4074 \\ AGA-RF & 837 & 1417 & 1935 & 3224 & 4870 \\ GA-XGB & 417 & 633 & 1017 & 1304 & 1551 \\ AGA-XGB & 252 & 525 & 568 & 863 & 969 \\ GA-SVR & 5 & 8 & 10 & 13 & 16 \\ AGA-SVR & 4 & 7 & 11 & 14 & 15 \\ GA-ANN-1 & 165 & 226 & 306 & 328 & 479 \\ AGA-ANN-1 & 132 & 154 & 243 & 447 & 459 \\ GA-ANN-2 & 154 & 183 & 315 & 444 & 565 \\ AGA-ANN-2 & 132 & 259 & 340 & 462 & 501 \\ GA-ELM-3 & 3 & 4 & 6 & 8 & 10 \\ AGA-ELM-3 & 4 & 6 & 8 & 11 & 14 \\ GA-ELM-4 & 5 & 8 & 11 & 11 & 15 \\ AGA-ELM-4 & 5 & 9 & 14 & 18 & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the computational time during the hyperparameter tuning experiments. the AGA-ELM-3 with 20 individuals and GA-ELM-4 with 50 individuals models, both of which demonstrated superior generalization performance on the testing dataset. According to the selection criterion defined in the methodology, the AGA-ANN-1 model with a population of 20 individuals was identified as the most effective. This model achieved \(MAE\), \(R^{2}\), and \(RMSE\) values of 0.1882, 0.9508, and 0.2283, respectively, for the testing dataset.