Multi-objective Optimization Design of Low-carbon Modular Building

In recently architectural research, there is a well-documented emphasis on energy-saving design optimization. However, there is a conspicuous deficiency in studies that address multi-objective optimization related to the long-term carbon emissions associated with building lifecycles. In this study, modular buildings in construction sites are taken as the research object, and box-type rooms are taken as the prototypical model. A set of multi-objective optimization methods for architectural design is established by series modeling tools, building performance simulation tools and NSGA-II non-dominated sorting genetic algorithm tools, combined with Python programming tools. This method is to optimize the reduction of carbon emissions, energy consumption and costs throughout the life cycle. The purpose of this investigation is to establish a methodology for assessing and optimizing architectural designs with a primary focus on carbon emissions during the design phase. The goal is to provide architects with practical insights to enhance their designs while simultaneously achieving intelligent, eco-friendly buildings.


Introduction
This study initially introduced a range of variables and optimization techniques, including building performance simulations, at the early design phase.It then employed a genetic algorithm to incorporate parameter variables and objective functions.This integration facilitated parameter modeling, performance simulation, carbon emission and cost calculations, as well as data visualization, ultimately achieving the optimization of multiple objectives.To realize this multi-objective optimization, it became essential to unify various tools for modeling, simulation, calculation, and visualization on a single platform, delivering intuitive results.Consequently, this research necessitated the use of compatible research tools to attain its objectives.Non-dominated sorting Genetic algorithm (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO) are the two most widely used methods in the field of building performance optimization algorithms, and their popularity has reached two-thirds of the research in this field [1].The research on multi-objective optimization design using particle swarm optimization [2][3] is less than that using genetic algorithm [4][5].Relative to NSGA-I, NSGA-II retains the outstanding individuals in the parent population and combines them with the child population to form the next generation population [6].At present, many optimization studies usually take a case as the research object for analysis and optimization [7].This approach provides insight and valuable lessons for building design and performance optimization.In addition, many researches on multi-objective optimization of building performance are about building renovation [8][9].This research direction is of great significance for improving the performance of old buildings, reducing the waste of resources and reducing the environmental impact.The purpose of this study is to reduce the possibility of unreasonable schemes in the initial stage of design so that designers can have more time to refine and perfect the design schemes.This method starts with the design optimization of modular buildings and can be applied to other types of buildings in the future, or for other optimization goals, to provide intuitive quantitative comparison results for engineers to make decisions.

Parameters
This study is based on the climate of Shenzhen, which belongs to the subtropical monsoon climate and is suitable for human habitation.Shenzhen is mainly located on the edge of the Pacific Ocean, with high temperatures and rain in summer and mild and little rain in winter.According to the climate data of Shenzhen, the annual average temperature is 23.3℃.

Model parameters and variables
The length, width and height of the model are 6mX3mX3m, of which the southern wall is 9m2.The box-type room in this study is mainly used for the office of staff in the construction site, which is a small closed office.The building performance simulation is set according to the working time of staff in the small office building, and the working time of the air conditioning system is the same.The building structure is designed according to the steel structure corresponding to the 2B climate zone.Climate data were simulated using data from Shenzhen.On the south side, a window-to-wall ratio of 0.1 corresponds to a window of 0.9m2, a window-to-wall ratio of 0.15 corresponds to a window of 1.35m2, and a window-to-wall ratio of 0.2 corresponds to a window of 1.8m2.The Windows are made of double-layer hollow tempered glass, 5mm tempered glass, 9mm hollow and 5mm tempered glass.There is shade around the window, and the wall is constructed with three layers of colored steel plate, glass wool and colored steel plate.

