Energy efficient design of rural prefabricated buildings based on ANN and NSGA-II

. The growing concern about global climate change and the rapid development of rural areas highlight the need for energy efficient building design. This study aims to establish a multi-objective optimization model based on artificial neural network (ANN) and non-dominated sorting Genetic algorithm II (NSGA-II) to optimize the energy consumption of rural prefabricated buildings. Firstly, ANN and simulation technology are used to build building models and predict building energy consumption. Then, NSGA-II algorithm was used to optimize the energy consumption and material selection of the building, and the best prefabricated building scheme was obtained. The experimental results show that the optimization efficiency of the model is about 95%, which is better than the traditional method. Specifically, compared with the NSGA-II algorithm, the model reduces energy consumption by 16.7%, operating costs by 20.0%, and carbon emissions by 20.0%. When the cost optimization, energy consumption optimization and carbon emission optimization are difficult to balance, the average optimization efficiency of the research design method is about 90% when the cost optimization rate is low, and the other optimization rates are about 85% when the cost optimization rate rises to 50%. When the cost optimization reaches the maximum, the optimization rate remains at about 80%. These results show that the proposed model is robust and efficient. This study provides a comprehensive framework for designing sustainable and energy efficient rural prefabricated buildings that can help reduce energy consumption and environmental impact. It has positive significance in the sustainable development of rural economy and provides a new way of thinking for rural construction.


Introduction
In recent years, the worsening global climate change and the rapid depletion of natural resources have heightened the global focus on energy conservation and emission reduction (Von Homeyer et al. 2021).Among various industries, the building sector accounts for a significant portion of energy consumption, making energy-efficient buildings a crucial and unavoidable topic (Li et al. 2022).In rural areas, prefabricated buildings are constructed using a factory-based production approach, followed by assembly and installation in rural regions (Wasim et al. 2022).Compared to traditional brick and timber structures, prefabricated buildings offer several energy-saving advantages (Luo et al. 2021).Rural prefabricated buildings utilize advanced energy-saving materials and technologies, such as efficient insulation materials like polystyrene boards and rock wool boards for walls and roofs, effectively reducing energy consumption by providing thermal insulation (Awad et al. 2022) and (Arjomandnia et al. 2023).However, energy-efficient building design in rural areas faces challenges related to varying climate conditions, financial and technological constraints, limitations in construction materials and techniques, building land and spatial constraints, as well as awareness and education levels (Doerr et al. 2023) and (Fakhr et al. 2023).Additionally, in the energy-efficient design of rural prefabricated buildings, artificial neural networks can be used for building energy consuming simulating, thermal comfort, daylighting, and other performance factors under different design parameters while employing complex nonlinear function approximation and pattern recognition (Hamida et al. 2021) and (Hobbie et al. 2021).Non-dominated sorting genetic algorithm, as a multi-objective optimization (MOO) algorithm, can be combined with artificial neural networks to significantly reduce the time required for performance evaluation during the rapid optimization process for building performance simulation (Jayakeerti et al. 2023) and (Jayashankara et al. 2023).In this context, this study considers the practical performance requirements of energy-efficient design, innovatively integrating objectives such as energy consumption, cost, and carbon emissions to comprehensively assess the sustainability of buildings (Khettabi et al. 2022).Furthermore, the study creatively considers the coupling effects between envelope structure design and renewable energy system design while also considering independent parameter optimization for different facade orientations to better meet energy-saving needs under different conditions.Ultimately, a MOO model for energy-efficient rural prefabricated buildings is proposed, based on artificial neural networks (ANN) and nondominated sorting genetic algorithm II (NSGA-II), integrating | 996 ISSN: 2252-4940/© 2024.The Author(s).Published by CBIORE building energy consumption simulation.This model assists designers in weighing and selecting among multiple objectives.
The study conducted technical exploration and analysis from four aspects.The first part discussed and summarized the current research on energy conservation in the building sector.The second part focused on researching building energy consumption simulation, ANN, and multi-objective algorithms, including the construction of a MOO model.The third part mainly validated the MOO model through experiments and analyzed the data.The fourth part provided a comprehensive overview of the entire article and reflected and summarized its shortcomings.

