Design optimization of daylighting for kindergarten in different light climate zones in China

ABSTRACT Kindergarten classrooms in China undertake the functions of teaching, activities, breaks and diet, so daylighting design is particularly important. This paper proposed using artificial neural network (ANN) model to replace the typical physical model to optimize the daylighting quality and daylighting quality uniformity in the classroom, in order to achieve efficient optimization calculation. In detail, the problems in the classroom daylighting design are firstly investigated, and a daylighting design structure that incorporates the south window and north skylight of a kindergarten classroom is proposed. Then, the evaluation indicators of daylighting quality and daylighting quality uniformity are determined. Finally, the ANN model is used to achieve efficient optimization calculation. The optimization effect of kindergarten classrooms in five light climate zones in China is discussed. The results show that compared with the benchmark scheme in the existing design codes, after single objective optimization, in the kindergarten classroom can be increased by at most 18.2%, while can be increased by at most 50.9%. After double-objective optimization, can be increased by at most 17.7%, and can be decreased by at most 87.7%; can be increased by at most 50.5%, and can be decreased by at most 97.6%.


Background
Daylighting is an important element in the building lighting environment and is often used as the objective of building design optimization. Compared with artificial lighting, daylighting has significant advantages in terms of health, comfort and energy savings but also has problems, such as glare (Samiou, Doulos, and Zerefos 2022). Therefore, the rational and efficient use of daylighting has always been one of the key points in building optimization (Fakhari, Fayaz, and Asadi 2021). Different types of buildings have different requirements for daylighting quality, and educational buildings pay special attention to daylighting because daylighting importantly affects the growth and development of students (Alkhatatbeh and Asadi 2021). Especially for children (4-6 years old) (Stankovic et al. 2015), daylighting not only affects their visual development but also directly affects a series of biological functions. Proper daylighting helps reduce the myopia rate of children and promote the healthy development of their visual perception system (Tsikra and Andreou 2017;. Kindergarten is a shelter for children's learning and activities, and the classroom is the most important living area. Considering the convenience of teaching and management, kindergarten classrooms in China undertake multiple functions, such as teaching, activities, lunch breaks and diet, so daylighting design is particularly important. In China's existing building codes (Code for design of school 2011, Code for design of nursery and kindergarten buildings 2019), the daylight factor (≥3%) and the window to ground ratio (≥1/5) in the kindergarten classroom have made requirements. However, current kindergarten classrooms adopt mostly the design scheme of single side window (Gao 2020;Zhang et al. 2021). Affected by the depth of the classroom, the daylighting effect and uniformity are poor. Therefore, optimizing the daylighting design of kindergarten classrooms in China is of great significance.

