## 4 Results and Discussion
### Machine Learning Model Performance  
This section analyzes the performance of four distinct machine learning algorithms in predicting building energy consumption (EC) based on the given dataset. These machine learning algorithms, which have demonstrated exceptional capabilities in energy prediction tasks in previous studies [10; 39; 42], included fast random forest, LightGBM, MVLR, and ANN. To evaluate the predictive performance of each model, metrics were employed, including the coefficient of determination (R\({}^{2}\)), mean absolute error (MAE), mean squared error (MSE), and root mean squared error (cv(RMSE)). A model with MAE, cv(RMSE), and MSE values closer to zero, and an R\({}^{2}\) value closer to one, is considered to have superior predictive accuracy. The target feature in this analysis was energy consumption (EC), and  
Figure 5: The Sensitivity index PCC and SRRC of optimization variables.  
the performance of each algorithm was assessed to identify the most reliable and efficient approach for energy prediction. The results of this evaluation provide valuable insights into the comparative strengths and weaknesses of these machine learning models.  
Figure 6 illustrates box plots of the performance metrics for the four machine learning models used in energy consumption prediction. The results reveal that the LightGBM model outperformed the other three ML models by demonstrating superior performance across all evaluated metrics. Additionally, the ANN and FRF models exhibited nearly identical predictive performance; however, the FRF box plot indicates a greater number of outliers, suggesting that the FRF algorithm generated a higher proportion of poorly performing predictive models. In contrast, the ANN algorithm displayed fewer outliers, indicating more consistent and stable predictive accuracy compared to the FRF model. Among the four models, MVLR exhibited the poorest performance, highlighting its limited capability to address the complexities of energy consumption prediction tasks.  
Table 6 provides a detailed comparison of the performance metrics for each machine learning model. The LightGBM model achieves significantly lower MAE, MSE, and RMSE values compared to the other three models, indicating its exceptional predictive performance. In contrast, the higher MAE, MSE, and RMSE values observed for the MVLR, FRF, and ANN models suggest relatively lower prediction accuracy. These findings underscore the suitability of gradient boosting models, such as LightGBM, for handling the inherent complexities of building energy consumption prediction tasks. Their superior accuracy and reliability position them as a more effective solution compared to simpler models. Based on this comparative analysis, the LightGBM model was identified as the optimal choice for predicting building energy consumption due to its outstanding stability and accuracy.  
Figure 7 illustrates the regression performance of the LightGBM model in predicting energy consumption (EC). The scatterplot compares the tested EC values (x-axis) with the predicted EC values (y-axis) generated by the LightGBM model. The results demonstrate a strong linear relationship between the predicted and true values. This indicates that the LightGBM model achieves high predictive accuracy and effectively captures the relationship between the input features and energy consumption. The clustering of points along the diagonal further supports the model's stability and reliability in predicting energy consumption across the dataset.  
Figure 6: Optimization results and Pareto front solutions.