## 4 Results and Discussion
### Case Study Results  
In this study, we applied both the AVG and the EB method in two different cases: case (A) where scores were calculated for individual forecaster of each one of the methods ANN, hybrid, RCGA-FCM, and SOGA-FCM, and case (B), where scores were calculated for each ensemble forecaster (ANN ensemble, hybrid ensemble, RCGA-FCM ensemble, and SOGA-FCM ensemble). Considering case (A), Table 1 shows the calculated errors and scores based on the EB method for individual forecaster of the two forecasting methods: ANN and hybrid for the city of Athens. The rest calculated errors and scores, based on the EB method, for individual forecaster for the other two remaining forecasting methods RCGA-FCM and SOGA-FCM for Athens can be found in Appendix A of the paper (Table A3). In Appendix A, parts of the corresponding results for the other two examined cities (Larissa and Thessaloniki) are also presented (Tables A4 and A5). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Validation**} & \multicolumn{2}{c}{**Testing**} & \multicolumn{3}{c}{**Testing**} \\ \hline \hline  & **MAE** & **MSE** & **MAE** & **MSE** & **Weights** & **MAE** & **MSE** & **Weights** \\ \hline ANN1 & 0.0334 & 0.0035 & 0.0350 & 0.0036 & 0.2552 & _Hybrid1_ & 0.0336 & 0.0034 & 0.2520 \\ \hline ANN2 & 0.0354 & 0.0041 & 0.0387 & 0.0043 & 0 & _Hybrid2_ & 0.0387 & 0.0043 & 0 \\ \hline ANN3 & 0.0350 & 0.0037 & 0.0375 & 0.0039 & 0.2442 & _Hybrid3_ & 0.0363 & 0.0037 & 0 \\ \hline ANN4 & 0.0341 & 0.0038 & 0.0365 & 0.0039 & 0 & _Hybrid4_ & 0.0352 & 0.0035 & 0 \\ \hline ANN5 & 0.0335 & 0.0036 & 0.0358 & 0.0037 & 0.2505 & _Hybrid5_ & 0.0339 & 0.0034 & 0 \\ \hline ANN6 & 0.0337 & 0.0039 & 0.0355 & 0.0038 & 0 & _Hybrid6_ & 0.0348 & 0.0036 & 0.2468 \\ \hline ANN7 & 0.0336 & 0.0037 & 0.0362 & 0.0038 & 0 & _Hybrid7_ & 0.0345 & 0.0035 & 0.2506 \\ \hline ANN8 & 0.0340 & 0.0039 & 0.0360 & 0.0039 & 0 & _Hybrid8_ & 0.0354 & 0.0036 & 0 \\ \hline ANN9 & 0.0341 & 0.0039 & 0.0367 & 0.0040 & 0 & _Hybrid9_ & 0.0349 & 0.0036 & 0 \\ \hline ANN10 & 0.0332 & 0.0036 & 0.0355 & 0.0037 & 0.2501 & _Hybrid10_ & 0.0359 & 0.0038 & 0 \\ \hline ANN11 & 0.0338 & 0.0038 & 0.0365 & 0.0039 & 0 & _Hybrid11_ & 0.0353 & 0.0038 & 0 \\ \hline ANN12 & 0.0345 & 0.0038 & 0.0349 & 0.0037 & 0 & _Hybrid12_ & 0.0347 & 0.0033 & 0.2506 \\ \hline \(AVG\) & 0.0336 & 0.0037 & 0.0359 & 0.0038 & & _AVG_ & 0.0350 & 0.0036 & \\ \hline EB & 0.0335 & 0.0036 & 0.0358 & 0.0037 & & _EB_ & 0.0340 & 0.0034 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case (A)-Calculated errors and weights for each ensemble forecaster based on scores for EB (error-based) method (Athens). Considering case (B), Table 2 presents the calculated weights based on scores for each ensemble forecaster (ANN (ensemble, hybrid ensemble, RCGA ensemble, and SOGA ensemble) for all three cities. The calculated weights, based on scores for the EB method, were computed using Equation (17). According to this equation, the weights of the component forecasts are inversely proportional to their in-sample forecasting errors, concluding that the model with more error is assigned less weight to it and vice versa [80]. In this work, as the values of errors were high for certain ensemble forecasters, the corresponding weights were approximately zero, so they were considered to have a zero value for further predictions. The obtained forecasting results of the individual and combination methods are depicted in Tables 3-8, respectively, for the three cities. In each of these tables, the best results (i.e., those associated with the least values of error measures) are presented in bold letters. In Figures 4 and 5, the forecasting results concerning Thessaloniki and Larissa are visually illustrated for both ensemble methods (AVG, EB). Moreover, Figure