Energy Consumption Prediction Using MLP-PSO Methods

Gemiten Gnmze Lingual Ortodontik Apareyler 1 1 Energy Consumption Prediction Using MLP-PSO Methods SELİM BUYRUKOĞLU 1 MOHAMMED RASHAD BAKER 2 1 Assoc. Prof. Dr.; Çankırı Karatekin University, Faculty of Engineering, Department of Computer Engineering, [email protected] ORCID No: 0000-0001-7844-3168 2 Assoc. Prof. Dr.; University of Kirkuk, College of Computer Science and Information Technology, Department of Artificial Intelligence, [email protected] ORCID No: 0000-0001-69864921 2 Energy Consumption Prediction Using MLP-PSO Methods SELİM BUYRUKOĞLU, MOHAMMED RASHAD BAKAR Design: All Sciences Academy Design Publication Date: December 2025 Publisher’s Certificate Number: 72273 ISBN: 978-625-8536-17-1 Doi: https://doi.org/10.5281/zenodo.17887556 © All Sciences Academy www.allsciencesacademy.com [email protected] 3 CONTENT ÖNSÖZ 4 PREFACE 5 ÖZET 6 ABSTRACT 7 INTRODUCTION 8 LITERATURE REVIEW 10 MATERIALS AND METHODOLOGY 12 Data Collection 14 Data Preparation 15 Machine Learning Algorithms 15 Single-Base Models 16 Deep Learning Model 21 Multi-Layer Perceptron (MLP) 21 The Proposed Multi-Layer Perceptron Trained with Particle Swarm Optimization (MLP-PSO) Model 22 Evaluation Metrics 23 Hyperparameter Tuning 24 RESULTS AND DISCUSSION 25 CONCLUSIONS AND FURTHER DIRECTIONS 30 REFERENCES 32 4 ÖNSÖZ Sevgili Okuyucular, Küresel ölçekte artan enerji talebi, sürdürülebilirlik hedeflerinin ve enerji verimliliği politikalarının önemini her zamankinden daha fazla ortaya koymaktadır. Özellikle konut sektöründe enerji kullanımının hızlı yükselişi, modern yaşamın gereklilikleri ve teknolojik gelişmelerle birleştiğinde, doğru ve güvenilir tahmin modellerinin geliştirilmesini zorunlu hâle getirmiştir. Bu doğrultuda elinizdeki çalışma, enerji tüketiminin öngörülmesi amacıyla makine öğrenimi ve optimizasyon yöntemlerini bütünleştiren kapsamlı bir araştırmayı içermektedir. Bu kitapta, klasik tekil tahminleyici modellerden (Doğrusal Regresyon, SVM, KNN) ileri topluluk yöntemlerine (Random Forest, Gradient Boosting, Stacking) uzanan geniş bir model yelpazesi değerlendirilmiş; ayrıca derin öğrenme yaklaşımlarından Çok Katmanlı Algılayıcı (MLP) ayrıntılı biçimde incelenmiştir. Çalışmanın özgün yönünü ise, MLP mimarisinin Parçacık Sürüsü Optimizasyonu (PSO) ile eğitilmesini sağlayan hibrit MLP-PSO yöntemi oluşturmaktadır. Bu yöntem, klasik geri yayılım algoritmasının iyileştirilmesi ve en uygun ağırlık-bias değerlerinin bulunması amacıyla geliştirilmiş; yapılan deneysel analizler, MLP-PSO’nun diğer tüm karşılaştırma modellerine kıyasla daha yüksek doğruluk ve daha düşük hata değerleri sunduğunu göstermiştir. Bu eser; enerji tüketimi tahmini alanında hem teorik hem de uygulamalı olarak sağlam bir temel oluşturmayı, araştırmacılar ve uygulayıcılar için güvenilir bir referans sunmayı amaçlamaktadır. Enerji yönetimi, akıllı bina sistemleri ve sürdürülebilirlik odaklı çalışmalara katkı sağlayacak yeni bakış açıları kazandıracağına inanıyoruz. Bu çalışmanın ortaya çıkmasında emeği geçen tüm meslektaşlarımıza ve ilgili araştırma topluluğuna teşekkür eder; kitabın bilimsel üretime değerli katkılar sunmasını temenni ederiz. Tüm meslektaşlarımıza iyi çalışmalar dileriz. SELİM BUYRUKOĞLU, MOHAMMED RASHAD BAKAR 5 PREFACE Dear Readers, The global rise in energy demand has underscored the growing importance of sustainability targets and energy-efficiency policies. In particular, the rapid increase in energy consumption within the residential sector—driven by modern lifestyle requirements and technological expansion—necessitates the development of accurate and reliable predictive models. In this context, the present work offers a comprehensive investigation that integrates machine learning and optimization techniques to forecast energy consumption effectively. This book evaluates a wide spectrum of predictive models, ranging from classical single-base learners (Linear Regression, SVM, KNN) to advanced ensemble approaches (Random Forest, Gradient Boosting, Stacking), while also examining deep learning methodologies, particularly the Multi-Layer Perceptron (MLP). The original contribution of this research lies in the hybrid MLP-PSO method, in which the MLP architecture is trained using Particle Swarm Optimization (PSO). Developed to enhance classical backpropagation and to