Optimization of daylighting design in school buildings
Many scholars have carried out design optimization research on the daylighting effect of school buildings. Boutet et al. measured the illuminance of schools in Northeast Argentina and adjusted the glass area of the school envelope according to the results. The results show that the optimized building scheme has a higher illumination level and better uniformity (Boutet, Hernández, and Jacobo 2016). Camacho Montano et al. studied the improvement of visual comfort in classrooms in Karlsruhe, Germany. Electrochromic window technology is used in optimization, but this technology affects the color rendering indicator (Camacho-Montano, Cook, and Wagner 2019). Tsikra et al. studied the daylighting effect of a primary school in Greece, improved the performance of daylighting through the design optimization of the envelope, and analyzed the energy-saving effect (Tsikra and Andreou 2017). Xu et al. studied the daylighting optimization of primary and secondary school classrooms in China; the authors focused on the effects of the outer corridor, window-to-wall ratio (WWR) and types of external windows (Xu et al. 2021a). Due to the influence of climate, culture and teaching philosophy, there are great differences in school buildings in different countries, regions and grades; consequently, optimization studies of school buildings have strong regional and grade characteristics.
Considering the impact of daylighting on children's development, the daylighting design of kindergarten classrooms is particularly critical. Samiou et al. conducted field investigation and research on the daylighting of typical kindergarten classrooms in Greece; the authors focused on the efficient combination of daylighting and artificial lighting (Samiou, Doulos, and Zerefos 2022). Pagliolico et al. measured and studied the kindergarten classroom in San Marcel (Aosta Valley, north-west of Italy) and analyzed the shading effect of the novel photo-bio screen in the kindergarten building (Pagliolico et al. 2019). Salleh et al. investigated the daylighting quality and glare of kindergartens in Malaysia through field visits and questionnaires, which laid a foundation for the kindergartens' subsequent transformation design (Salleh et al. 2015). Zhang et al. studied the design of kindergartens in Urumqi, China; discussed the impact of passive layout on daylighting; and focused on the comprehensive utilization of daylighting and solar energy resources (Zhang et al. 2021). Although the above studies have optimized the daylighting of kindergartens, considering the large differences in the shapes and characteristics of kindergartens in different regions, the results of the research on daylighting design optimization of foreign kindergartens are of low reference value for daylighting design of kindergartens in China. According to Reference (Standard for daylighting design of buildings 2013), China is divided into five different light climate zones. Different light climate zones exhibit great differences in direct sunlight, sky diffuse light and ground reflected light. At present, there is a lack of relevant research on the optimization of daylighting design of kindergartens in different light climate zones in China.

Evaluation indicators of daylighting
The evaluation indicators of daylighting are divided mainly into static indicators and dynamic indicators. Static indicators include the daylight factor (DF) and daylight uniformity, which are often used in current design codes in China (Wong 2017;Xu et al. 2021b). Compared with static evaluation indicators, dynamic evaluation indicators consider the time change of the whole year, and the evaluation results of dynamic evaluation indicators are more reliable. At present, the research hotspot of daylighting has gradually shifted from static indicators to dynamic indicators. Commonly used dynamic evaluation indicators include daylight autonomy (DA), annual sun exposure (ASE), spatial daylight autonomy (sDA) and useful daylight illuminance (UDI). Zhang et al. compared the advantages and disadvantages of DA, UDI and ASE in the daylighting optimization of school buildings and finally selected UDI as the optimization objective (Zhang et al. 2017). Zhu et al. compared UDI and sDA in a study of daylighting in rural tourism buildings in northern China. Considering that sDA can better analyze the daylighting conditions of various areas in the room, sDA is finally selected as the optimization objective (Zhu, Wang, and Sun 2020). Xu et al. improved the UDI indicator, used UDI NO to measure the quality of daylighting in the occupied period of the whole year, and optimized the envelopes of primary and secondary school classrooms in China according to this indicator (Xu et al. 2021b). Bakmohammadi et al. studied the daylighting design optimization of primary school classrooms in Iran and compared the optimization results of five visual indicators: UDI, DA, daylight glare probability (DGP) and ASE (Bakmohammadi and Noorzai 2020). Brzezicki studied the useful daylight illuminance in an office with a light shelf and translucent ceiling, and used UDI 300-3000 , Us(i) and DGP to measure the quality and uniformity of daylight (Brzezicki 2021). The above dynamic evaluation indicators measure the indoor or zone daylighting quality through the annual illumination value change of indoor monitoring points, but these indicators cannot evaluate the uniformity of indoor daylighting quality. As mentioned in Section 1.1, kindergarten classrooms in China have many functions, such as teaching, activities, lunch breaks and diet, so classroom areas are large. In daylighting design optimization for largearea classrooms, the problem of daylighting quality uniformity needs to be considered.

