Design and analysis of energy efficient urban buildings based on BIM model

Construction of multi-objective optimization model for building energy-saving design

In building ES design, building EC and user comfort are two important indicators. However, typically, these two indicators conflict with each other. To solve this problem, it is necessary to combine building EC with user comfort and construct an MO optimization model. ¹² However, due to limitations in construction costs and time, decision-makers are unable to repeatedly build real buildings to evaluate the merits and demerits of various design schemes. To simplify modeling work, this EnergyPlus building EC simulation software in view of BIM technology is used to describe building EEF design issues. ¹³ The EC analysis model for building design in view of BIM is shown in Figure 1.OPEN IN VIEWER

In the BIM energy consumption analysis model in Figure 1, a diagnosis of building energy consumption will be obtained through the evaluation of multiple aspects of the building. Through energy consumption diagnosis, effective construction strategies will be provided for building construction, achieving energy-saving optimization design of the building. The specific process is to establish a multi-objective optimization model for building energy efficiency design based on the EnergyPlus building energy consumption simulation software. By considering system control parameters such as room orientation, wall insulation thickness, and external wall solar absorption rate as decision variables, this model can solve the optimal design solution that minimizes building energy consumption and user discomfort hours. ¹⁴ The decision variables for the energy-saving design of urban buildings in the project study are shown in Table 1. The research decision variables are mainly based on the study area, and there are differences among different regions.

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Table 1.

Value table of some variables in urban building energy-saving design.

Energy-saving design variables	Unit	Value range	Reference value
Living room lighting density	W/m2	[4.5, 6]	5
Insulation thickness	m	(0.0001, 0.1)	0.0473
Bathroom lighting density	W/m2	[5.5, 8]	7
The heat transfer coefficient of the window	W(m2 k)	(2, 6)	4.3
Solar heat gain coefficient of windows	—	(0.0001, 0.7)	0.65
Living room window	m	(0, 4.9)	1.8
External wall solar absorption rate	—	(0.1, 1)	0.6
Bedroom window long	m	(0, 6.9)	1.8
Bedroom window width	m	(0, 3.19)	1.2
Air conditioning system cooling set temperature	°C	[24, 28]	25
Wide kitchen window	m	(0, 3.19)	1.2
Building orientation	Spend	[0, 360]	0
Bathroom window width	m	(0, 2.19)	1.2
Bathroom window long	m	(0, 3.9)	1.8
Bedroom lighting density	W/m2	[5,8]	6
Kitchen lighting density	W/m2	[5,6]	5.5
Long kitchen window	m	(0, 5.9)	1.8
Air conditioning system heating set temperature	°C	[18, 23]	20

This study assumes that x represents the decision variable, which is the value of the system control parameter. Considering minimizing building EC and minimizing user discomfort hours as optimization objectives, the objective function can be expressed by two objectives as shown in equation (1). ¹⁵

{ Minimize f 1 ( x ) Minimize f 2 ( x )

(1)

In equation (1), f 1 ( x ) represents the objective function for minimizing building EC; f 2 ( x ) represents minimizing the number of uncomfortable hours for users. In building ES design, there are some constraints, such as the maximum EC limit of the building and the size limit of the building’s exterior walls and windows. Its assumption is that g i ( x ) represents the i -th constraint condition, which can be represented as shown in equation (2).

g i ( x ) ≤ 0 , i = 1 , 2 , … , n

(2)

The building EC model is a complex nonlinear model that can be modeled in view of the EnergyPlus building EC simulation software. This study assumes that B E C ( x ) represents the annual EC of a building, and the building EC model can be represented as shown in equation (3).

B E C ( x ) = EnergyPlus 1

(3)

In equation (3), EnergyPlus represents the EC simulation result. The user discomfort model is a measure of user comfort, which can be modeled in view of the annual user discomfort hours (UDH) output by EnergyPlus software. Assuming U D H ( x ) represents the number of uncomfortable hours per year, the user discomfort model can be expressed as follows:

U D H ( x ) = EnergyPlus 2

(4)

In equation (4), EnergyPlus 2 represents the simulation result of user discomfort. Establish an MO optimization model by comprehensively considering the optimization objectives of building EC and user discomfort. Assuming that f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) represents the vector of the optimization objective, the MO optimization model can be represented as shown in equation (5).