Related works
The increasing depletion of global non-renewable resources and the enormous energy consumption in the construction industry have led to a further demand for energy-efficient buildings.Constructing efficient and energy-saving construction methods has become an important research area for some scholars.Deng et al., (2022) addressing the issue of urban building energy modeling, proposed a city building energy model based on clustering and random forest algorithms, thereby enhancing the control over building energy usage and conservation and emissions reduction.Ali et al., (2021) focusing on the analysis of energy consumption and potential energy savings in a particular institution in Malaysia, proposed an energy consumption analysis method based on energy audits, thereby improving the targeted and feasible measures for building energy conservation.Berawi et al., (2023) addressing the energy performance, indoor comfort, and life-cycle cost efficiency of office buildings, proposed an intelligent integrated workspace design framework based on IoT technology, thereby enhancing building energy performance and efficiency.Shafie et al., (2021) addressing the energy efficiency management issue in university campus buildings, proposed energy and energy efficiency management strategies based on expert interviews and the collection of electronic materials and books, thereby providing sustainable solutions for energy and energy efficiency management in university campus buildings.Mahapatra and Nayyar (2022) addressing the optimization of energy management in residential housing, proposed an impromptu creative building design method based on green building principles, thereby enhancing the efficiency and reliability of residential energy management systems.Ye et al., (2021) addressing the impact of energy efficiency measures on medium-sized office building energy consumption in the United States, proposed an optimization strategy for energy efficiency retrofit measures based on sensitivity analysis combined with standard regression coefficients and sensitivity analysis methods, thereby providing decision support for energy-saving retrofitting of medium-sized office buildings.Long R et al., addressing issues related to energy-efficient building design, proposed an energy-efficient building design framework based on building information modeling simulation technology combined with artificial intelligence technology, thereby improving energy utilization efficiency in the building design process (Long and Li 2021).
In addition, Amani et al., addressing the issue of improving energy efficiency in residential buildings, proposed a residential building energy efficiency optimization model based on ecological technology analysis software, thereby enhancing the energy utilization efficiency of residential buildings under different environmental and climatic conditions (Amani et al. 2022).Zekić-Sušac et al., (2021) focusing on the prediction of energy consumption costs in public buildings, proposed an energy cost prediction model based on ANN, thereby improving the prediction capability in the field of energy management and estimating the surplus generated after reconstruction measures.Al-Habaibeh et al., (2021) addressing the heat performance preservation issue during building retrofit processes, proposed a building heat performance assessment model based on deep learning ANN, thereby enhancing energy-saving effects during building retrofit processes.Nazari et al., (2023) addressing the reduction of energy consumption and improving indoor environment quality in commercial buildings, proposed a commercial building energy efficiency improvement model based on NSGA-II, thereby improving the indoor environmental quality while reducing energy consumption in commercial buildings.Li et al., (2023) addressing the issues of sustainable development and energy system construction in public buildings, proposed a structure of renewable energy microgrids based on an improved NSGA-II, thereby enhancing the sustainable development and energy utilization efficiency of public buildings.
From the research conducted by scholars from different countries, most of the building energy-saving studies mainly focus on optimizing a single aspect, neglecting the systematic parameter optimization of the entire system composed of the building and its environment.Therefore, the proposed MOO model for energy-saving in rural prefabricated buildings, based on ANN and NSGA-II combined with building energy consumption simulation, exhibits certain innovativeness.

Research and design of energy-efficient models for rural prefabricated buildings
Compared to traditional models, a multi-objective optimization model can automatically extract the complex relationships of building energy consumption by learning from a large amount of data, thereby accurately predicting building energy consumption.Additionally, this model can simultaneously consider multiple optimization objectives, such as energy saving, cost reduction, and improved comfort, enabling more comprehensive optimization.Therefore, the design and implementation of the algorithm model are particularly important to ensure continuous optimization.Hence, this section mainly analyzes the fundamental principles of the model and the construction of the system.