Research gaps and main contributions
According to the above analysis, a knowledge gap has been identified. At present, the daylighting of kindergarten classrooms in different light climate areas in China needs further optimization, especially in terms of the uniformity of daylighting quality. Therefore, in order to further optimize the daylighting of kindergarten classrooms, this paper proposes a method to optimize the daylighting design of kindergarten classrooms in China. In view of the poor daylighting effect of the single side window in the kindergarten classroom at present, this paper probes into the feasibility of strengthening the daylighting effect through the skylight. A daylighting design structure that incorporates the south window and the north skylight of a kindergarten classroom is proposed, and the application of this design structure in five light climate zones in China is discussed. On this basis, this paper focuses on the single-objective optimization effect of different daylighting quality evaluation indicators and the double-objective optimization effect while considering daylighting quality and daylighting quality uniformity. Therefore, this study can effectively improve the daylighting effect of kindergartens in different light climate zones in China, which is of great significance to optimize children's visual comfort.
The remainder of this paper is arranged as follows. In the second section, the overall process of the daylighting design optimization method for kindergarten classrooms is introduced in detail. In the third section, the method is applied to kindergarten classrooms in five light climate zones, and the results are analyzed. In the fourth section, the shortcomings of this paper are discussed and the future research is prospected. The last section summarizes and discusses this paper. Figure 1 shows the framework of the proposed daylighting design optimization method for kindergarten classrooms, and this section details the method involved.

Investigation and information acquisition before design
Before the actual design, it is necessary to investigate the information on all aspects of the target building. Figure 2 (a) shows the axonometric view of a typical kindergarten in Nanjing, China. Figure 2(b) shows the plan of the kindergarten. The daylighting simulation result of a classroom (Classroom 102) is shown in Figure 2(c). Since only the south side is equipped with side windows, the daylighting effect in the classroom is poor.
In addition, this study also used field visits and questionnaires to investigate the situation of three kindergartens in Nanjing; the results are shown in Table 1. Most children and teachers believe that due to the influence of the depth of the classroom, the daylighting effect on the inner side of the classroom is very poor, so it is often necessary to turn on artificial lighting as a supplement even in the daytime. Due to the lack of adjustable external and interior shading equipment in some classrooms, the glare problem in the classroom is more serious in strong direct sunlight.

Optimizing the daylighting design structure of the kindergarten classroom
The classroom design optimization in this study is only for single-story kindergarten buildings. Considering the layout of kindergarten classrooms and the limitations of single side window daylighting, this study intends to use skylights to improve the indoor daylighting effect. References (Martín-Chivelet et al. 2022;Marzouk, ElSharkawy, and Mahmoud 2022) show that compared with the flat skylight and the south skylight, the north skylight can make better use of diffuse light, so the north skylight can not only enhance the indoor   Insufficient illumination on the inner side; Glare; Lunch break too bright Insufficient illumination on the inner side illumination but also avoid glare. In addition, the Chinese government issued carbon peaking and carbon neutrality policies in 2020. At present, most regions have proposed clear requirements for setting photovoltaic modules on the roofs of public buildings. Therefore, this study adopts the kindergarten classroom design structure incorporating the south side window and the north skylight (the roof adopts the form of a double slope, with photovoltaic modules on the south roof and a skylight on the north roof).