Minimize f ( x ) = ( f 1 ( x ) , f 2 ( x ) ) g i ( x ) ≤ 0 , i = 1 , 2 , … , n x ∈ X n

(5)

In equation (5), X serves as the value space of the decision variable. The final MO optimization model for building ES design can be obtained by solving the non-dominated solution (DS) set of the optimization problem to obtain the optimal design scheme.

Construction of building energy efficiency optimization design model based on MOEA/D

For addressing the MO optimization issue of constructing EEF design, MOEA/D (Multi-objective Evolutionary Algorithm in view of Decomposition) algorithm in the MO Evolutionary algorithm can be used in this research. The MOEA/D model can simultaneously consider multiple independent objective functions and has good adaptability in multi-objective processing in construction. At the same time, the MOEA/D model also has fast convergence and excellent constraint processing ability, so MOEA/D is used to construct a multi-objective optimization model. Firstly, this study needs to define an MO optimization model for the issue. The goal of its hypothetical research is to minimize EC and discomfort hours in buildings, while meeting other design requirements. The optimization process of the MOEA/D model is shown in Figure 2. ¹⁶ OPEN IN VIEWER

This study redefines the MO optimization model for building ES design, as shown in equation (6).

{ minimize f 1 ( x ) = f 1 ( x ) = Energy Consumptionminimize minimize f 2 ( x ) = f 2 ( x ) Discomfort Hourssubject , x ∈ Ω

(6)

Among them, x is the structural parameter vector of the building; Ω is the feasible region of the parameter. The purpose is for finding a set of Pareto optimal solutions that simultaneously minimize f 1 and f 2 , rather than converting the two objectives into a single scalar through trade-offs. The MOEA/D algorithm uses the Chebyshev decomposition method for decomposition operations. ¹⁷ This decomposition method transforms MO optimization problems into a series of single objective optimization problems, which can be addressed using single-objective optimization algorithms. Firstly, its initial population: randomly generate an initial population of building structural parameters as shown in equation (7).

P 0 = { x 1 , x 2 , . . . , x N }

(7)

In equation (7), N is the population size. Then perform a decomposition operation, using the Chebyshev decomposition method to calculate the decomposition target value z i for each individual x i ; its expression is shown in equation (8).

z i = ( z i 1 , z i 2 ) = ( max j { Energy Consumption j − Energy Consumption i } , max j { Discomfort Hours j − Discomfort Hours i } )

(8)

In equation (8), Energy Consumption j and Discomfort Hours j represent the EC and uncomfortable hours of individual x j , respectively, Then it performs neighborhood updates. For each individual x i , it selects a group of individuals in its neighborhood B ( i ) and calculates the decomposition target value of its neighborhood individuals as shown in equation (9).

z B ( i ) = { z j | j ∈ B ( i ) }

(9)

Finally, it analyzes the solution of the sub problem, and for each individual x i , it uses a single-objective optimization algorithm; In the study, an improved PSO algorithm was utilized for addressing the sub-problem, as shown in equation (10).

minimize g i ( x i ) = max j { w i j · ‖ z j − z i ‖ } , x i ∈ Ω

(10)

In equation (10), $ w _ { i j } $ is the weight used to calculate the decomposition target value. The updated population is in view of the set of sub individuals { x 1 , x 2 , . . . , x N } obtained by solving the sub-problem, and population P t is updated using a certain strategy. This study uses the strategy tournament to select individuals from P t and { x 1 , x 2 , . . . , x N } to form a new population P t + 1 and updates population P t + 1 using the strategy. If the maximum quantity of iterations is reached or a Pareto optimal solution set that meets certain convergence conditions is found, the model completes training. Through the above steps, the MOEA/D algorithm can gradually search for the Pareto optimal solution set of building ES design models, thereby providing a series of efficient design solutions.