Multi-objective Parameters
This study seeks to achieve three objectives: reducing carbon emissions, minimizing energy consumption, and cutting overall expenses throughout the life cycle.Achieving these goals involves a comprehensive analysis encompassing the quantification of carbon emissions, energy utilization, and expenses.Energy consumption is determined by employing the EnergyPlus model to assess the annual energy consumption per unit area (EUI).Calculating the carbon emissions from materials is a crucial aspect of this study, which involves factors like material thickness, area, density, and carbon emission coefficients.
Cost estimation is conducted by multiplying the unit cost by the area, yielding the cost associated with each material.Various variables within the model, including the window-to-wall ratio, have a significant impact on the overall energy consumption, carbon emissions, and expenses.These variables influence material consumption proportions and consequently affect the final calculations, along with factors like glass wool thickness and shading depth.Glass 5

Simulation Calculation
In this study, Grasshopper parameter platform combined with NSGA-II non-dominated sorting genetic optimization algorithm Wallacei was used to explore the influence of multiple variables of architectural design on multiple objectives.In this simulation, there are three genetic variables, namely window-to-wall ratio, glass wool thickness and shade depth, and three optimization goals, namely energy consumption, carbon emission and cost.This simulation calculation is set for 20 generations, with 20 groups in each generation, and the calculation time is about 1 hour and 50 minutes, as shown in Figure 1.According to the line chart, the energy consumption of optimization goal 1 is opposite to the carbon emission and cost of the other two optimization goals, and the lower the energy consumption, the higher the carbon emission and cost.According to the dot plot in the lower right corner, there are three results of the final multi-objective Pareto solution set optimization.

Analysis
This simulation iterates 20 times in each generation, and a total of 20 generations are iterated, from generation 0 to generation 19.Among the 20 results, there are mutual repeats.After removing the duplicate results, the genetic variables had 4 different sets of results, as shown in Figure 2 and Figure 3, and the optimization target results of group 0 and group 5 of the 19th generation were the same, that is, the different dependent variables did not affect the final optimization result, and the final optimization target had 3 different sets of results.3. Duplicate results have been removed for clarity.Among all the optimal solution sets, a consistent window-towall ratio of 0.1 is observed, signifying the importance of minimizing the window size within the model parameters.This reduction in window size is associated with lower energy consumption, decreased carbon emissions, and reduced costs.It's worth noting that the window-to-wall ratio exhibits a uniform impact on all three optimization objectives.Specifically, as the thickness of the glass wool increases, energy consumption decreases, while carbon emissions and costs increase.This influence of glass wool thickness on carbon emissions and costs remains constant, while its effect on energy consumption is the opposite.3, only shading depth is different in the gene variables of Group 0 of the 19th generation and Group 5 of the 19th generation in the optimal solution set, but the result of the optimization goal is the same.Therefore, does it mean that shading of 0.15m depth or 0.2m depth has no influence on the optimization goal and result?Table 2 lists some non-optimal gene variables and corresponding optimization results.In Table 4, the window-to-wall ratio of Group 2, Group 4 and Group 9 of the 0 generation is the same as the thickness of glass wool, only the shading depth is different, but the energy consumption decreases with the increase of shading depth.Therefore, the shading depth does not have an impact on the optimization goal, but sometimes it has an impact, the impact is limited by conditions, and it no longer has an impact after reaching a critical point.At present, the sample of genetic variables is small, so the specific impact and critical point value need to be further studied.12519.912519.912519.9According to Wallacei's NSGA-II non-dominated sorting genetic optimization algorithm, the target value results for the calculation of multiple parameters of the modular box room are the points in the dot plot at the lower right corner in Figure 1, where the optimal solution set for multi-objective optimization is the three yellow squares closest to the origin, and the purple points are the non-optimal solutions.If the decision maker wants to optimize energy consumption, choose the solution of the minimum value of goal 1, that is, (1) and (3) in Figure 3.Because carbon emissions and costs change in the same way, if the decision maker wants to optimize carbon emissions and costs, choose the solution of the minimum values of goal 2 and 3, that is, Figure 3(2).If decision-makers want the three goals to be as optimal as possible and relatively balanced, they can choose the solution (4) in Figure 3, with relatively low energy consumption, carbon emission and cost.Over 400 iterations, this study identified unique genetic variables and optimization results.Windowto-wall ratio consistently affects energy consumption, carbon emissions, and costs.Glass wool thickness inversely impacts energy consumption and directly affects carbon emissions and costs.Shading depth's impact varies depending on conditions, occasionally influencing the optimization goals.

Table 2 .
Model material parameters

Table 3 .
The optimal solution sets gene variables and corresponding optimization results

Table 4 .
The optimal solution sets gene variables and corresponding optimization results