identify optimal weight–bias configurations, the proposed hybrid approach demonstrates superior predictive accuracy and lower error rates compared to all benchmark models evaluated in this study. This work aims to provide a robust theoretical and practical foundation for researchers, practitioners, and decision-makers in the field of energy consumption forecasting. It is our expectation that the findings will contribute novel perspectives to energy management, smart building systems, and sustainability-focused applications. We extend our sincere gratitude to our colleagues and the broader research community whose efforts have supported the development of this study. We hope that this book will serve as a valuable contribution to scientific inquiry and ongoing advancements in the field. Wishing all our colleagues success in their work. Sincerely, SELİM BUYRUKOĞLU, MOHAMMED RASHAD BAKAR 6 ÖZET Son yıllarda konutlarda enerji talebi; ev tipi cihazların artışı, aşırı enerji kullanımı ve demografik büyüme gibi etmenler nedeniyle önemli ölçüde yükselmiştir. Bu çalışma, söz konusu sorunlara çözüm üretmek amacıyla binalardaki enerji tüketimini tahmin etmek için makine öğrenimi yöntemlerini incelemektedir. Bu alan, giderek gelişen bir araştırma konusudur. Çalışma, klasik çok katmanlı algılayıcı (MLP) ile parçacık sürüsü optimizasyonu (PSO) kullanılarak eğitilen çok katmanlı algılayıcının karşılaştırmalı bir değerlendirmesini nesnel biçimde sunmayı amaçlamaktadır. Ayrıca doğrusal regresyon, destek vektör makineleri ve en yakın komşular gibi tekil tabanlı öğreniciler; torbalama yöntemi (rastgele orman), artırmalı öğrenme (gradyan artırma) ve istifleme (stacking) gibi diğer makine öğrenimi teknikleri de analiz edilmiştir. Modellerin performansını değerlendirmek amacıyla MSE, MAE, RMSE ve R² gibi istatistiksel ölçütler kullanılmıştır. Bulgular, MLP-PSO yönteminin en iyi sonucu ve en yüksek R² değerini (62.08%) elde ettiğini göstermektedir. Doğrusal regresyon, destek vektörü ve istifleme yöntemi de başarılı sonuçlar ortaya koymuştur. Anahtar Kelimeler – Makine Öğrenimi Modeli, Enerji Tketimi Tahmini, Tahmin, Paracık Srs Optimizasyonu 7 ABSTRACT In recent years, Energy demand in residential buildings has significantly increased due to the growth of household appliances, excessive energy use and demographic expansion. This study explores machine learning methods to predict energy consumption in buildings in order to address these problems. This is an emerging field of research. This paper has the objectivity to evaluate and compare classical multi-layer perceptron and multi-layer perceptron trained with particle swarm optimization (PSO). Other machine learning techniques were also assessed such as single base learners (linear regression, support vector machines, K-nearest neighbors), bagging (random forest) boosting (gradient boosting), stacking methods. In order to evaluate the performance of these models, statistical methods such as MSE, MAE, RMSE, and R2 were used. MLP-PSO method provided the best result and the highest R² (62.08%). Linear regression, support vector, and stacking technique achieved good results. Keywords – Machine Learning Model, Energy Consumption Prediction, Prediction, Particle Swarm Optimization 8 INTRODUCTION Energy contributes to economic and social development in all countries, but it depends on various factors, such as production, transportation, and the way it is used. Energy can be defined as the capacity to do work and is a measurable quantity. It can come in many different forms, including electrical, kinetic, nuclear, thermal, chemical, mechanical, gravitational, and sound. It can be stored and converted according to its use. It can be fossil (petroleum, natural gas, etc.), renewable (biomass, solar, geothermal, hydrogen, etc.) (Klass, 2004). Energy is used for several sectors such as buildings, transportation, industries, etc. Energy consumption in residential buildings has significantly increased with the expanding population, technological development, and economic growth. Buildings represent nearly one-third of worldwide energy consumption and around one-quarter of CO2. Russia, the European Union, Japan, and the United States are the largest energy consumers in the world, representing (42%, 41% ,37%, and 34%, respectively (World Energy Balances - Data Product, 