Building energy efficiency optimization design model based on agent-assisted MOPSO

For enhancing the performance of the MOEA/D evolutionary optimization algorithm in dealing with expensive MO optimization problems, this study introduces an agent-assisted MO PSO model for diminishing the quantity of actual evaluations of individuals, thereby reducing the running cost of the algorithm. The SMO approximately simulates the behavior of the real evaluation function by modeling the existing sample data. ¹⁸ In this algorithm, two methods can be used for optimization, including agent-based particle location update and SMO construction and management. The proxy-assisted optimization framework is shown in Figure 3.OPEN IN VIEWER

Firstly, this study needs to define some symbols and variables: X represents the search space of the solution, X = { X 1 , X 2 , . . . , X n } ; where N represents the size of the population; M represents the quantity of targets; P represents the population; the population expression is shown in equation (11).

P = { p 1 , p 2 , . . . , p N }

(11)

In equation (11), p i serves as the position of the i -th particle, and the particle group velocity set is shown in equation (12).

V = { v 1 , v 2 , . . . , v N }

(12)

In equation (12), v i represents the velocity of the i -th particle. The set of fitness functions for individual populations is shown in equation (13).

F = { f 1 , f 2 , . . . , f N }

(13)

In equation (13), f i represents the fitness of the i -th particle. Firstly, it is necessary for evaluating each individual in the population in view of the real evaluation function to obtain the initial fitness value. In view of the current fitness value and individual optimal solution, it updates the velocity and position of particles. ¹⁹ The velocity update for the i -th particle is shown in equation (14).

v i t + 1 = w · v i t + c 1 · r a n d ( ) · ( p b e s t i − p i t ) + c 2 · r a n d ( ) · ( G b e s t t − p i t )

(14)

In equation (14), w represents the inertia weight; c 1 and c 2 represent individual and social learning factors, respectively; r a n d ( ) serves as a random number uniformly distributed within; G b e s t represents the global optimal solution; t serves as the quantity of iterations; P b e s t represents the optimal solution for individual particles. Then, it updates the position of the particles in view of the new velocity, as shown in equation (15).

p i t + 1 = p i t + v i t + 1

(15)

Next, it evaluates the updated particle position in view of the real evaluation function and updates the fitness value and individual optimal solution, as shown in equation (16).

{ F n e w = [ f n e w 1 , f n e w 2 , . . . , f n e w N ] P b e s t = [ p b e s t 1 , p b e s t 2 , . . . , p b e s t N ]

(16)

In each iteration process, it saves the non-DS in the population and uses non-dominated sorting and crowding distance calculation methods to sort the non-DS. The purpose of non-dominated sorting is to sort individuals in view of their strengths and weaknesses, while the purpose of crowding distance is to maintain population diversity. Firstly, it calculates the set of DS and the quantity of dominated individuals for each individual, as shown in equation (17).

{ S i = { j | j = 1 , 2 , . . . , N , j ≠ i , f j ≺ f i } n i = | { j | j = 1 , 2 , . . . , N , j ≠ i , f i ≺ f j } |

(17)

In equation (17), ≺ represents a partial dominance relationship. Next, it calculates the original crowding distance for each individual:

D i = 0 , D i = D i + ( f i + 1 − f i − 1 ) / max f − min f

(18)

In equation (18), f i + 1 represents the individual immediately following f i in the non-dominated ranking; f i − 1 represents the individual immediately preceding individual f i in non-dominated sorting; max f and min f represent the maximum and minimum values of all individuals in the target space, respectively. Finally, it sorts the non-DS in the population in view of non-dominated sorting and crowding distance, and selects a new population. Meanwhile, to improve the overall optimization effect of the population, it introduced the SMO for optimization. ²⁰ Firstly, in view of the current population and fitness values, it selects a portion of individuals as the new sample set (SSE) M n e w . Then, it merges M n e w with the existing training SSE M t r a i n to obtain a new training SSE M t r a i n n e w . Then, it uses M t r a i n n e w to train the SMO and selects the support vector machine as the SMO in the study. By modeling M t r a i n n e w , an SMO that approximates the real evaluation function is obtained. Finally, it uses the trained SMO for replacing the real evaluation function to update and evaluate the particle position. That is, it uses the SMO to predict the fitness value of particles and updates the speed and position of particles according to the predicted fitness value. The entire MO optimization model process is shown in Figure 4.OPEN IN VIEWER

