## 3 Data Explanation
### Model Development

Table 3: Performance evaluation of the developed models. Figure 14: R\({}^{2}\) value of XGBoost model in both training and testing phases. Figure 15: R\({}^{2}\) value of XGBoost-HHO, XGBoost-JSO, XGBoost-DA, and XGBoost-FA models in both training and testing phases. The results of predicted peak load values for each training and testing dataset are compared in Figures 16 and 17, which depict a series of comparative graphs, each showcasing the performance of the XGBoost model alongside different optimisation algorithms in predicting the peak load (kN) over varying data points. Each graph contrasts the actual peak load values (marked by coloured points) with the predicted values generated by XGBoost, enabling a detailed visual analysis of the model's performance. In the raining process, the data spans a broader range, displaying fluctuating trends in peak load values. The model predictions, while close to the actual values, reveal slight deviations, with the optimisation algorithms (HHO, JSO, DA, and FA) aiming to enhance the accuracy of the baseline XGBoost model. These graphs allow for a clear comparison of the efficacy of each algorithm, especially in capturing the variability in the higher data range. The testing process focuses on a smaller data range with periodic variations in the peak load. The XGBoost model, aided by the various optimisation algorithms, demonstrates a better fit in this scenario, closely following the actual data points. The cyclical nature of the data in these graphs appears well captured by the model, though slight discrepancies can still be observed. The overall structure of both figures emphasises the model's predictive capability and the impact of algorithmic enhancements in improving model accuracy. Based on the presented figures,  
In both training and testing plots, the actual peak load data points are well approximated by the XGBoost model. However, the degree of alignment with actual data varies depending on the algorithm employed. The testing plots, in particular, showcase smoother, periodic data, whereas the XGBoost-JSO seems to exhibit the closest alignment with the actual values. The predictions' consistent pattern and minimal deviation indicate that the JSO-enhanced model offers superior accuracy in these particular instances. This is highlighted by how well it captures the data's peaks and troughs with fewer noticeable errors or discrepancies compared to other models. Regarding overall model performance, the JSO-optimised XGBoost model emerges as a leading contender for accuracy. It handles the periodic data in the testing plots and the more variable data in the training plots with commendable precision. Thus, the JSO-enhanced XGBoost is the most reliable and accurate model for all the scenarios. The comparison of the results revealed that JSO had the best performance among all other hybrid XGBoost models, which can be attributed to its flexible exploration and exploitation phases, allowing it to navigate the search space and avoid local optima efficiently. On the other hand, HHO showed a slightly lower performance due to its tendency for early convergence in some instances, which may lead to suboptimal solutions. Figure 17: Prediction results of developed XGBoost models in testing phase. The comparison highlighted that while all the techniques significantly enhanced XGBoost's predictive capabilities, the choice of optimisation method should be informed by the specific problem's complexity and data characteristics. For example, JSO's adaptability makes it suitable for datasets with complex, nonlinear interactions, as in this case. However, the computational cost of each method should also be considered, as methods like DA and FA may require more iterations to converge compared to JSO. Despite the improvements, it is noteworthy that while applying hybrid models improves prediction accuracy, their scalability is more extensive and needs to be assessed, as metaheuristic optimisations can be computationally expensive.