## 4 Results and Discussion
### Day-Ahead Forecast Results  
In the day-ahead DNN model, 6 out of 24 inputs (\(E_{d}\), \(E_{uv}\), \(\mathcal{C}_{n}\), \(\mathcal{R}\), \(h_{d}\), and \(d_{t}\)) are used in the forecasting stage and equation for each polynomial are rigorously illustrated in Table 5.  
The result equation of the day-ahead DNN model is summarized in Equation (4). \[\hat{E}=6961.16+0.27N_{1}+0.71N_{13}+2N_{1}^{2}\times 10^{-6}+8.95N_{13}^{2} \times 10^{-7}+N_{1}N_{13}\times 10^{-6} \tag{4}\]  
In the day-ahead GEP model, 5 out of 24 inputs (\(E_{d}\), \(I_{SW}\), \(\mathcal{R}\), \(y\), and \(d_{w}\)) are employed as indicated in Equation (5) and illustrated as an expression tree in Figure 8.  
\[\hat{E}=\mathcal{R}_{c}+E_{d}+(y\times 3.876)+d_{w}\times(\mathcal{R}_{fl}-9.345) \times 266.926-8.508\times(I_{SW}\times d_{w}+17.015) \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & & & \\ \hline \(y\) & \(x_{i}\) & \(x_{j}\) & \(a_{0}\) & \(a_{1}\) & \(a_{2}\) & \(a_{3}\) & \(-a_{4}\) & \(-a_{5}\) \\ \hline \(N_{3}\) & \(\mathcal{C}_{c}\) & \(I_{SW}\) & 615,694.10 & 0.05 & 248.62 & \(5\times 10^{-6}\) & \(3.45\times 10^{-9}\) & \(-5.70\) \\ \(N_{6}\) & \(E_{h}\) & \(I_{SW}\) & 7297.94 & 0.98 & 141.46 & \(3.9\times 10^{-4}\) & \(2.05\times 10^{-8}\) & \(0.74\) \\ \(N_{2}\) & \(N_{3}\) & \(N_{6}\) & \(-7961.21\) & 0.02 & 0.99 & \(1.83\times 10^{-8}\) & \(1.26\times 10^{-8}\) & \(3.81\times 10^{-9}\) \\ \(N_{9}\) & \(\mathcal{R}_{l}\) & \(\mathcal{C}_{c}\) & 735,294 & 718,227.6 & 0.04 & 0.04 & \(1,060,738\) & \(3.01\times 10^{-9}\) \\ \(N_{8}\) & \(N_{9}\) & \(N_{6}\) & 15,627.08 & 0.04 & 0.88 & \(1.77\times 10^{-7}\) & \(8.43\times 10^{-8}\) & \(1.31\times 10^{-8}\) \\ \(N_{1}\) & \(N_{2}\) & \(N_{8}\) & 404.32 & 0.83 & 0.17 & \(8\times 10^{-6}\) & \(4\times 10^{-6}\) & \(4\times 10^{-6}\) \\ \(N_{13}\) & \(\mathcal{R}_{fl}\) & \(I_{SW}\) & 683,121.2 & \(6.36\times 10^{14}\) & 258.09 & \(-1186.02\) & \(6.36\times 10^{14}\) & \(-5.75\) \\ \(N_{15}\) & \(E_{h}\) & \(\mathcal{C}_{n}\) & 4122.96 & 1.00 & 0.17 & \(-3.14\times 10^{-7}\) & \(3.13\times 10^{-9}\) & \(3.97\times 10^{-8}\) \\ \(N_{12}\) & \(N_{13}\) & \(N_{15}\) & \(-442,160.7\) & 1.10 & 0.81 & \(2.61\times 10^{-7}\) & \(6.59\times 10^{-7}\) & \(1.80\times 10^{-8}\) \\ \(N_{11}\) & \(N_{12}\) & \(N_{8}\) & \(-2545.44\) & 0.82 & 0.18 & \(6\times 10^{-6}\) & \(3\times 10^{-6}\) & \(3\times 10^{-6}\) \\ \hline \(\hat{E}\) & \(N_{1}\) & \(N_{11}\) & \(-161.54\) & \(6.78\) & \(-5.78\) & \(2.86\times 10^{-4}\) & \(1.46\times 10^{-4}\) & \(1.40\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Polynomial representation of the best hour-ahead DNN model. In Table 6, the day-ahead model performance results of the proposed methods are demonstrated in detail. According to Table 6, the day-ahead DNN model shows superior performance in comparison with the corresponding GEP model from any perspective. Compared to the GEP model, the DNN model indicates 14.32% and 78.56% better performances in terms of nRMSE and elapsed time. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**DNN**} & \multicolumn{4}{c}{**GEP**} \\ \cline{2-9}  & \(\mathbf{R}^{2}\) & **nMAE** & **nRMSE** & **Run Time** & **R\({}^{2}\)** & **nMAE** & **nRMSE** & **Run Time** \\
**Performance** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline
1 h-Ahead Model & 98.29 & 3.57 & 5.66 & 30.70 & 97.97 & 3.58 & 6.17 & 178.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performances of the proposed models for an hour-ahead electricity demand forecasting.