## 6 Conclusions and Remarks  
Recent years have witnessed the development of new models to give an accurate approximation from the energy consumption of the buildings. In this paper, we employed two metaheuristic algorithms to overcome the drawbacks of the backpropagation algorithms for this aim. In this sense, a typical multilayer-perceptron neural network (ANN) was synthesized with genetic algorithm (GA-ANN) and imperialist competition algorithm (ICA-ANN) to estimate the heating load (HL) and cooling load (CL) of a building with residential use. To this end, eight influential energy parameters, including relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution were considered as the inputs of the designed networks. Considering twelve different buildings, four glazing areas, five distribution scenarios, and four orientations, 768 buildings were modelled and analyzed in Ecotect environment. Among those, 80% (614 records) were devoted to training the ANN, GA-ANN, and ICA-ANN models, and the efficiency of them was evaluated by the remaining 20% (154 records). The proposed models were implemented in their optimal conditions and three famous statistical indices of the coefficient of determination (R\({}^{2}\)), mean absolute error (MAE), root mean square error (RMSE) was used to evaluate the accuracy of each method. We achieved the following results in this study:  
* Artificial intelligence techniques can act as an efficient approach for analyzing the heating and cooling load of the buildings. * Optimizing the computational parameters (i.e., the weights and biases) of the ANN using the GA and ICA has a significant effect on its performance in terms of both pattern learning and prediction. * The computed R\({}^{2}\) for both training (HL: 0.8710, 0.8711, and 0.8816--CL: 0.9119, 0.9102, and 0.9216) and testing (HL: 0.9017, 0.9076, and 0.9115--CL: 0.9179, 0.9232, and 0.9287) showed that ICA helps the ANN to increase the correlation of the results an also outperforms GA. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & \\ \cline{2-13} \multirow{2}{*}{**Models**} & \multicolumn{6}{c}{**Training**} & \multicolumn{6}{c}{**Testing**} \\ \cline{2-13}  & \multicolumn{3}{c}{**HL**} & \multicolumn{3}{c}{**CL**} & \multicolumn{3}{c}{**HL**} & \multicolumn{3}{c}{**CL**} \\ \cline{2-13}  & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** \\ \hline ANN & 0.8710 & 3.6535 & 3.0014 & 0.9119 & 4.3588 & 3.4320 & 0.9017 & 3.6481 & 2.9382 & 0.9179 & 3.9489 & 3.2835 \\ GA-ANN & 0.8711 & 2.9986 & 2.1797 & 0.9102 & 3.4376 & 2.4330 & 0.9076 & 2.8878 & 2.0622 & 0.9232 & 2.8598 & 2.0982 \\ ICA-ANN & 0.8816 & 2.8050 & 2.0068 & 0.9216 & 3.2892 & 2.3565 & 0.9115 & 2.7819 & 2.0089 & 0.9287 & 2.7995 & 2.1054 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Obtained MAE, RMSE, and R\({}^{2}\) for ANN, GA-ANN, and ICA-ANN results. Based on the calculated RMSE, the training error of ANN decreased as 17.92% and 23.22% for the HL, and 21.13% and 24.53% for CL, respectively by applying GA and ICA. These values were 20.84% and 23.74% for HL and 27.57% and 29.10% for CL about the validation error. * As for MAE, the training error of ANN decreased as 27.38% and 33.14% for the HL, and 29.11% and 31.34% for CL, respectively by applying GA and ICA. These values were 29.81% and 31.63% for HL and 36.10% and 35.88% for CL about the validation error. * From the comparison viewpoint, ICA outperformed GA in performance improvement of multi-layer perceptron neural network in the case of this study. [PERSON] and [PERSON] performed experiments and field data collection; [PERSON] wrote the manuscript, discussion and analyzed the data. [PERSON], [PERSON], edited, restructured, and professionally optimized the manuscript. This research received no external funding. This work was financially supported by Ton Duc Thang University.