2025). Energy use causes environmental problems, including climate change, air, and water pollution. With the aim of saving energy and reducing environmental impact. Predicting energy consumption is essential to ensure sustainability, energy management, and efficiency. In general, three techniques are used to predict energy consumption in buildings: physical methods (Lü et al., 2015), hybrid approaches and artificial intelligence techniques (machine learning and deep learning algorithm) ( Wang & Srinivasan, 2017). Physical models are based on the partial differential equations to explain energy flows in buildings. This technique makes use of building energy balance. It takes into account such important aspects as indoor air and interior internal heat gains like occupancy, electrical equipment, and lighting. The building envelope comprises of walls, floors, roofs, windows, and doors. It also considers heat loss by the use of windows and ventilation. These approaches provide very useful insights, which are restricted to simple systems. The hybrid approach is the combination of both physical and datadriven models. It applies the concepts of thermodynamics to predict the use of energy in buildings. The method is aimed at enhancing precision of energy 15 Mean: 77.056 Data Preparation Data preparation is a fundamental step to ensure high-quality datasets, efficient models, and accurate predictions, since the precision of the prediction depends on the quality of the data. Data preprocessing is time-consuming but necessary. Our features have a different scale. If we do not scale the features, some of them with a high numerical value will dominate the training phase. In order to fix this problem, the data were standardized using the standardscaler method, which means that the standard deviation of the data is zero, while the mean is one. It is calculate by substracting the mean of the feature from each value and then dividing by the standard deviation (Kumar, 2023). After preprocessing, it is necessary to split the data into training and testing sets. The models are trained at 70% of the data points, while 30% are used for testing. 𝑥′=𝑥−𝑥 𝑆𝑑 (1) x′ = standard value, x = original value, 𝑥 = mean of the values of x, Sd = standard deviation of the values of x. Machine Learning Algorithms In this study, a comprehensive set of five distinct machine learning methodologies was employed to predict energy consumption in residential buildings. The task is to examine the non-linear multifaceted relations between the characterization of the input features and the target variable. Through the comparison of a range of models, including the simplest base learners and the most advanced ensemble and deep learning designs, we create a strong baseline that will allow us to compare the suggested hybrid approach. 16 Single-Base Models Linear Regression (LR) Linear Regression is a basic foundation of predictive modeling because it can be readily interpreted and it is computationally inexpensive. But its major significance is it creates a clear picture on how the change in the independent variables has a direct impact on the target outcome, and thus it is a crucial standard by which more complex non-linear models can be compared. This method is functionally similar to examining the correlation between independent variables and a dependent target variable by determining a straight line or a hyperplane that passes through the data points. The algorithm aims at finding the best weights and bias that minimize the sum of squared differences between the actually observed values and the values that the model predicts (Buyrukoglu & Yilmaz, 2021). Figure 2 is the structure of LR model. Figure 2: Structure of LR model K-Nearest Neighbor (KNN) K-Nearest Neighbor algorithm is greatly appreciated because of its simplicity and it is non-parametric in nature, that is, it does not assume anything about the distribution of the data. This flexibility can be especially applied in situations where the relationship between the data is not regular or can be difficult to characterize using typical mathematical formulas. KNN is an instance-based learning method, which is not designed to create an internal 17 representation of learning but rather it stores all the training cases. To make a prediction of a new data point, the algorithm computes