# Plum Tree Algorithm and Weighted Aggregated Ensembles for Energy Efficiency Estimation
## 7 Conclusions  
This article presents a novel approach based on the PTA for the estimation of energy efficiency in which the weights of an ensemble composed of the RFR, the GBR, the AdaBoost, and the ETR is used in the prediction of cooling and heating loads. Fivefold cross-validation was used to validate the method, and the results obtained for the cooling and heating predictions were 1.519352 and 0.433806, respectively, when no standardization was applied, and they were 0.159903 and 0.043124, respectively, when standardization was applied. The obtained results were also compared to those in the literature. The principal outcomes are the following:  
* The PTA is a performant nature-inspired algorithm, as shown by the comparison to six other nature-inspired algorithms using 24 benchmark objective functions;
* The PTA has fewer configuration parameters compared to the HOA and CSO algorithms, which makes it easier to configure for certain optimization problems;
* On the other hand, the PTA has more configuration parameters than the GWO, the CS algorithm, and the CSA, which might be an advantage for other types of optimization problems; \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **Approach** & **Description** & **Method** & **Coiling (RMSE)** & **Heating (RMSE)** \\ \hline
2023 & this & A method based on a PTA ensemble of RFR, GBR, AdaBoost, and ETR is compared to the performance of other nature-inspired algorithm-based ensembles. & CS-S, CSA-S, GWO-S, PTA-S & 1.519352 & 0.433806 \\  & & & & 0.159903 & 0.043124 \\ \hline  & & & TNN and MRMR & 0.81391 & 0.45689 \\  & & GPR & 1.31090 & 0.46479 \\  & & Boosted Trees & 1.63640 & 0.66731 \\  & & Fine Tree & 1.80640 & 1.02460 \\
2022 & [PERSON] et al. [97] & A method based on the Tri-Layer Neural Network (TNN) and Maximum Relevance Minimum Redundancy & Bagged Trees & 1.99780 & 0.79549 \\  & & (MRMR) is compared to other prediction methods. & Medium Tree & 1.87700 & 1.11810 \\  & & SLR & 1.93530 & 1.09030 \\  & & LR & 2.30970 & 2.15290 \\  & & SVM & 2.19510 & 2.32150 \\ \hline
2019 & [PERSON] et al. [98] & A method based on the Naive Bayes Classifier (NBC). & NBC & 0.1412 & 0.1491 \\ \hline
2019 & [PERSON] et al. [99] & A method in which the weights and the biases of an ANN & ANN & 3.9489 & 3.6481 \\  & & are optimized using the GA and the Imperialist & GA-ANN & 2.8598 & 2.8878 \\  & & Competition Algorithm (ICA). & ICA-ANN & 2.7795 & 2.7819 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparison to the Literature Results. * The PTA and PTA-S ensembles showed better prediction results in terms of RMSE, \(R^{2}\), MAE, and MAPE compared to the average ensemble and the individual components of the PTA-based ensembles;
* The quantitative results obtained by using the PTA and PTA-S methods to predict energy efficiency were equal to those obtained by using the CS algorithm, the CSA, the GWO, the CS-S, the CSA-S, and the GWO-S;
* The results obtained by using the nature-inspired algorithm-based methods for the prediction of energy efficiency are comparable to those obtained in the literature with state-of-the-art methods. As future research work, the following directions are proposed:
* The evaluation of the PTA using more objective benchmark objective functions and the comparison to other nature-inspired algorithms;
* The improvement of the performance of the PTA through hybridization with other nature-inspired algorithms or the modification of the equations applied to update the positions of the flowers;
* The application of the PTA to more types of engineering problems;
* The development of a multi-objective version of the PTA. This research received no external funding. Not applicable. The dataset which supports this article is from the UCI machine learning repository, which can be found at \"[[https://archive.ics.uci.edu/ml/index.php](https://archive.ics.uci.edu/ml/index.php)]([https://archive.ics.uci.edu/ml/index.php](https://archive.ics.uci.edu/ml/index.php)) (accessed on 5 December 2022)\".