# Plum Tree Algorithm and Weighted Aggregated Ensembles for Energy Efficiency Estimation
## 2 Background
### Machine Learning Approaches to Energy Efficiency Estimation  
Energy efficiency estimation using machine learning techniques was considered in the literature from different perspectives. Moreover, the literature contains a variety of review studies which focus on the application of machine learning techniques to energy performance, such as the ones presented in [70; 71].  
In [72], the authors proposed an estimation model for heating energy demand in which a methodology based on a two-layer approach was developed using a database of approximately 90,000 Energy Performance Certificates (EPCs) of flats from Italy's Piedmont region. The proposed methodology consisted of two layers: the classification layer, which was used to estimate the segment of energy demand, and the regression layer, which was used to estimate the Primary Energy Demand (PED) of the flat. The four algorithms which were used and compared in both layers were the Decision Tree (DT) algorithm, the Support Vector Machine (SVM) algorithm, the Random Forest (RF) algorithm, and an Artificial Neural Network (ANN). Another approach, the one presented in [73], considered the application of two ANNs, one for actual energy performance and another for key economic indicators. The data was collected from the energy audits of 151 public buildings from four regions of South Italy. The prediction of their energy performance was done using a decision support tool based on these two ANNs.  
In [74], an ensemble learning technique method was applied to energy demand prediction in the case of the residential buildings. The data was collected from residential buildings located in Henan, China. The applied model was used to forecast the heating load 2 h ahead. The ensemble learning method combined the algorithms Extreme Learning Machine (ELM), Extreme Gradient Boosting (XGB), and Multiple Linear Regression (MLR) with the Support Vector Regression (SVR) algorithm to obtain a model that was more accurate. The authors of [75] considered a PSO-based ensemble learning approach for the energy forecast. The proposed optimized ensemble model was used for the management of the smart home energy consumption. The PSO algorithm was used to fine-tune the hyper-parameters of the ensemble model. The results showed that the performance of the optimized ensemble was better than the performance of both the non-optimized ensemble and the individual models.  
The authors of [76] developed an ensemble machine learning model for the prediction of building cooling loads. The model was created and evaluated using data from 243 buildings. The results show that cooling loads can be predicted quickly and accurately in the early design stage. Energy demand management was approached in [77] using a method based on a weighted aggregated ensemble model. The ensemble consisted of the weighted linear aggregation of the Least Square Boosted Regression Trees (LSB) and Gaussian Process Regression (GPR) algorithms, and the design parameters were evaluated using the Marine Predators Algorithm (MPA) [78].  
Building energy prediction was approached in [79] using energy consumption pattern classification. The DT algorithm was used for mining energy consumption patterns and classifying energy consumption data, whereas ensemble learning was used to establish energy consumption prediction models for the patterns. The data used in the work was hourly meteorological data collected from a meteorological station, and the energy consumption data was collected from an office building from New York City.