#### Abstract

The contradiction between the indoor environment and building energy consumption has been controversial. The design of building envelope involves many parameters such as window size and exterior wall material. These parameters have significant influence on building energy-saving design and indoor environment. In this paper, nondominant sorting genetic algorithm-II (NSGA-II) is utilized to calculate winter heat consumption, indoor total lighting energy consumption, and thermal comfort. The Pareto method is used to select the compromise solution and effective value of each building parameter. Different from other studies, we add more architectural design variables into the model calculation, which can bring architects more detailed energy-saving design content.

#### 1. Introduction

With global energy shortages, many countries have adopted corresponding energy policies, and global energy intensity declined by 1.8 percent in 2016, based on primary energy demand for gross domestic product (GDP). China's energy intensity has declined sharply, reflecting the continuing impact on energy efficiency policies [1]. But, the final energy consumption of buildings rose steadily from 119EJ in 2010 to 124EJ in 2016, at a rate that went beyond reduction in energy intensity. Along with the advancement of China's urbanization process, more than 97% of new buildings each year are high energy-consuming buildings, and the total energy consumption of buildings accounts for about 30% of the total energy consumption of Chinese society. China’s building energy consumption accounts for about 6.0% of global energy consumption, equal to the total energy consumption in the Middle East, twice that of Africa and twice that of Japan and South Korea combined [2]. In China, urban buildings are mainly divided into residential buildings and nonresidential buildings. Nonresidential buildings (public buildings) such as government buildings, commercial buildings, and school buildings account for a large proportion of building energy consumption, and the comprehensive energy consumption per square meter is more than twice that of residential buildings [3]. Therefore, energy conservation in public buildings is of great significance.

The highest potential for green building energy-saving design lies in the renovation of building envelope structures to reduce the use of air conditioning system. Effective design scheme can not only respond to the needs of green energy-saving and long-term economic benefits brought by government investment but also meet the user’s comfort level. Through the local climatic conditions and site conditions, architects can maximize the control of architectural design and construction techniques [4]. Building envelope parameters can affect building energy performance and comfort to a considerable extent. Building envelope is usually composed of transparent and opaque components, and the solar energy and shading characteristics transmitted by materials’ heat conduction, windows, and the total projection rate of composite materials affect the cooling and heating load of buildings and energy consumption of lighting system [5, 6].The geometric configurations of buildings, such as the building volume, the aspect ratio of windows, and the window wall ratio [7, 8], are counted as additional factors influencing the energy load of buildings.

In this article, indoor thermal performance, thermal comfort, and lighting energy consumption of NSGA-II are optimized by building geometry and physical boundary. Building energy consumption, indoor basic thermal comfort, and indoor use lighting are the three objectives of this study. The value range of each building parameter (design variable) is taken according to the national standard specification. The Pareto method selects the optimal solution set, and the different nondominated solutions correspond to discrete building parameters.

#### 2. The Mathematical Model

We have built three objective functions. The first objective function () includes the winter heat consumption of the enclosure and the summer cooling load. We use the heat consumption as the positive here. Therefore, to calculate their total energy consumption, we must subtract. The second () is to calculate the total lighting energy consumption for the whole year, and finally we use the PMV (predicted average voting) value to analyze the thermal comfort of the room in summer. The design variables of these three objective functions have some coupling. It can be seen from the model of the objective function later. For example, the window design in also affects . And and also have contradictory relations. More design variables help to provide a richer context for the architect, which is the novelty of this article. The model created in this article does not limit the maximum or minimum of the solution goal. This is to get more solutions. This solution set is more flexible and diverse. The final choice will be decided by the architect.