Building energy consumption simulation and artificial neural network
The building system studied in this paper is the rural prefabricated building system.The system focuses on combining advanced building technologies with energy efficient materials and renewable energy technologies.A key element of the system is high-performance insulation materials for walls and roofs, such as polystyrene and rockwool, which significantly improve thermal efficiency.In addition, the system includes solar photovoltaic panels for on-site renewable energy generation, an efficient heating, ventilation and air conditioning (HVAC) system for maintaining an optimal indoor climate, and a smart energy management system for real-time monitoring and control of energy consumption.Together, these features aim to optimize energy use, reduce carbon emissions, and improve the sustainability of rural prefabricated buildings.
Buildings are considered as thermodynamic systems comprising closely connected and interacting indoor and outdoor environments (Mehboob 2021) and (Ma et al. 2023).Various factors, such as heat radiation within the rooms and building equipment, can influence the internal environment,

= + + +
all conv CE IV sys q q q q q (1) Equation ( 1), qall represents the building's energy consuming, qconv represents the convective energy consumption on the building surfaces, qCE represents the convective energy consumption indoors, qIV represents the energy consumption due to airflow infiltration and ventilation, qsys represents the energy consumption of the air conditioning system.The convective energy consumption outdoors and indoors is shown in Equation (2).
In Equation ( 2), h represents the convective heat transfer coefficient, A represents the surface area for heat conduction, ∆T represents the temperature difference between the object surface and the fluid, hCE represents the convective heat transfer coefficient for indoor loads, ACE represents the surface area affected by indoor loads, and ∆TCE represents the temperature difference between the indoor environment and the load surface.Additionally, the energy consumption due to airflow infiltration and air conditioning is shown in Equation (3).
In Equation ( 3), m represents the mass flow rate of the airflow, Cp represents the specific heat capacity of the air, ∆TIV represents the temperature difference between indoor and outdoor airflow UA represents the thermal conductivity coefficient, and ∆Tsys represents the temperature difference in the return water of the air conditioning system.Due to the complexity and uncertainty of real buildings, simulations may not accurately capture all factors.By introducing ANN into the simulation, the accuracy and precision of predictions for nonlinear problems can be improved through training with a large amount of data, enabling better prediction of actual building energy consumption (Fan et al. 2021).The ANN model is illustrated in Figure 2.
From Figure 2, the ANN model is composed of multiple neurons (or nodes) arranged in a network structure, which contains input, hidden, and output layer.Input from the previous layer is imported and calculated a weighted sum using weights, which is then passed through an activation function to generate an output (Verma et al. 2023) and (Vijayan et al. 2022).ANN can be used to process various types of data, including σ represents the activation function, Z 1 represents the output of the weights from the input layer to the hidden layer, W 1 represents the weight matrix from the input layer to the hidden layer, X represents the input data vector, b 1 represents the bias vector of the hidden layer, Z 2 represents the output of the weights from the hidden layer to the output layer, W 2 represents the weight matrix from the hidden layer to the output layer, b 2 represents the bias vector of the output layer, and A 1 represents the activation value of the hidden layer.The output is then passed through the weight matrix added with the bias and sequentially through the activation function.After obtaining the predicted result, it is necessary to measure the error between the predicted value and the actual value using a loss function.
The loss function is defined by Equation (5).
( ) J represents the loss value, m represents the number of samples, Yi represents the actual value of the sample, A 2 represents the predicted value from the output layer, and Z 2 represents the input to the output layer.After calculating the error using the loss function, the error needs to be backpropagated.The mathematical expression for backpropagation is shown in Equation ( 6).
In Equation ( 6), dZ 2 represents the error in the output layer, dZ 1 represents the error in the hidden layers, T represents the transpose operation, and σ' represents the derivative of the activation function.After calculating the error, it is necessary to compute the weight gradients for weight update, as shown in Equation (7).
In Equation ( 7), dW 2 represents the weight gradient from the hidden to the output layer, dW 1 represents the weight gradient from the input to the hidden layer.The computed errors and weight gradients are then used to update the weights according to Equation (8).
Equation ( 8) introduces the learning rate, α.The artificial neural network adjusts the weights gradually during training through the forward and backward propagation processes, controlling the step size of weight updates using the learning rate.This iterative adjustment of weights helps the network approach the true values and achieve the goal of performance prediction.(Verma et al. 2023).The general process of combining ANN with building energy consumption simulation is depicted in Figure 3 From Figure 3, the general process involves several steps: preprocessing the collected data, selecting an appropriate ANN architecture, simulating the building energy consumption and inputting relevant parameters, aligning the input data from ANN with the output data from building energy consumption simulation, training ANN using the aligned data as input, extracting feature values from the output of each training iteration to form a feature database, analyzing and evaluating the trained feature data, and periodically updating the model parameters based on the analysis results.