the distance between the point to all the points in the dataset, determines the particular number of closest neighbors which is specified by the user, and sums up the values of the closest neighbors. In case of regression tasks, the value of the nearest neighbors is averaged to obtain the prediction (Buyrukoğlu et al., 2025). The model of KNN is depicted in Figure 3. Figure 3: Structure of KNN model Support Vector Machine (SVM) The Support Vector Machine is commonly known to be robust in high dimensional space and also in cases where the dimensions are more than the number of samples. This is because of its high generalization capability which reduces the possibility of overfitting in the event of less data. The process entails building a hyperplane to segregate information or forecast continuous values. When it comes to regression, it is to fit the error within a certain tolerance range and as much as possible maximize the distance to the closest data points, the so-called support vectors. The algorithm is able to model complex non-linear relationships by using the kernel functions to map the input data into higher dimensional feature spaces without necessarily performing the computations of the coordinates (Alwazy et al., 2025). Figure 4 is the design of SVM model. 18 Figure 4: Structure of SVM model Random Forest (RF) Random Forest is a very important machine learning tool as it solves the high variance that is characteristic of individual decision trees, which is prone to unreliable and unstable predictions. Of specific significance is its capacity to prioritize the significance of various input features, and thus, assisting the researcher to establish the factors that cause energy consumption. This is a more effective way of predicting because it builds an ensemble of hundreds or thousands of decorrelated trees. The algorithm uses two important randomizing methods, including bagging whereby each tree is trained on a random sample of the data with replacement and feature randomness wherein only a random sample of features is used to split at a given node. This last prediction is obtained by averaging the results of all the single trees and this helps to reduce noise and also enhances generalization (Buyrukoğlu, 2024) The structure of RF model is described in Figure 5. 19 Figure 5: Structure of RF model Gradient Boosting (GB) Gradient Boosting is now regarded as among the strongest methods of structured data analysis, and can offer state-of-the-art predictive power. It is important because it minimizes bias as well as variance by successively correcting the errors of the earlier models and thus, it is very useful in complex regression processes such as the forecasting of energy demands. Gradient Boosting builds the model in a stage-wise manner as opposed to Random Forest which builds the tree in parallel. Every new tree is introduced as a weak learner that is specially created to eliminate the remaining errors caused by the last tree in the sequence. The conceptual approach of the method is based on the gradient descent to reduce the loss function by introducing new models that are in agreement with the negative gradient of the error (Baker & Solanki, 2024). Figure 6 is the structure of GB model. 20 Figure 6: Structure of GB model Stacking Ensemble The importance of stacking or Stacked Generalization is that it takes advantage of the individual strengths of various algorithms to create a prediction that is better than individual models. It can also use the weaknesses of one algorithm to be filled by the strengths of another, resulting in the greatest possible accuracy in competitive modeling. The mechanism of working is the two level architecture. The former level is comprised of a variety of base models that will make independent predictions using the initial dataset. The input features of a second-level meta-learner are then based on these predictions. The meta-learner becomes trained to combine these inputs in a way that they give the optimal output in terms of creating a final prediction that is robust (Divina et al., 2018). Figure 7 is a stacking methodology that will be used in this study. Figure 7: Methodology of stacking methods 21 Deep Learning Model Multi-Layer Perceptron (MLP) The Multi-Layer Perceptron is important for its general estimate capability, allowing it