##### 2.1. Lighting Energy Consumption

The assumption of diffuse reflection lighting conditions leads to another metric commonly referred to as the daylight factor (DF) [9], which is the ratio of indoor and outdoor illumination under standard CIE cloudy conditions. Due to the simplified sky model, given a certain daylight open configuration, regardless of direction, geographic location, and climate change, the DF at a particular point will remain approximately constant; for the purpose of design, the vector flux splitting method [10] is used. The DF consists of three separate components: sky (SC), external reflection (ERC), and internal reflection (IRC) components:

About complex design calculations, ERC can be determined by multiplying the external obstacle (, i.e., obstacles can be seen in the sky area) by the obstacle reflectivity (, this paper takes a value of 0.2), and the calculation for IRC is also taken from [11]:

In order to achieve a more practical design, additional calibration was performed in this paper, taking into account the maintenance factor (), glass factor (), and window frame factor (), with values of 0.9, 1, and 0.85 [12], respectively. The final calculated DF is

For the case where the calculation point is close enough to daylight, SC can be considered as the most important component of the three. SC is pure geometric calculation as shown in Figure 1. The calculation equation of SC is as follows:.

In the lighting design, there are roughly two possibilities for the position of the window relative to the calculation point; this paper refers to the position of the calculation point by Mangkuto [14]. The projection of the calculation point is located in the window area and internal or external (Figure 2); the height of the working surface is 0.75 m and is higher than the window sill position. Let the distance from the observation point to the left wall be *x*, which is calculated as follows: when , when ,

**(a)**

**(b)**

Annual lighting energy demand () refers to the total demand for electric lighting and energy lighting throughout the year. According to the national standard [15], the maximum value of the library building lighting power density limit target is 8 (), and each point of the illumination is multiplied by the relevant DF multiplied by the outdoor diffuse, The selected value of the illuminance is calculated. If the value of is less than 300 lx (reading room illuminance standard value), then additional lighting is needed, and at all points is averaged with a positive difference of 300 lx and multiplied by *η* = 37.5 lm/W (i.e. 300 lx per 8 W/) to obtain the desired illumination power density [14]. is the total working time (8 hours/day × 5 days/week × 52 weeks/year), and we finally get the estimated :

##### 2.2. Heat Consumption

The calculation of the basic heat consumption of the envelope structure refers to the national standard [16]. The heat consumption of the external protection structure of the universal layer is mainly composed of the outer window and the outer wall. The outer wall is composed of a concrete wall, interface mortar (or bonding layer), insulation layer (or insulation board), crack protection layer (or plaster layer), and veneer layer.

The heat consumption of the enclosure consists of basic heat consumption (9) and additional heat consumption. The heat transfer coefficient is composed of the heat transfer coefficients of each structure, and their relationship is shown in formula (10). The additional heat consumption is determined as a percentage of the basic heat consumption. It mainly includes the orientation correction rate, the wind attachment rate, the external door attachment rate, the height addition rate of the building (except the stairwell), and the intermittent addition rate. The outdoor temperature air temperature is a harmonic time parameter with an angular frequency. Therefore, a simple prediction [17] can be performed using equation (10). The indoor air temperature is determined by the indoor setting temperature. And the interior design temperature is designed according to the level of thermal comfort, as can be seen from Table 1. The calculation method of the heat consumption of the envelope structure is shown in formula (11).

In formula (10), represents the heat transfer coefficient of the inner surface of the envelope, represents the heat transfer coefficient of the outer surface of the enclosure, and represents the correction coefficient of material thermal conductivity. Their values are shown in Tables 2 and 3, respectively [18].

##### 2.3. Cooling Load

The heat transfer process of the building envelope is a very complex process involving convection, conduction, and radiation. At the same time, the outdoor air temperature and heat radiation density also change greatly with the change of outdoor time, and the indoor air temperature also changes. In this paper, the heat transfer equation of external thermal mass and internal air is used to calculate the hourly cooling load of the enclosure. The following assumptions are made:(i)The air distribution within the building, the temperature distribution of the internal thermal mass, and the internal surface temperature of the external thermal mass are balanced.(ii)All thermal gain and heat generation in the building are assembled into a heat source *E* during the working period, while there is no room thermal gain during the nonworking period, and the radiant heat exchange between the heat source and other surfaces is ignored.(iii)The direct thermal solar radiation gain and permeability thermal gain through the opening were ignored.(iv)During the nonworking period, the air conditioning system is closed and night ventilation mode is adopted. The ventilation rate is .