Determination of the evaluation indicators and optimization variables of daylighting
In this study, a variety of dynamic evaluation indicators of daylighting are introduced in Section 1.2. Too high illuminance can be reduced by interior shading, but too low illuminance can only be supplemented by artificial lighting. Considering that the selection of interior shading belongs to the scope of interior decoration in China, interior shading is sometimes not included in the business scope of building design. In these studies or projects, glare caused by excessive illuminance is usually not considered. In the subsequent interior decoration, users will consider whether to set internal sunshades according to the users' own needs. Therefore, according to References (Mardaljevic, Andersen, and Roy 2012;Galatioto and Beccali 2016;Xu et al. 2021b;Zhang, Zhang, and Li 2022), this study selects DA and UDI, the two most commonly used dynamic evaluation indicators. DA is defined as the percentage of annual daytime hours that a given point in a space is above a specified illuminance level (Reinhart and Weissman 2012;Galatioto and Beccali 2016), as shown in Equation 1.
The key to calculating DA is to determine the E lim value, which is different in different studies. In this study, the recommended value for school classrooms (450 lux) in the Standard for Daylighting Design of Buildings (Standard for daylighting design of buildings 2013) is used as the value of .
UDI is defined as the annual time fraction that indoor horizontal daylight illuminance at a given test point reaches in a given domain, as shown in Equation 2 (Nabil and Mardaljevic 2005); this equation contains lower and upper thresholds and an acceptable range, which are denoted as UDI Underlit , UDI Overlit and UDI Useful , respectively. In this study, in accordance with Reference (Bakmohammadi and Noorzai 2020), the value of is set to 100 lux, and the value of is set to 2000 lux (exceeding this illuminance value easily causes glare).
where denotes each occupied hour in a year, denotes the horizontal illuminance at a given point in lux, denotes a weighting factor, E lim denotes the preset minimum value of horizontal illuminance at a given point in lux, denotes the preset upper limit value of horizontal illuminance at a given point in lux, and E Lowerlim denotes the preset lower limit value of horizontal illuminance at a given point in lux.
Although DA and UDI can evaluate the indoor daylighting quality, they cannot evaluate the uniformity of indoor daylighting quality. As mentioned in Section 1.2.2, kindergarten classrooms in China have multiple functions and large areas, so the uniformity of daylighting quality must be considered. Therefore, it is necessary to arrange multiple daylighting monitoring points in the classroom and observe the differences between the data of each monitoring point. In this study, the standard deviation method is used to measure the uniformity of daylighting quality, and the calculation process is shown in Equations 3 and 4. In these equations, the higher the value of lim is, the greater the difference in the DA values among indoor areas and the worse the uniformity of indoor daylighting quality. The higher the value of UDI SD is, the greater the difference in the UDI values among indoor areas, thus also indicating that the uniformity of indoor daylighting quality is poor. In addition, due to the existence of multiple daylighting monitoring points, the daylighting quality in the room is measured by the average values of DA and UDI, that is, DA av and UDI av , respectively. The higher the values of DA av and UDI av are, the better the overall daylighting quality of each indoor area.
where DA SD denotes the standard deviation of the DA value of each measuring point, DA j denotes the DA value of each measuring point, DA denotes the average value of the DA value of each measuring point, n denotes the number of monitoring points, UDI SD denotes the standard deviation of the UDI value of each measuring point, UDI j denotes the UDI value of each measuring point, and UDI denotes the average value of the UDI value of each measuring point.
The above four evaluation indicators (DA av , UDI av , DA SD and UDI SD ) are the optimization objectives of this study. Considering that the target building of this study is the kindergarten classroom, the optimization variables involved should include building orientation, window composition, window size and external shading. In addition, in order to measure the glare in the classroom, in this study, the number of occupied hours with glare index greater than 22 (GIH) is used as the glare evaluation indicator (Kim, Han, and Kim 2009). The larger the GIH is, the more serious the glare in the occupied period of the classroom.

Physical modeling and parameter setting
After determining the optimization objectives and variables, this study will use DesignBuilder to establish the physical model of the kindergarten classroom and then import the IDF file into EnergyPlus for parameter setting. The model used in this study has many parameters, and the four key parameters are described in detail below.
(1) Weather data: Section 1.2.1 introduces that China is divided into five light climate zones, and the different light climate zones exhibit great differences in direct sunlight, sky diffuse light and ground reflected light. Therefore, in this study, typical cities in the five light climate zones will be selected for simulation.
(2) Materials involved: Considering the window composition indicated by the optimization variables used in this study, it is necessary to import various commonly used window material parameters into the IDF file.
(3) Occupation period of personnel: The optimization objectives of this study are closely related to occupancy time. Therefore, it is necessary to set the parameters according to the personnel occupation time obtained from the survey.
(4) Sensor grid density determination: The calculation method of DA av , UDI av , DA SD and UDI SD is introduced in Section 2.3. The density of the sensor grid determines the value of n (Equations 3 and 4). The uniformity of daylighting quality calculated by high-density sensor grid is more accurate, but the calculation time cost is higher. To explore the influence of sensor grid density on the calculation of daylighting, the grid independence verification method is used in this study (Samiou, Doulos, and Zerefos 2022), that is, adjust the sensor grid density on the working face (the working face height is set as 0.5 m in this study) to explore the optimal value of sensor grid density.