to model practically any continuous function nevertheless of its complexity. This makes it the foundation of modern deep learning and an essential tool for capturing the highly non-linear and dynamic patterns found in building energy consumption data. An MLP is a feedforward artificial neural network composed of an input layer, one or more hidden layers, and an output layer. In the feedforward phase, inputs are processed through weighted sums and non-linear activation functions to produce an output. During training, the backpropagation algorithm calculates the error between the prediction and the actual value, then propagates this error backward through the network to adjust the internal weights and biases to minimize the global error (Oludolapo et al., 2012). Figure 8 represents the structure of MLP model. Figure 8: Structure of MLP model 22 The Proposed Multi-Layer Perceptron Trained with Particle Swarm Optimization (MLP-PSO) Model MLP-PSO uses particle swarm optimization algorithms to update the weight and the bias of the model in order to minimize mean square error (MSE). PSO is an optimization algorithm inspired by the behaviour of swarm. Each potential solution is represented by a particle that explore the search space. These particles adjust their position based on their own experience (best position reached individually) and that of the entire group (best global position). The goal is to converge toward an optimal solution by exploring both individual exploration and social cooperation. PSO is effective optimization method for its simplicity, speed and efficiency in optimizing complex functions, such as updating weights and bias in MLP model. MLPPSO take the advantage of PSO method in order to adjust the parameters (weight and bias). L2 regularization is also employed to prevent overfitting. During the training phase of the MLP-PSO, we set hidden layer size of 256, this comes from MLP optimized via Grid Search, L2 of 0.000001. The algorithm of proposed work is giving below in Algorithm 1. Algorithm 1: The proposed Hybrid MLP-PSO ALGORITHM: Hybrid MLP-PSO Input: Dataset, MLP Architecture (Hidden Layer = 256), L2 Regularization (10-6) Output: Optimal Weights for the Neural Network 1. Initialize a swarm of particles with random positions (Note: Each particle represents a candidate set of weights and biases) 2. While termination condition is not met Do: 3. For each particle in the swarm Do: a. Construct the MLP network using the particle's current weights. b. Calculate Fitness: Compute MSE on training data + L2 penalty. c. Update Personal Best: If current fitness is better than historical best, save it. End For 4. Update Global Best: Identify the particle with the lowest error in the entire swarm. 5. For each particle in the swarm Do: 23 6. a. Update Velocity: Calculate movement based on Personal Best and Global Best. b. Update Position: Move particle to new coordinates (new weights). 7. End For 8. End While 9. Return Global Best positions as the final MLP model weights. Evaluation Metrics In ML, there are several evaluation metrics that allow to measure the performance and quality of the models. It is essential to choose the appropriate evaluation metrics based on the objective of the model and regression problems. However, using multiple metrics provides a more comprehensive view of the model’s performance and helps with decision-making. To identify which model predicts energy consumption well, statistical methods such as MAE, RMSE, and MSE were used (Buyrukoglu & Philipson, 2025). MAE is the absolute difference between the sums of the actual and predicted values. MSE refers to the aggregate squared differences between the predicted and the observed values and this is divided by the total population. The square root of MSE is the RMSE. The R-squared (R2) (also known as coefficient of determination) is the measure of variability of the input variables, which is dependent on the output features (Hosamo & Mazzetto, 2024). MAE= 1 𝑛∑ |𝑦𝑖−𝑦𝑖| 𝑛 𝑖 (2) RMSE=√1 𝑛∑(𝑦𝑖−𝑦𝑖)2 𝑛 𝑖 (3) MSE=1 𝑛∑(𝑦𝑖−𝑦𝑖)2 𝑛 𝑖 (4) R²=1- ∑(𝑦𝑖−𝑦𝑖 )2 𝑛 𝑖 ∑(𝑦𝑖−𝑦𝑖    )2 𝑛 𝑖 (5) 24 yi = actual value yˆi = predicted value Hyperparameter Tuning All ML models utilized in this work were tuned systematically in order to have a fair and rigorous evaluation. The external configuration variables, which are not optimized by