Model performance testing

To test the performance of the proposed MO optimization model, Rastrigin function, Ackley function, ZDT1 function, and ZDT2 function were used as test benchmark functions, and simulation experimental analysis was completed through the MATLAB platform. The hardware platform is Windows 10 system, the processor is INTEL i7 32 core, and the graphics card is RTX3070. The initialization parameters of the experimental model are showcased in Table 2.

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Table 2.

Model initial parameters.

Parameter indicator type	Numerical value
Inertia weight	0.5
Reserve set size	50
Acceleration coefficient	2
Iterations	500
Learning factor	2.05

The MOEA/D model and the traditional MO Particle Swarm Optimization (MOPSO) algorithm were selected as the benchmark models for testing. The proposed proxy assisted MO particle swarm model is represented as S-MOPSO. It selects the Ackley function and Rastrigin function to test the optimization effect of the model, as shown in Figure 5.OPEN IN VIEWER

Figure 5 shows the optimization results of MO optimization models under different functions. Figure 5(a) and (b) show the outcomes of the Ackley function and Rastrigin function tests, respectively. The test curve demonstrates that in the Ackley function, the MOEA/D model performed the worst, tending to converge after 300 iterations with an optimal fitness value of 0.752. The proposed S-MOPSO model performed the best, tending to converge after 100 iterations with an optimal fitness value of 0.452. In the Rastrigin function, the proposed M-MOPSO model performs best and tends to converge after 46 iterations, with an optimal fitness value of 0.149. According to the test results, the proposed S-MOPSO model performs best in both convergence and fitness value search. Simultaneously selecting the ZDT1 and ZDT2 benchmark functions, the model frontier results are shown in Figure 6.OPEN IN VIEWER

It selects two functions, ZDT1 and ZDT2, to reflect the cutting-edge optimization performance of the model. Among them, Figure 6(a)–(c) and Figure 6(d) represent the results of the Pareto Frontier Test for the ZDT1 function, the Pareto Frontier Test for the ZDT2 function, the actual frontiers of the ZDT1 function, and the actual frontiers of the ZDT2 function. The test results indicate that all three models can be uniformly distributed in the target space, indicating that the three models have MO optimization capabilities. However, the frontier outcomes of the MOPSO model and the S-MOPSO model are closer to the real results, and different models have significant differences in training effectiveness, as shown in Table 3.

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Table 3.

Test results of three types of indicators for two benchmark functions.

Benchmark function type	Test indicators		MOEA/D model	MOPSO	M-MOS PSO
ZDT1 benchmark function	Time-consuming test		9.154 s	8.654 s	7.120 s
	Model iteration convergence	The best	0.0032	0.0023	0.0025
		Mean	0.0226	0.0126	0.0013
		Var	0.0052	0.0041	0.0031
	Diversity	Ms	0.7265	0.6965	0.6456
	Uniformity	Sp	0.0067	0.0065	0.0064
ZDT2 benchmark function	Time-consuming test		19.654 s	16.654 s	8.985 s
	Model iteration convergence	The best	0.0039	0.0037	0.0036
		Mean	0.0121	0.0118	0.0142
		Var	0.0013	0.0012	0.0010
	Diversity	Ms	0.7245	0.7156	0.6845
	Uniformity	Sp	0.0039	0.0036	0.0035

Table 3 shows the detailed Pareto frontier test results of the three models. In the ZDT1 benchmark function and ZDT2 benchmark function, the proposed M-MOPSO model performs best in both optimal and average values, with values of 0.0025 and 0.0013 in the ZDT1 function, respectively. It also performs best in diversity and equilibrium, with values of 0.6456 and 0.0064 in the ZDT1 function, and 0.6965 and 0.0065 in the MOPS model, indicating that the proposed model performs better. In the comparison of time consumption, under the ZDT2 function, the MOEA/D model, MOPSO model, and M-MOSPSO model were 19.654 s, 16.654 s, and 8.985 s, respectively. In the comparison of optimal values, the MOEA/D model, MOPSO model, and M-MOSPSO model were 0.0039, 0.0037, and 0.0036, respectively, which still showed the best performance of the proposed model. It can be seen that the proposed M-MOPSO model has the best performance in Pareto cutting-edge testing.