Efficient optimization calculation
After completing the physical modeling and parameter setting, the optimization calculation can be carried out. The traditional optimization method takes the simulation software (EnergyPlus) directly as the objective function of the optimization algorithm. Considering the time cost involved in the calculation, an artificial neural network (ANN) model is used in this study to improve the efficiency of the optimization calculation. Our team has described the process of this method in detail in References (Xu et al. 2021b;, so this process is only briefly described in this paper.
In this optimization process, EnergyPlus software coupled with the Python programming language is used to generate the sample space through Latin hypercube sampling. Then, we use the machine learning library scikit-learn based on Python as the platform to train the ANN model. Finally, the optimal ANN model is taken as the objective function of the optimization algorithm.
The optimization calculation used in this study is divided into two parts: the single-objective optimization calculation and the double-objective optimization calculation. In the single-objective optimization calculation, the optimal design scheme of the kindergarten classroom with DA av and UDI av as optimization objectives will be obtained. In the double-objective optimization calculation, the Pareto solution sets with DA av and DA SD as optimization objectives and UDI av and UDI SD as optimization objectives will be obtained. Finally, the optimization effect will be evaluated according to the benchmark scheme (according to design codes).

Case study
Section 2 introduces the optimization method of daylighting design of kindergarten classrooms in China. This section will take an actual kindergarten classroom as a case to study the optimization effect of daylighting in five light climate zones in China to verify the effectiveness of the proposed method.

Case information
In Section 2.2, this study proposes a kindergarten classroom design scheme that incorporates a south side window and a north skylight. In this section, design optimization is carried out on this basis. This study selects a common kindergarten classroom in China as a case, as shown in Figure 3. Through the field visits of several kindergartens before, the basic information of the case is set, as shown in Table 2. During the winter and summer vacations and weekends, all teachers and students in the kindergarten have a holiday, while the work day is from 7:00 to 16:00 every day.

Optimization calculation under weather conditions in each light climate zone
The classification of optimization variables is introduced in Section 2.3. According to the design code (Standard for daylighting design of buildings 2013) and the characteristics of the case classroom, the optimization variables selected in this study are shown in Table 3.
After determining the optimization variables, according to the contents in Section 2.4, this study adopts DesignBuilder (version 6.1.6.005) modeling and imports the IDF file into EnergyPlus (version 9.0.1) for parameter setting. The typical cities in the five light climate zones include Lijiang (level I), Kunming (level II), Lanzhou (level III), Nanjing (level VI) and Chengdu (level V). The weather data of these five cities will be used as representatives for the optimization calculation. The basic geographic information and the site exterior horizontal sky illuminance throughout the year are shown in Table 4. In addition, according to the occupied period shown in Table 2 and the window material shown in Table 3, the related parameters of schedule and material in EnergyPlus are set.
Considering the influence of sensor grid density on daylighting quality calculation, we take the kindergarten classroom in Nanjing as an example to test the influence of 12 grid densities on the four optimization objectives (DA av , UDI av , DA SD and UDI SD ) in Section 2.3. Figure 4 is the layout diagram of sensors, and the test results are shown in Figure 5. The test results show that when the sensor grid density is less than 0.1 m, the changes in the four optimization objective values are relatively stable. Considering that the denser the sensor grid is, the higher the time cost of calculation is, the sensor grid density selected in the simulation of this study is 0.1 m.   Then, according to Section 2.5, the sample spaces under weather conditions in five cities are generated. In Reference (Xu et al. 2021b), our team introduced the process and typical methods of ANN model training and hyperparametric optimization in detail. In this study, the input of the model is the optimization variable, while the output is DA av , UDI av , DA SD and UDI SD , as shown in Figure 6. The grid search method is selected as the optimization method to obtain the optimal ANN models under the weather conditions of five cities, as shown in Table 5. During training, ANN's batch size is 100. The mean relative errors of the five ANN models are lower than 1%, and R 2 is higher than 0.98. These results show that the quality of these ANN models is good and that these models can be used as the objective function of the optimization algorithm for optimization calculation.