Based on the above assumptions, the heat balance equations of the inner surface temperature and the indoor air temperature of the outer envelope structure are as shown in equations (13) and (14) [17]:

The calculation of outdoor air temperature in summer is similar to formula (11):

Substitute equation (15) into equation (13):

Let , where is the time constant based on night ventilation rate ; , where is the dimensionless external convective heat transfer; and , where is the dimensionless internal convective heat transfer.

Substitute , , and into formula (16):

and , respectively, measure the external and internal convective heat transfer intensities of the surface of the outer envelope. In buildings with large external or internal convection heat transfer, the efficiency of internal or external convection heat transfer is higher than that of indoor air mixing.

The general solution of equation (17) [17] iswhere is a constant and is the relative delay parameter of cooling load with respect to outdoor air temperature; it is evaluated from 0 to .

Substitute equation (18) into equation (14) [17]:

In equation (18), *q* represents the cooling load that needs to meet the indoor hot air balance in summer and *T* represents the temperature rise caused by indoor heat source, . The cooling load is mainly composed of three parts. The first part is the steady-state cooling load, which is jointly caused by the steady-state heat source and the heat gain generated by the temperature difference between indoor and outdoor through the convective heat transfer of hot substances. The second part is the periodic fluctuation cooling load , whose amplitude depends on the fluctuation of outdoor air temperature. The third part (exponential part) is caused by its initial conditions, which will decay to 0 with the increase of time and external convective heat transfer or the decrease of time constant.

##### 2.4. Evaluation of Indoor Thermal Environment Model

PMV is the most comprehensive evaluation considering many factors of human thermal comfort. Table 4 shows the thermal and cold ruler of ASHRAE corresponding to PMV. ISO defines the thermal comfort range as . In order to reduce energy consumption of building air conditioning, China reduces the comfort range to .

There are coupling effects among various factors affecting thermal sensation, for example, the increase of temperature can be compensated by the decrease of humidity or the increase of wind speed. ASHRAE defines thermal comfort as a psychologically satisfying thermal environment, which mainly includes six major factors, namely, air temperature, average radiant temperature, relative humidity, air velocity, human metabolism, and clothing [17]. Due to the complexity of PMV calculation, it is not conducive to engineering practice. Therefore, this paper chooses a simple calculation method for thermal environment assessment proposed [19].

The molecule of formula (21) represents heat loss through sensible heat of skin, and the denominator represents total heat production of human body. Since invisible latent heat is inevitable, the value of the fraction must be less than 1, and its value represents the ratio of sensible heat dissipation to total heat production [19]. represents the average skin temperature. Since the skin temperature is relatively constant, the change range is very small in an environment close to thermal comfort. Here, the average skin temperature in the thermal comfort state is calculated at 33.5°C.

According to ISO-7730 [20], when the wind speed is less than 0.2 m/s or the temperature difference between the average radiation temperature and the air is less than 4°C, the calculation of the acting temperature is as follows:

represents thermal resistance of clothing. represents the clothing area coefficient, and its calculation method is shown in (23). represents the thermal resistance of air outside the garment, which is a function of air temperature and wind speed and is calculated according to formula (24) [19].

represents the average surface temperature of the area of surfaces in a room, and its simplified calculation method is as follows:

#### 3. Case Study

##### 3.1. Building Information

The proposed library is located in Chengdu, Sichuan province, with the coordinates of 30.67° north latitude and 104.02° east longitude. The building floor is the sixth floor, and the model verification object in this paper is the standard floor. Figure 3 shows the library’s 3D model and standard layer. The standard floor consists of a reading room and a catalogue room. The entire area has a length of 21.27 m, a width of 11.9 m, and a height of 4.5 m. The total wall area is 221.4 , the floor area is 253.16 , and the ceiling area is 266.9 . The remaining initial input values are rendered in Table 5. What needs to be noted here is that in this calculation, we calculate Pareto values of 10 times of a day in winter and summer, respectively. Here, the average outdoor temperature in Chengdu is on a certain day in winter and *T* = 2 on a certain day in summer.

