# Plum Tree Algorithm and Weighted Aggregated Ensembles for Energy Efficiency Estimation
## 6 Discussions
### Comparison to Other Nature-Inspired Algorithm-Based Ensembles  
This section compares the performance of the PTA ensemble to the performance of the ensembles based on other nature-inspired algorithms both for when no standardization was considered and for when the data was standardized. For each nature-inspired algorithm considered in the experiments, the same specific configuration parameters values were applied as the ones presented in Table 4. For each algorithm and for each fold, 30 runs were performed. The results did not present a lot of differences during the runs; therefore, the best runs were the ones for which the RMSE \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Approach** & **RMSE** & **R2** & **MAE** & **MAPE** \\ \hline Cooling & PTA ensemble & 1.519352 & 0.974118 & 1.016108 & 0.03663 \\  & average ensemble & 1.712945 & 0.96694 & 1.13183 & 0.040357 \\  & RFR & 1.758939 & 0.964869 & 1.050144 & 0.036053 \\  & GBR & 1.523731 & 0.973964 & 1.028088 & 0.037196 \\  & AdaBoost & 2.44213 & 0.933135 & 1.897533 & 0.075278 \\  & ETR & 1.892635 & 0.959707 & 1.067652 & 0.036198 \\ \hline Heating & PTA ensemble & 0.433806 & 0.998119 & 0.296516 & 0.012694 \\  & average ensemble & 0.660918 & 0.995658 & 0.490883 & 0.023875 \\  & RFR & 0.481654 & 0.997662 & 0.328409 & 0.014023 \\  & GBR & 0.477339 & 0.997731 & 0.340544 & 0.01553 \\  & AdaBoost & 1.892841 & 0.96484 & 1.529491 & 0.077095 \\  & ETR & 0.45755 & 0.997912 & 0.308258 & 0.01284 \\ \hline Standardized Cooling & PTA ensemble & 0.159903 & 0.974098 & 0.107013 & 0.169855 \\  & average ensemble & 0.179606 & 0.967172 & 0.119465 & 0.212976 \\  & RFR & 0.184274 & 0.965269 & 0.109801 & 0.204687 \\  & GBR & 0.160374 & 0.973942 & 0.108143 & 0.167695 \\  & AdaBoost & 0.252388 & 0.935285 & 0.198629 & 0.282862 \\  & ETR & 0.200184 & 0.959175 & 0.113029 & 0.21786 \\ \hline Standardized Heating & PTA ensemble & 0.043124 & 0.998111 & 0.02945 & 0.031894 \\  & average ensemble & 0.066474 & 0.995548 & 0.049229 & 0.058983 \\  & RFR & 0.048122 & 0.997628 & 0.03277 & 0.038727 \\  & GBR & 0.047517 & 0.997717 & 0.033849 & 0.03378 \\  & AdaBoost & 0.189049 & 0.963962 & 0.151101 & 0.16832 \\  & ETR & 0.045553 & 0.997896 & 0.030651 & 0.033626 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison to the Average Ensemble and the Individual Components of the Ensemble. value was minimal. If more runs returned the same minimal RMSE value, then the run that corresponded to the minimum running time was selected. For each dataset, the mean values of the evaluation metrics were computed as averages of the values which corresponded to each fold. The values of RMSE, \(R^{2}\), MAE, MAPE, and of the weights of the ensembles were almost identical for all 30 runs for all algorithms, except for the CSO algorithm and the PSO algorithm. For example, for the CSO-based ensemble, the RMSE had values from [1.394474, 1.47675] for fold 1 of the Cooling Dataset. Similarly, for the PSO-based ensemble, the RMSE had values from [0.3438, 0.3522] for fold 1 of the Heating Dataset. However, the best runs out of the 30 runs for both the PSO and CSO algorithms were similar or identical to the ones of the other nature-inspired algorithms, except for the running time. Figure 15 presents the summary of the average running time for all nature-inspired algorithm-based ensembles considered in the experiments, with separate graphs for each experimental dataset showing the runs that returned the best RMSE values. As shown in Figure 15, the standardization of the data did not greatly influence the average running times of the nature-inspired algorithms. The worst performance was that of the HOA, whereas the best performance was that of the GWO for the Cooling Standardized Dataset and that of the CSO algorithm for the other three datasets. As an overall remark, from the perspective of running time and the variation in the results, the GWO-based ensemble returned the best results.