## 3 Data Explanation
### Model Development
Hence, the XGBoost-JSO model's superior performance is attributed to its ability to both accurately fit the training data and generalise effectively to new data, making it the best predictive model among those evaluated. Table 4 presents the rankings of the developed models based on their performance in both the training and testing phases. The XGBoost model emerged as the top performer with a total rank of 14, consistently achieving first place in all metrics across both phases. This indicates its superior accuracy and generalisation capabilities. The XGBoost-HHO model, optimised using Harris hawk optimisation, ranked fourth overall, scoring 18. Despite its strong performance in the training phase, where it excelled in several metrics, its testing phase results were less impressive. The XGBoost-JSO model, which used the jellyfish search optimiser, ranked the lowest, scoring 50. It consistently performed poorly across all metrics in both phases, reflecting the limited effectiveness of the optimisation approach in enhancing predictive performance. In contrast, the XGBoost-DA model, optimised with the dragonfly algorithm, secured the second position with a total score of 40. This model demonstrated balanced performance, maintaining solid rankings across training and testing phases. Lastly, the XGBoost-FA model, utilising the firefly algorithm, achieved a total rank of 28, placing it third overall. This model showed strong performance, especially in the testing phase, indicating its effectiveness in attaining accurate predictions and generalising new data well. This study introduced four optimised XGBoost techniques with high training effectiveness, typically yielding R\({}^{2}\) values above 0.950. Post-training, the models were evaluated and validated against the testing dataset. Figures 14 and 15 demonstrate that the training and testing datasets are distributed mainly close to the ideal fit line when comparing actual and predicted values, indicating minimal error. However, as evident from the figures, the R-squared values of testing datasets of XGBoost, XGBoOST-HHO, XGBoost-DA, XGBoost-JSO, and XGBoost-FA were 0.952, 0.957, 0.987, 0.976, and 0.963, respectively. Although all XGBoost algorithms and the other four hybrid metaheuristic techniques could successfully predict the peak load values of pull-out tests, the XGBoost-JSO performed the best in predicting the target values. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{5}{c}{**Training Phase**} & \multicolumn{5}{c}{**Testing Phase**} & \multirow{2}{*}{**Total Rate**} & \multirow{2}{*}{**Mode Rank**} \\ \cline{2-2} \cline{5-10}  & **MAE** & **R\({}^{2}\)** & **RMSE** & **VAF** & **Bias** & **MAE** & **R\({}^{2}\)** & **RMSE** & **VAF** & **Bias** \\ \hline XGBoost & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 2 & 1 & 14 & 5 \\ XGBoost-HHO & 1 & 2 & 1 & 2 & 1 & 3 & 2 & 2 & 1 & 3 & 18 & 4 \\ XGBoost-JSO & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 50 & 1 \\ XGBoost-DA & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 40 & 2 \\ XGBoost-FA & 3 & 3 & 3 & 3 & 2 & 3 & 3 & 3 & 2 & 28 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ranking of the developed models. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{5}{c}{**Training Phase**} & \multicolumn{5}{c}{**Testing Phase**} \\ \cline{2-11}  & **MAE** & **R\({}^{2}\)** & **RMSE** & **VAF** & **Bias** & **MAE** & **R\({}^{2}\)** & **RMSE** & **VAF** & **Bias** \\ \hline XGBoost & 2.653 & 0.958 & 3.111 & 95.111 & 2.653 & 1.759 & 0.952 & 2.186 & 95.052 & 1.759 \\ XGBoost-HHO & 2.795 & 0.961 & 3.180 & 95.531 & 2.795 & 1.298 & 0.957 & 1.624 & 94.374 & 1.298 \\ XGBoost-JSO & 1.355 & 0.988 & 1.562 & 98.737 & 1.355 & 0.668 & 0.987 & 0.823 & 98.662 & 0.668 \\ XGBoost-DA & 1.904 & 0.976 & 2.196 & 97.563 & 1.904 & 1.137 & 0.971 & 1.318 & 96.771 & 1.137 \\ XGBoost-FA & 2.387 & 0.967 & 2.708 & 96.731 & 2.387 & 1.425 & 0.963 & 1.500 & 96.256 & 1.425 \\ \hline \hline \end{tabular}
\end{table}