North skylight
According to References (Hamdy, Nguyen, and Hensen 2016;Xu et al. 2020), the single-objective optimization algorithm selected in this study is genetic algorithm (GA), and the double-objective optimization  algorithm is non-dominated sorting genetic algorithm II (NSGA-II). The parameter settings of the two algorithms are shown in Table 6. The following is the analysis of the optimization results.

Optimization of kindergarten classroom design in Lijiang (level I light climate zone)
Lijiang is a typical city in China's level I light climate zone. The city's basic geographic information and site exterior horizontal sky illuminance are introduced in Table 4. Table 7 lists the single-objective optimal scheme calculated with DA av and UDI AV as the optimization objectives. In addition, to facilitate comparison, the scheme obtained from the parameters in the existing design codes (Code for design of school 2011, Code for design of nursery and kindergarten buildings 2019) is used as the benchmark scheme. Table 7 shows that after single-objective optimization, DA av and UDI av can reach high values. Compared with the UDI av optimal scheme, the DA av optimal  scheme tends to increase the illumination of the indoor working surface in all ways. The WWR of the side window and skylight is 0.8, and the control setpoint is 200 W/m 2 . Overall, compared with the benchmark scheme, the two optimal schemes have significant advantages, in which the DA av value of the DA av optimal scheme is increased by 7.8%, while the UDI av value of the UDI av optimal scheme is increased by 50.9%. Figure 7 shows the results of two doubleobjective optimizations under Lijiang weather conditions. For convenience of display, in this study, the reciprocal of DA SD and UDI SD is used to replace DA SD and UDI SD as the coordinate in the drawing. Figure 7(a) shows that in the optimal schemes obtained by double-objective optimization, the DA av value of all schemes is lower than the DA av optimal scheme (which is shown in Table 7). However, only two schemes have higher DA SD values than the DA av   optimal scheme (accounting for 4% of the Pareto scheme set). As Figure 7(b) shows, among the optimal schemes obtained by double objective optimization, the UDI av value of all schemes is lower than the UDI av optimal scheme (which is also shown in Table 7). Additionally, the UDI SD value of all schemes is lower than that of the UDI av optimal scheme. The above shows that the uniformity of daylighting quality is better than that of single-objective optimization in most of the optimal schemes obtained by doubleobjective optimization. Compared with the values obtained by the benchmark scheme, the following   values obtained by double-objective optimization increased or decreased as follows: the value of DA av increased by at most 2.22%, the value of DA SD decreased by at most 81.8%, the value of UDI av increased by at most 49.2% and the value of UDI SD decreased by at most 97.6%.