What needs to be explained here is that the value of constant is obtained according to the case study in literature [17]. Of course, can be different values for the general solution of ordinary differentiation. When the indoor temperature is 26°C, we calculated the value of for the verification of this model. In order to simplify the calculation, this paper assumes that the windows are integral and ignores the influence of different window positions on indoor lighting. We have set a total of 625 lighting calculation points in the room, as shown in Figure 4.

##### 3.2. Data Input

We set a total of 20 design variables, which will provide architects with more abundant energy-saving building design parameters. The value range of these variables meets the national design standards [15, 16, 18], as shown in Table 6.

##### 3.3. Method

NSGA-II is based on the evolution of the “individual” group. When the algorithm performs nondominated sorting, each individual in the *N*-sized population is compared against *M* objective functions and *N* − 1 individuals in the population. NSGA-II needs to save two quantities during sorting:(i)The number of dominant : this amount is the number of all individuals who can dictate the individual in the feasible solution space(ii)The controlled individuals gathered : this quantity is a collection of all individuals in the feasible solution space that is dominated by individual

In this paper, a total of three objective functions are set, which are in conflict with each other and cannot be compared. It is impossible to obtain the global maximum or minimum like single-objective problems. According to the objective function (fitness function) proposed above, NSGA-II is used to obtain a compromise solution set (nondominant solution) with initial input data and design variables, which does not favour any objective function. Its flow is shown in Figure 5.

The optimizer was drawn up and run by Python 3.7 with a crossover probability of 0.8, a mutation probability of 1/20, an overall size of 100, and a maximum number of iterations of 200 generations.

##### 3.4. Results

It should be reiterated here that is the total output result of the basic heat consumption of typical climate in Chengdu in winter and the cooling load of typical climate in summer. We calculated 11 moments in winter and summer, respectively. And represents the annual lighting energy consumption per hour per square meter.

In this process, and have a certain coupling, for example, the change of window size will affect the change of and output at the same time. Therefore, as changes in calculation, will also change correspondingly. In total, we obtained the Pareto solution sets at 11 different moments in a day and the values of corresponding design variables.

According to the calculation result of the above case, for the convenience of the architect to more quickly get detailed building energy efficiency design data, we propose that when two different choices are adopted in the minimum value at 11 moments, the output value of each building parameter is as shown in Tables 7 and 8.

Finally, we give the PMV output results of different selection methods. As can be clearly seen from Figure 6, when at each moment is selected as the minimum value, the interval of PMV remains at −0.5∼0.5. In the other case, all values are higher than 0.5. However, in China, in order to make buildings more energy efficient, the range of PMV is extended to −1∼1. Accordingly, these two kinds of choices are to accord with indoor thermal and comfortable requirement. The main reason for this gap is that we only calculate thermal comfort in summer. But, the computational models used are the same in winter and summer. Here, we give more specific design variables of building parameters.

To evaluate the effectiveness of NSGA-II in this article, we use the spacing () [21] method to verify the consistency of the solution set. Firstly, given a solution set ,where represents the average of and represents the norm distance (Manhattan distance) of and established .where represents the number of objectives and represents the solution of the th objective. When the SP value is close to 0, an excellent consistent solution is obtained. Table 9 shows the values at different moments.

From the values of at each of the above moments, it can be seen that the solutions at each moment have certain stability. Therefore, we have put forward the most suitable options for architects in the solution set at these moments.

#### 4. Conclusion and Recommendations for Future Work

This paper introduces a design method of building energy conservation. To implement the model, the nondominant sorting genetic algorithm-II (NSGA-II) is written in the Python environment. In the design questions raised, the design parameters include window size, glass material and specification, floor veneer material, wall veneer material, external wall building material and specification, etc. In addition, the three objective functions of building thermal load, indoor thermal comfort, and lighting energy consumption are considered. Finally, 1100 solution sets are obtained at 11 different moments. In these solution sets, we choose two representative solution sets, which are, respectively, based on the minimum value of building cooling and heating load and the minimum value of lighting energy consumption.