MOO Model for Rural Prefabricated Buildings
In rural areas, the economic level is relatively low and resources, including land, materials, and energy, are relatively limited.Optimizing the building structure and material selection can reduce material waste, construction and maintenance costs, and energy consumption of buildings (Ve et al. 2021) and (Wei et al. 2024).The optimization model that combines ANN structure with building energy consumption simulation can only achieve single-objective optimization.Therefore, a MOO model is needed to fully consider the environmental impact of buildings and take corresponding measures in the design process.The overall technical roadmap of the MOO model for rural prefabricated buildings is shown in Figure 4.
From Figure 4, the overall technical roadmap of the MOO model for rural prefabricated buildings consists of three modules: parameter design, research stage, and optimization objectives.The NSGA-II can be used to achieve MOO of the system.and find a set of non-dominated solutions among multiple objectives (Doerr and Qu 2023).The general process of the NSGA-II algorithm is shown in Figure 5.
From Figure 5, the algorithm first randomly generates an initial population.Then, it calculates the fitness value and generates offspring individuals through crossover, mutation, and merging operations to generate a new population.This process is repeated until the termination condition is met, and the population is updated to return the optimal solution.The initialization of the population and the fitness value calculation are mathematically expressed in Equation ( 9) (Yan et al. 2021).
In Equation ( 9) population represents the initial population, Gi represents the gene of an individual, fitnessi represents the fitness value of an individual, and f(Gi) represents the fitness function.The formula for the selection operation on the randomly generated initial population is shown in Equation ( 10).
In Equation ( 10), Pi represents the probability of an individual being selected, and N represents the total number of individuals in the population.The mathematical expression for the crossover and mutation operations on the selected individuals is shown in Equation ( 11).
In Equation ( 11 The combination of the NSGA-II, ANN structure, and building energy consumption simulation is depicted in Figure 6. From Figure 6, the overall technical roadmap consists of three parts: dataset generation, construction of artificial neural network, and solution using the NSGA-II MOO algorithm.Firstly, building simulation is performed using the constructed building model to calculate the objective functions and obtain a dataset with building energy consumption, operational costs, carbon emissions, etc.Then, the determined ANN structure is trained using the dataset to obtain prediction models for energy consumption, costs, and carbon emissions.Finally, in the process of MOO based on the NSGA-II algorithm, the ANN prediction models are used for prediction and correction of the data, and the non-dominated sorting is employed to generate a set of multi-objective optimal solutions (Fang et al. 2022).When combined with the multi-objective building optimization technique, a cost calculation for production and construction can be derived as shown in Equation ( 12).
ICo represents the construction costs of buildings of the same type, and ICM represents the additional costs.Additionally, the calculation formula for operational costs is shown in Equation ( 13).represents the energy consumption of the heating system, Ec represents the energy consumption of the cooling system, El represents the energy consumption of the lighting system, Ew represents the energy consumption of the hot water system, Ee represents the energy consumption of appliances, Er represents the energy output of rooftop photovoltaic systems, Wh represents the heating energy price, W2 represents the average energy price, and W3 represents the price of renewable energy grid connection.Lastly, the cost calculation for the recycling stage is shown in Equation ( 14).
RCD represents the dismantling cost, RCT represents the cost of waste transportation, and RCC represents the cost of waste treatment.By summing up these various costs, the final cost calculation formula can be obtained.Additionally, the calculation of carbon emissions during the lifecycle is shown in Equation ( 15).
CA represents the carbon emissions generated during the production and manufacturing process, CB represents the continuous carbon emissions generated during operation and management, and CC represents the carbon emissions generated during the dismantling and recycling process.In summary, the energy consumption optimization of rural prefabricated buildings is a MOO problem that needs to consider multiple objectives, such as energy consumption, comfort, and economy.Building energy consumption simulation provides data, ANN can analyze and predict these data, and NSGA-II can optimize multiple objectives.Therefore, combining ANN, NSGA-II, and building energy consumption simulation for MOO of rural prefabricated buildings can help designers balance between multiple objectives and obtain a set of optimal solutions to achieve energy consumption optimization.

