## 6 Results and Discussions
The results of the XGBoost model (i.e., RMSE = 1.651, R\({}^{2}\) = 0.977, MAE = 0.720, VAF = 97.664, MAPE = 0.028, total ranking of 17) recognized the significant optimization capabilities of the PSO algorithm in this study. Observing closely in Table 3, it can be seen that the XGBoost model had provided lower performance than the RF model (RMSE = 1.589, R\({}^{2}\) = 0.978, MAE = 0.557, VAF = 97.835, MAPE = 0.026, total ranking of 25). However, the XGBoost model had become even more potent than the RF model when optimized by the PSO algorithm (i.e., PSO-XGBoost). The remaining models provided a lower performance than the proposed PSO-XGBoost model. Figures 12-16 illustrate the accuracy level of the XGBoost, SVM, RF, GP, and CART models, respectively, on the testing dataset. Figure 12: The results of HL prediction from the XGBoost model. Figure 13: The results of HL prediction from the support vector machine (SVM) model. Figure 16: The results of HL prediction from the CART model. Figure 14: The results of HL prediction from the RF model. Figure 15: The results of HL prediction from the GP model. Considering the advantages and disadvantages of the other methods (i.e., XGBoost, SVM, RF, GP, and CART), it can be seen that the development of these models was more straightforward than the proposed PSO-XGBoost model, especially the GP and CART models with only one parameter used to build the models. The RF and SVM models are a bit more complicated when using two parameters to build predictive models. Most notably, the XGBoost model used seven parameters to build the model (i.e., \(k\), \(d\), \(\eta\), \(\gamma\), \(\delta\), \(\varsigma\), and \(\mu\)). The higher the number of variables used, the more processing time and model construction. This is one of the disadvantages of complex models. Besides, although the construction of the single models (i.e., XGBoost, SVM, RF, GP, and CART) was more straightforward than the proposed PSO-XGBoost model; however, their performance was proven to be lower than the proposed PSO-XGBoost model. Herein, the proposed PSO-XGBoost model had performed very well in estimating the HL of buildings systems with very high accuracy based on input variables. However, the number of input variables used in the present study was high; therefore, a thorough consideration of the relationship, as well as the importance of the input variables used in this study is necessary. The sensitivity indices based on the Csiszar f-divergence method was used to determine the significance of the inputs [68; 69; 70]. This technique implements a sensitivity analysis based on the density. The influence of the input variables was established in terms of the difference between the density function of the entire output and the density function of output. Note that the input variables were fixed. The difference between density functions was measured with Csiszar f-divergences. Finally, an evaluation was performed through the estimation of kernel density. The results of the estimation were shown in Figure 17. The results revealed that OH, RA, WA, and SA were the most critical variables in estimating the HL of buildings systems.