## 3 Data Explanation
### Model Development  
As mentioned, the dataset was split into training and testing datasets to predict peak load values. The randomly selected training dataset included 80% of the dataset, while testing was carried out on the rest of the dataset, 20%. The models' accuracy was assessed using several performance indicators, including R\({}^{2}\), MAE, RMSE, VAF, and Bf, as outlined in Equations (2)-(6). Notably, consistency was maintained by training and testing all prediction models on the same dataset. The proposed method was used to optimise the XGBoost models. The relevant XGBoost parameters were initially set up, and then the optimal parameters for each optimisation algorithm were determined. Table 2 presents the hyperparameter tuning results for various XGBoost models optimised using four different algorithms: HHO, JSO, DA, and FA. The tuning methods yielded distinct optimal hyperparameters for each model. The values of optimal hyperparameters selected for each model, precisely the learning rate, maximum depth, and the number of estimators, are given in Table 2. For the manually adjusted XGBoost model, hyperparameter values were selected based on iterative testing and cross-validation. To fine-tune these parameters, the optimisation-based models, i.e., XGBoost-HHO, XGBoost-JSO, XGBoost-DA, and XGBoost-FA, utilised their respective optimisation algorithms (HHO, JSO, DFO, and FO). Each algorithm searched for the optimal combination of parameters that minimised the error metrics in the model's performance during the training phase. The hyperparameter search space was predefined, and the algorithms iteratively explored and evaluated various combinations to identify the optimal values for learning rate, maximum depth, and the number of estimators. These algorithms use different mechanisms, such as population-based searches and swarm intelligence, to find the most suitable parameters, improving model performance significantly. The tuning process ensures that each model balances underfitting and overfitting. For the XGBoost-HHO model, the optimal hyperparameters were a learning rate of 0.109, a maximum depth of 3, and 140 estimators. This configuration revealed a balance between model complexity and learning efficiency, aiming to prevent overfitting while maintaining good performance. The learning rate, maximum depth, and number of estimators for the developed XGBoost-JSO model were 0.102, 3, and 131, respectively. The slightly lower learning rate suggested a more cautious approach to model training, which could improve stability and generalisation. In contrast, the XGBoost-DA model caused a higher learning rate of 0.131, with a maximum depth of 3 and 170 estimators, allowing for potentially more flexible learning. However, it may result in an increased overfitting risk. Eventually, the XGBoost-FA model achieved a learning rate of 0.174, a maximum depth of 3, and 165 estimators, indicating a more aggressive learning strategy. This configuration could lead to faster convergence, but additional measures might be needed to control overfitting. Each optimisation algorithm thus provides a different set of hyperparameters, reflecting varied strategies for balancing learning efficiency and model complexity. The convergence of the error loss over iterations is a vital indicator of the accuracy and reliability of machine learning models. Convergence diagrams for four selected models--XGBoost-JSO, XGBoost-HHO, XGBoost-DA, and XGBoost-FA--are presented in Figures 10-13. The behaviour of the models as they were trained over multiple iterations is