## 6 Experiments
### Experiment V: Comparison with Three Combined Models (Two Objective Functions)  
We proposed three other combined models with two objective functions in Section 5.2. In this experiment, we tested the accuracy and stability between our proposed system and the other three combined models. Here, wind-speed data from Site 3 were used in our experiments, and all of the models in this part were run 100 times. (a) The results in Tables 7 and 8 show the following:  
(1) Table 7 shows the average AE, MAE, and MSE. It can be seen that the forecast performance and the results of our proposed combined model were better in accuracy. (2) The average results of the three two-objective-function models were close to the combined system (three objective functions). Especially on Friday, the difference between the combined model (three objective functions) and the combined models (two objective functions) was only 0.65%. (3) As shown in Table 8, after running the models for 100 times, the standard-deviation MAPE and the MAPE range of the two-objective-function models was much higher and larger than the combined model. This shows that the stability of our combined model's performance was much better than the combined models with the two objective functions. (b). Figure 6 shows the following;  
(1) Part A shows that, with regard to the minimum, maximum, and average results of MAPE from 100 experiments, our proposed combined model with three objective functions reached the lowest values compared with the other combined models on each day. (2) Part C presents that the MAE and MSE of our proposed combined model with three objective functions were also lower than the other models. **Remark 4**. : _The results show that the performance of the combined model with two objective functions was close to the combined model with three objective functions when we chose the result average. However, the single results of the combined model with three objective functions could be given a high degree of trust, as accuracy and stability were successfully enhanced by our combined model based on NSGA-III in the forecasting problems._ \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Combined Model \({}^{*}\)**} & \multicolumn{3}{c}{**Combined Model \({}^{**}\)**} & \multicolumn{3}{c}{**Combined Model \({}^{***}\)**} & \multicolumn{3}{c}{**Combined Model \({}^{***}\)**} \\ \cline{2-13}  & **AE** & **MAE** & **MSE** & **AE** & **MAE** & **MSE** & **AE** & **MAE** & **MSE** & **AE** & **MAE** & **MSE** \\ \hline Monday & 0.01815 & 0.33185 & 0.00233 & 0.01568 & 0.32888 & 0.00225 & 0.07684 & 0.34506 & 0.00590 & 0.03088 & 0.26371 & 0.00095 \\ Tuesday & \(-\)0.03139 & 0.36454 & 0.00099 & \(-\)0.03672 & 0.30132 & 0.00135 & 0.00497 & 0.35975 & 0.00249 & 0.02454 & 0.30748 & 0.00060 \\ Wednesday & \(-\)0.00956 & 0.28940 & 0.00204 & \(-\)0.01435 & 0.28707 & 0.00221 & 0.04960 & 0.29631 & 0.00466 & 0.03342 & 0.21287 & 0.00110 \\ Thursday & 0.03749 & 0.32268 & 0.00341 & 0.03271 & 0.32185 & 0.00307 & 0.09834 & 0.33558 & 0.00967 & 0.04553 & 0.22493 & 0.00207 \\ Friday & \(-\)0.05878 & 0.55131 & 0.00345 & \(-\)0.06042 & 0.54689 & 0.00365 & 0.02861 & 0.55014 & 0.00082 & 0.01317 & 0.50229 & 0.00017 \\ Saturday & \(-\)0.00960 & 0.49825 & 0.00484 & \(-\)0.007203 & 0.40999 & 0.00519 & 0.01423 & 0.50229 & 0.00020 & 0.02069 & 0.00001 \\ Sunday & \(-\)0.05840 & 0.38680 & 0.00341 & \(-\)0.06404 & 0.38548 & 0.00410 & 0.02042 & 0.38329 & 0.00042 & 0.01426 & 0.29934 & 0.00020 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The results for the combined model compared with combined model with two objective functions.