## 5 Results and Discussion
### Model Assessment  
Using the programming software of MATLAB version 14.0 all three models were coded and implemented with their optimal architecture and the results are presented through various ways. A graphical comparison between the actual and predicted values of HL and CL is presented in Figures 11 and 12, as well as a chart showing the error of each sample (i.e., the difference between the actual and predicted values) and a histogram of the errors depicting the frequency of each error value.  
Figure 10: The sensitivity analysis for ICA-ANN, based on the number of countries.  
Figure 9: The sensitivity analysis for GA-ANN, based on the number of hidden neurons.  
Figure 11: _Cont_.  
Figure 11: _Cont._  
Figure 11: A graphical view of the obtained results and the calculated errors for HL prediction.  
Figure 12: \(Cont\).  
Figure 12: _Cont._  
Moreover, the accommodation between the targets and the outputs of ANN, GA-ANN, and ICA-ANN is depicted in the form of regression charts in Figures 13 and 14, respectively, for HL and CL modelling. The coefficient of determination (R\({}^{2}\)) is also calculated, which indicates the correlation between the mentioned parameters. This is noteworthy that R\({}^{2}\) is a statistical index which varies between 0 and 1 so that 1 represents an ideal prediction and vice versa.  
Figure 12: A graphical view of the obtained results and the calculated errors for CL prediction.  
Figure 13: The regression between the actual and predicted HL.  
In the following, Table 3 summarizes the values of R2, RMSE, and MAE acquired for the training and testing phases of HL and CL prediction. It shall be noted that, to have a coherent presentation of the results, calculated values of R2, RMSE, and MAE are reported in the respective order for ANN, GA-ANN, and ICA-ANN in all explanations below. According to this table, by comparing the obtained R2 for the training HL (0.8710, 0.8711, and 0.8816) and testing HL (0.9017, 0.9076, and 0.9115), it can be concluded that all three models have shown better performance for the testing dataset. In this  
Figure 14: The regression between the actual and predicted CL.  
regard, the outputs produced by ICA-ANN has the highest correlation with the actual HLs for both training and testing data. Also, the training RMSE (3.6535, 2.9986, and 2.8050) and MAE (3.0014, 2.1797, and 2.0068) show that applying the GA and ICA evolutionary algorithms have a significant effect in decreasing the performance error. Similarly, the testing RMSE (3.6481, 2.8878, and 2.7819) and MAE (2.9382, 2.0622, and 2.0089) demonstrate that ICA-ANN has shown a higher accuracy compared to the GA-ANN and typical ANN in forecasting the HL of residential buildings. As for CL prediction, the calculated R\({}^{2}\) for the training (0.9119, 0.9102, and 0.9216) and testing samples (0.9179, 0.9232, and 0.9287) prove that ICA has performed slightly better than GA in improving the ANN performance. This is while ANN has achieved a higher value of R\({}^{2}\) compared to GA-ANN model (0.9119 \(>\) 0.9102). The computed RMSE for the training (4.3588, 3.4376, and 3.2892) and testing phases (3.9489, 2.8598, and 2.7995) revealed that combining ANN with GA and ICA has led to decreasing the root mean square error as 0.9212 and 1.0696, and 1.0891 and 1.1494, respectively for the training and testing instances. Referring to Table 3, however, GA-ANN outperformed ICA-ANN in the case of testing MAE (3.2835, 2.0982, and 2.1054), but the results of the training MAE (3.4320, 2.4330, and 2.3565) support the previous claims (i.e., the superiority of ICA-ANN method).