Experimental verification and data analysis
For confirming the performance of the MOO Model (MOM) that incorporates ANN, the NSGA-II, and building energy consumption simulation in optimizing energy consuming of rural prefabricated buildings, the MOM model is compared with traditional optimization algorithms including NSGA, Strength Pareto Evolutionary Algorithm (SPEA), Indicator-Based Evolutionary Algorithm (IBEA), Multi-Objective Genetic Algorithm (MOGA), and Pareto Archived Evolution Strategy (PAES) using 10 datasets that include different parameters of rural single-story standard buildings.The results of the parameter optimization comparison are presented in Figure 7. From Figure 7, MOM achieves approximately 1% improvement over NSGA, about 4% improvement over SPEA, about 7% improvement over IBEA, about 10% improvement over MOGA, and about 11% improvement over PAES.Since rural single-story building designs are relatively simple with fewer parameters, the improvement of MOM compared to NSGA is relatively small, and the overall optimization efficiency is similar.However, thanks to the artificial neural network model in MOM, it has gained advantages even with fewer parameters.Further research compares different algorithms in single-story irregular structure building parameters, as shown in Figure 8. From Figure 8, as parameter structures vary, the optimization efficiency decreases, leading to differences in optimization efficiency among the algorithms.Among them, MOM achieves approximately 4% improvement over NSGA, about 6% improvement over SPEA, about 9% improvement over IBEA, about 13% improvement over MOGA, and about 15% improvement over PAES.As the economic conditions in modern rural areas gradually improve, some rural buildings are evolving into villa-type structures.Further research compares the optimization efficiency of different algorithms in villa-scale buildings, as shown in Figure 9.
From Figure 9, in the optimization efficiency comparison of villa buildings, the MOM model still maintains an average optimization efficiency of over 95%, while the traditional NSGA algorithm's average optimization efficiency decreases to about 88%, SPEA's average optimization efficiency is about 85%, IBEA's average optimization efficiency is about 80%, MOGA's average optimization efficiency is about 78%, and PAES's average optimization efficiency is about 72%.As mentioned earlier, further research refines the optimization objectives to Comprehensive Energy Consumption Optimization (CEO), Integrated Cost Optimization (ICO), and Integrated Carbon Emission Optimization (IEO), and compares the algorithms as shown in Figure 10.
From Figure 10, the MOM model consistently maintains a comprehensive optimization efficiency of over 90% in different category optimization tests.Its optimization efficiency is approximately 7%, 8%, and 5% higher than the SPEA algorithm, and approximately 10%, 15%, and 20% higher than the PAES algorithm.
Figure 9 compares the optimization efficiencies of different algorithms specifically for villa-scale buildings, showing how the MOM algorithm outperforms others like NSGA, SPEA, IBEA, MOGA, and PAES in this context.Figure 10, on the other hand, breaks down the MOM algorithm's performance across three specific optimization objectives: CEO, ICO, and IEO.It highlights the algorithm's ability to balance these distinct goals.In summary, Figure 9 focuses on overall efficiency in villa buildings, while Figure 10 details the MOM algorithm's performance in specific categories.A set of parameters for a 2-story villa is optimized using the MOM algorithm, and the optimization results are shown in Table 1.
From Table 1, the MOM model provides specific optimization strategies for different optimization types.The solutions with the lowest energy consumption and the lowest carbon emissions tend to use three-layer glass windows with low emissivity coatings.All recommended solutions suggest using a 10mm insulation layer and recommend insulation thickness of around 50mm for the suspended floor.Additionally, all recommended solutions have a permeability rate of 0.2, and the installation scale of the photovoltaic system is 8 kW.The experimental data above fully demonstrate that the MOM model can design different optimization solutions based on different objectives (energy consumption, carbon emissions, cost, etc.) to achieve optimal energy efficiency and environmental performance in transparent envelope structures.Furthermore, as modern rural areas are also transitioning to more dense construction, large-scale villages are starting to emerge.The optimization efficiency of different algorithms for large-scale villages is compared in Figure 11.
From Figure 11, it is evident that it is difficult to balance cost optimization with energy consumption and carbon emission optimization.PAES maintains an average optimization rate of about 80% when the cost optimization rate is low, but as the cost optimization rate increases to 50%, the other optimization rates start to decrease significantly, averaging around 65%.When the cost optimization is at its maximum, the other optimization rates are close to 0%.SPEA maintains an average optimization rate of about 85% when the cost optimization rate is low, and as the cost optimization rate increases to 50%, the other optimization rates decrease to approximately 75%.When the cost optimization is at its maximum, the other optimization rates are around 50%.MOM maintains an average optimization rate of about 90% when the cost optimization rate is low, and as the cost optimization rate increases to 50%, the other optimization rates decrease to approximately 85%.When the cost optimization is at its maximum, the other optimization rates are around 80%.Therefore, it can be concluded that as the cost optimization rate increases, MOM shows a more stable and higher optimization rate compared to SPEA, with an average   2. As can be seen from Table 2, compared with NSGA-II algorithm, MOM algorithm significantly improves the optimization efficiency of all targets.Specifically, the MOM algorithm reduced energy consumption by 16.7%, operating costs by 20.0%, and carbon emissions by 20.0%.