NSGA-II has certain limitations. At present, in the research of energy-saving optimization, many scholars still use NSGA-II to solve three target problems and get excellent results [22–24]. It has developed for nearly 20 years, and the established objective functions are basically no more than three. Due to the proportion of nondominated individuals in the population will rise of power series with the increase of the target space dimension [25]. Therefore, we will adopt more efficient methods to address optimization problems in future studies.

The construction plan set out in the present paper does not mean specific cost analysis because cost analysis involves the impact of labour costs, construction technology, and local material price fluctuations. Identifiable cost issues can be further analysed on a case-by-case basis. Finally, the contradiction between building energy consumption and indoor environment is closely related to related climate characteristics and renewable energy. We will continue to explore the application and benefits of renewable energy in energy-efficient buildings in the next study.

#### Nomenclature

: | Facade height with window |

: | Heat consumption |

: | Total annual lighting consumption |

: | Cooling load |

: | The glazing transmittance |

: | Window area |

: | The total room surface area |

: | The area-weighted mean surface of the room |

: | Temperature difference correction factor |

: | The area of the envelope |

: | Summation heat transfer coefficient |

: | Heating interior design temperature |

: | Outdoor design temperature for heating |

: | Heat transfer coefficient of inner surface of envelope |

: | Outdoor temperature fluctuation range in winter |

: | The angular frequency |

: | Orientation correction rate |

: | The wind attachment rate |

: | The external door attachment rate |

: | The height addition rate of the building |

: | The intermittent addition rate |

: | Ventilation rate |

: | Weight of the envelope |

: | Density |

: | Mean skin temperature |

: | Operating temperature |

: | Clothing thermal resistance |

: | The air thermal resistance |

: | Window height |

: | Window width |

: | Thickness of concrete |

: | Thickness of mortar |

: | The thickness of insulating material |

: | The thickness of the window pane |

: | The heat capacity of the air |

: | Density of mortar |

: | The density of insulating material |

: | Set the indoor temperature in winter |

: | Density of concrete |

: | The area-weighted mean reflectance of the ceiling and walls above the midheight of the window excluding the window wall |

: | Facade width with window |

: | A coefficient depending on the obstruction angle |

: | The area-weighted mean reflectance of the floor and walls below the midheight of the window excluding the window wall |

: | The area-weighted mean reflectance of the ceiling and walls above the midheight of the window excluding the window wall |

: | The length of the window pane |

: | The vertical distance between the observation point and the window |

: | The illuminance |

: | The outdoor diffuse illuminance |

: | The envelope basically consumes heat |

: | The thickness of the material |

: | Correction coefficient of material thermal conductivity |

: | Thermal conductivity of each layer of envelope |

: | Thermal resistance of closed space layer |

: | Heat transfer coefficient of outer surface of envelope |

: | Average calculated outdoor temperature in winter |

: | The heat capacity of the envelope |

: | Inner surface temperature of the enclosure |

: | The convective coefficient between the external material and the external air |

: | Area of external wall |

: | Outdoor air temperature in summer |

: | Convection coefficient between the envelope and the indoor air |

: | The indoor heat source |

: | Average outdoor air temperature in summer |

: | Outdoor temperature fluctuation range in summer |

: | Garment area coefficient |

: | Thermal equilibrium coefficient |

: | Metabolic rate |

: | Mean radiation temperature |

: | Heat transfer coefficient of concrete |

: | Heat transfer coefficient of the whole window with closed space and window frame area accounting for 20% |

: | Heat transfer coefficient of concrete |

: | Heat transfer coefficient of insulating material |

: | Set indoor temperature in summer |

: | Floor reflection ratio |

: | Wall reflection ratio |

: | The reflection ratio of window glass |

: | Ceiling reflection ratio |

: | The total transmittance of the window |

: | The area-weighted mean reflectance of the floor and walls below the midheight of the window excluding the window wall |

: | A coefficient depending on the obstruction angle. |

#### Data Availability

The data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare no conflicts of interest.

#### Acknowledgments

This research is partially supported by the Youth Foundation for Humanities and Social Sciences of Ministry of Education of China (no. 19YJC630063) and the Youth Project of Education Department of Sichuan Province (no. 17ZB0335).