the data, but have to be specified beforehand, are hyperparameters; the choice of these hyperparameters is critical to the tradeoff between bias and variance and avoiding overfitting (Ogunsanya et al., 2023). Table 2 describes the search space that is being used by every algorithm, the specific parameters that were tested, the range of values that were tested (through the use of the Grid Search) and the best combination that produced the best results on the validation set. Table 2: Hyperparameter tuning of energy consumption dataset Model Parameter Range Best SVM Kernel ‘linear’, ‘poly’, ‘rbf’ linear C [0.001, 0.01, 0.1, 1, 10, 100] 10 gamma ’scale’,’auto’ scale KNN n_neighbors [3,5,7, 11,13, 15] 13 p 1,2 1 Weights ‘uniform’, ‘distance’ distance RF n_estimators [50,100,150,200,300,400,50 0,1000] 100 max_depth [1,6,10, 20] 20 min_samples_leaf [1,2,3,4,5,6,7,8,9,10,20] 1 min_samples_split [1, 4,8,9,10,11,15,19,20] 8 GB n_estimators [50, 100,150,200,300,400,500,10 00] 50 max_depth [2, 4,5,7,8,10,20] 2 min_samples_leaf [1,3,4, 6] 3 31 prediction. The main aim was to compare the capability of a hybrid optimization strategy to the existing industry standards. This study has made important contributions to the understanding of the behavior of various algorithms when used with residential energy data through extensive experimentation and statistical analysis. The single and ensemble model analysis established that the complexity of the models is not necessarily associated with high performance. Although it is widely acclaimed that ensemble methods such as Random Forest and Gradient Boosting are robust, the results of this study were that they were not as effective as the simpler linear models (Linear Regression) or the Stacking ensemble in this particular case. Stacking, making use of a Support Vector Regressor meta-learner to combine the output of various base models, showed a significant ability to generalise well, with an R2 of 60.76. This highlights the significance of the algorithmic diversity in ensemble learning, which implies that the integration of the benefits of linear and non-linear models is more likely to produce more reliable forecasts than decision-trees based on ensembles. On the other hand, the K-Nearest Neighbor algorithm was the least effective possibly because it is sensitive to noise and the dimensions of feature space are high. The greatest value of this study is the fact that the proposed Hybrid MLP-PSO model is actually validated. The experimental findings clearly show that the predictive accuracy of a Multi-Layer Perceptron optimized by Particle Swarm Optimization on the weights and biases is better than the classical backpropagation training and other ensemble training. The MLPPSO model with a Mean Absolute Error (MAE) value of 4.0379 and Root Mean Square Error (RMSE) of 5.0692 and the largest Coefficient of Determination (R2) of 62.08 was able to overcome the limitations of the standard gradient descent, including the propensity to get stuck in local minima. This result demonstrate the effectiveness of meta-heuristic algorithms to fine-tune deep learning architectures, which is a more stable and accurate solution to complex regression problems in the energy industry. The application of these findings in practical use is immense in the context of designing smart systems of energy management. The high accuracy of MLP-PSO model implies that it can be used as a valid driver of real-time energy monitoring and decision making in smart grids. With more accurate predictions, utility companies and homeowners should be able to predict the 32 peak demand periods with more accuracy, optimize heating and cooling schedules, and eventually help reduce carbon footprints. Although such results are promising, this study does not ignore that there are some limitations that open future research opportunities. Although the performance of the MLP-PSO was the best, the R2 of about 62% implies that the percentage of the variance in energy consumption is not completely explained and it may be because of the unobserved external factors, including granular occupancy patterns or weather variations under micro-climatic conditions. Future research must aim at incorporating these exogenous variables to improve on the precision of the models. 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