5.Conclusion
For the energy optimization problem of rural prefabricated buildings, a MOO Model was proposed, combining ANN and NSGA-II, and building energy consumption simulation.Experimental comparisons and data analysis were conducted for optimizing various types of building performance and MOO.The experimental results show that in the case of ordinary single-story rural prefabricated buildings, MOM achieves approximately 1% improvement over NSGA, about 4% improvement over SPEA, about 7% improvement over IBEA, about 10% improvement over MOGA, and about 11% improvement over PAES.In the case of multi-story rural buildings, MOM achieves approximately 4% improvement over NSGA, about 6% improvement over SPEA, about 9% improvement over IBEA, about 13% improvement over MOGA, and about 15% improvement over PAES.In the optimization efficiency comparison of villa buildings, MOM still maintains an average optimization efficiency of over 95%, while NSGA's average optimization efficiency decreases to about 88%, SPEA's average optimization efficiency is about 85%, IBEA's average optimization efficiency is about 80%, MOGA's average optimization efficiency is about 78%, and PAES's average optimization efficiency is about 72%.In the scenario where cost optimization and energy consumption and carbon emission optimization are difficult to balance, MOM maintains an average optimization efficiency of about 90% when the cost optimization rate is low, and as the cost optimization rate increases to 50%, the other optimization rates are around 85%.When the cost optimization is at its maximum, the optimization rates remain around 80%.The experiments demonstrate that MOM has certain advantages in optimizing different types of rural prefabricated buildings and in MOO.However, it should be noted that the computational resources required for the fusion model are relatively large, leading to higher resource consumption.Further exploration is needed to optimize the performance and energy consumption of the model itself.
-4940/© 2024.The Author(s).Published by CBIORE while external factors like solar radiation and climatic conditions can affect the thermal conduction and optical properties of the building's structural components(Jin et al. 2023).The general process is illustrated in Figure1.From Figure1, building energy consumption simulation converts building information into a computer model.Based on the building model, boundary conditions, and material properties, it calculates internal heat transfer, energy consumption, and other factors, and then analyzes the results for improving the energy efficiency and sustainability of the building(Patil et al. 2024).The mathematical expression for building energy consumption calculation is shown in Equation (1)(Saber et al. 2021) and(Singh Rajput et al. 2023).

Fig. 1
Fig. 1 Flow chart of building energy consumption simulation

Fig. 3
Fig. 3 Flow chart of building energy consumption simulation combined with ANN ),   ′ represents the new individual obtained from crossover and mutation operations on different individuals, x and y represent the parent individuals, r represents a random number, Pc represents the crossover probability, and Pm represents the mutation probability.The new individuals generated until the termination condition is met form a new population, which represents the optimal solutions.

Table 1
Comparison of villa optimization results

Table 2
Optimization results of three kinds of objective functions under two models Objective function NSGA-II Efficiency (%) MOM Efficiency (%) Improvement (%)