Case experiment analysis

This study selected common urban commercial single-room office buildings and traditional northern residential buildings as ES optimization design objects, and tested the practical application effect of the proposed M-MOPSO model. Figure 7 shows two 3D models of buildings.OPEN IN VIEWER

In the optimization of building ES design, the main decision variables to consider are the thickness of the external insulation layer of the wall, the solar absorption rate of the external wall, etc. The specific range of decision variables can be found in Table 1. To effectively reflect the effectiveness of different models in building EEF optimization design, the Hypervolume Indicator (HV) is introduced. The larger the value, the better the optimization and convergence effect. Figure 8 shows the Pareto frontier results of urban single-room office buildings.OPEN IN VIEWER

Figure 8(a) and (b) show the frontier results of the MOPSO model and the M-MOPSO model, respectively. Figure 8(b) shows the comprehensive comparison results. The vertical axis represents the quantity of uncomfortable hours, and the horizontal axis represents the total EC of the building. By comparing three models, the optimization solution set for building EEF can be obtained, but the MOEA/D model has a longer search time, the longest uncomfortable hours, and higher EC, which clearly cannot meet the requirements; on the contrary, the MOPSO model is similar to the M-MOPSO solution set, but the search time is shorter. Meanwhile, the minimum number of uncomfortable hours is 2408 h, and the total EC is 47.5. Compared with traditional single-room buildings, MOEA/D optimized buildings, and MOPSO optimized buildings, the EC is reduced by 47.6%, 24.6%, and 6.2%, respectively. Figure 9 shows the cutting-edge results of traditional residential buildings in the north.OPEN IN VIEWER

Figure 9(a) and (b) show the frontier results of the MOPSO model and M-MOPSO model, respectively; Figure 9(c) shows the comprehensive comparison results. The M-MOPSO model has the worst optimization results in terms of uncomfortable hours and total EC among the three models, with the optimal solution set accounting for 9.5% of the M-MOPSO model. The M-MOPSO model is significantly superior in convergence and time consumption to the other two models, and the Pareto frontier results are also good. The comprehensive performance comparison of the model is showcased in Table 4.

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Table 4.

Comprehensive comparison of model building energy-saving design.

Optimization model	Method	HV(Best)	HV(Worst)	HV(Average)	HV(Std)	T-test	Time(h)
Urban office building	MOEA/D	25,312	12,923	19,832	6849	R+	1.5
	MOPSO	25,321	23,117	24,313	1136	R+	1.6
	NSGAII	25,456	23,122	24,756	1023	R+	1.7
	M-MOPSO	26,473	25,691	26,391	802	—	1.3
Traditional Northern Residential Architecture	MOEA/D	10,321	4500	6058.4	2063	R+	5.8
	MOPSO	9887	5697	6964.2	1879	R+	4.5
	NSGAII	12,352	6524	7562	1658	R+	4.1
	M-MOPSO	50,132	48,796	49,393	1098	—	3.5

Table 4 shows the total HV values for energy-saving optimization of the three models, while introducing a genetic algorithm with elite strategy and non-dominated sorting (NSGAII) for comparison. From the results, it can be seen that the M-MOPSO model performs best in both types of buildings. The optimal HV values for the MOEA/D model, MOPSO model, NSGAII model, and M-MOPSO model in urban office buildings are 25,312, 25,321, 25,456, and 26,473, respectively. It can be seen that the proposed models have excellent optimization capabilities, and the energy consumption is the lowest and the comfort is the best in building energy efficiency optimization.