## 5 Prediction of Heating Load (HL) by the Genetic Algorithm-Artificial Neural Network (GA-ANN) Model  
Before predicting the HL of EEB systems by the stated models, the dataset was split into two clusters, i.e., training and testing. According to the previous studies, the original dataset should be divided into two parts by randomly according to the 80/20 ratio [76; 77]. Thus, for the training process, 80% of the whole dataset (672 experimental datasets) was selected randomly to develop the models. The remaining 20% (165 experimental datasets) was used for the testing process, which is the method for evaluating the quality/performance of the GA-ANN, PSO-ANN, ICA-ANN, and ABC-ANN models.  
For the prediction of HL of EEB systems by the GA-ANN model, an initialization ANN model was developed first; then, the GA was used to optimize the developed ANN model, where the weights and biases were optimized. According to [PERSON] et al. [68], one or two hidden layers of the ANN model  
Figure 5: Framework of artificial neural network (ANN) model for estimating heating load (HL) of buildings’ energy efficiency (EEB) systems.  
can implement very well all regression problems. Therefore, a \"trial and error\" (TAE) procedure was conducted with one and two hidden layers of ANN models. To avoid overfitting of the initial ANN model, the min-max scale method was applied with the scale lies in the range of [-1,1]. Ultimately, the ANN model 8-24-18-1 was defined as the best ANN technique for predicting HL of EEB systems in this study. This was the moment for the optimization of the weights and biases of the ANN 8-24-18-1 model by the GA. The number of populations (\(p\)), crossover probability (P\({}_{c}\)), mutation probability (P\({}_{m}\)), and the number variable (\(n\)), are the parameters of the GA, that needed to be set up before optimizing herein. In this study, the TAE procedure of \(p\) with different values was conducted, i.e., \(p\) = 100, 200, 300, 400, 500; \(P_{m}\) was set equal to 0.1; \(P_{c}\) was set equal to 0.9; \(n\) = 4. To evaluate the performance of the optimization process, RMSE was used as the fitness function according to Equation (4). The searching operation were performed in 1000 iterations to ensure the optimal searching for the weights and biases of the selected ANN model. The optimal values of weight and bias for the ANN 8-24-18-1 model after optimizing by the GA (i.e., GA-ANN model), were corresponding to the lowest RMSE. The performance of the optimization process by the GA for the ANN 8-24-18-1 model is shown in Figure 6. The final ANN model, after optimized by the GA (i.e., GA-ANN model), is shown in Figure 7.  
Figure 6: Genetic algorithm-artificial neural network (GA-ANN) performance for estimating HL of EEB systems.  
As stated above, 672 experimental datasets were investigated and analyzed to develop the models. The back-propagation algorithm was applied to training the GA-ANN model. Note that the min-max scale with the range [\(-\)1,1] was used for all the models to avoid underfitting/overfitting. The performance of the training process for predicting HL of EEB systems is interpreted in Figure 8. Subsequently, 165 experimental datasets were used to evaluate GA-ANN performance as the new dataset. The results of HL prediction on the new data (i.e., 165 experimental datasets) were estimated by the developed GA-ANN model and are shown in Figure 9.  
Figure 8: HL predictions on the training dataset of the GA-ANN model.  
Figure 7: Structure of the GA-ANN model for determining HL of EEB systems.