Optimization of kindergarten classroom design in Kunming (level II light climate zone)
Kunming is a typical city in China's level II light climate zone. The city's basic geographic information and site exterior horizontal sky illuminance are introduced in Table 4. Like Table 7, in Section 3.3.1, Table 8 lists the   DA av optimal scheme, UDI av optimal scheme and the benchmark scheme.
As Table 8 shows, compared with results shown in Section 3.3.1, the DA av optimal scheme changes only the building orientation because the optimal daylighting direction will also change due to different light climate zones. In addition, the DA av and UDI av values of the three schemes listed in Table 8 have decreased because the annual average total illuminance of outdoor daylight in the light climate zone of level II is lower than that of level I. Overall, compared with the benchmark scheme, the two optimal schemes have significant advantages, in which the UDI av value of the DA av optimal scheme is increased by 10.5%, while the I av value of the UDI av optimal scheme is increased by 50.6%. Figure 8 shows the results of two doubleobjective optimizations under Kunming weather conditions. For convenience of display, the reciprocal of DA SD and UDI SD is still used to replace DA SD and UDI SD as the coordinate in the drawing. Compared with the values obtained by the benchmark scheme, the value of DA av can be increased by at most 8.7%, the value of DA SD can be decreased by at most 72.7%, the value of UDI av can be increased by at most 50.5%, and the value of UDI SD can be decreased by at most 97.1%.

Optimization of kindergarten classroom design in Lanzhou (level III light climate zone)
Lanzhou is a typical city in China's level III light climate zone. The city's basic geographic information and site exterior horizontal sky illuminance are introduced in Table 4. Like Table 7 in Section 3.3.1, Table 9 lists the DA av optimal scheme, UDI av optimal scheme and the benchmark scheme.
As Table 9 shows, compared with values shown in Section 3.3.2, the DA av values of the three schemes have increased because although the annual average total illuminance of outdoor daylight in the level III light climate zone is lower than that in level II, due to the differences in building orientation, building daylighting structure and solar incidence angle in different cities, the daylighting quality of buildings in the level III light climate zone can still be higher than that in the level II light climate zone. Overall, compared with the benchmark scheme, the two optimal schemes have significant advantages, in which the DA av value of the DA av optimal scheme is increased by 10.5%, while the UDI av value of the UDI av optimal scheme is increased by 44.2%. Figure 9 shows the results of two doubleobjective optimizations under Lanzhou weather conditions. For convenience of display, the reciprocal of

Optimization of kindergarten classroom design in Nanjing (level VI light climate zone)
Nanjing is a typical city in China's level VI light climate zone. The city's basic geographic information and site exterior horizontal sky illuminance are introduced in Table 4. Like Table 7 in Section 3.3.1, Table 10 lists the DA av optimal scheme, UDI av optimal scheme and the benchmark scheme. As Table 10 shows, compared with the previous optimization results, the optimization effect of the two optimal schemes in Nanjing is higher than that in Kunming but lower than that in Lijiang and Lanzhou. Compared with the benchmark scheme, the two optimization schemes still have significant advantages, in which the DA av value of the DA av optimal scheme is increased by 12.3%, while the UDI av value of the UDI av optimal scheme is increased by 45.7%. Figure 10 shows the results of two double-objective optimizations under Nanjing weather conditions. For convenience of display, the reciprocal of DA SD and UDI SD is still used to replace DA SD and UDI SD as the coordinate in the drawing. Compared with the benchmark scheme, the value of DA av value obtained by double-objective optimization can be increased by at most 12.1%, the value of DA SD can be decreased by at most 83.7%, the value of UDI av can be increased by at most 45%, and the value of UDI SD can be decreased by at most 94.8%.

Optimization of kindergarten classroom design in Chengdu (level V light climate zone)
Chengdu is a typical city in China's level V light climate zone. The city's basic geographic information and site exterior horizontal sky illuminance are introduced in Table 4. Like Table 7 in Section 3.3.1, Table 11 lists the DA av optimal scheme, UDI av optimal scheme and the benchmark scheme.
As Table 11 shows, compared with the previous optimization results, the optimization effect of the two optimal schemes in Chengdu is higher than that in Kunming and Nanjing but lower than that in Lijiang and Lanzhou. Compared with the benchmark scheme, the two optimization schemes still have significant advantages, in which the DA av value of the DA av optimal scheme is increased by 18.2%, while the UDI av value of the UDI av optimal scheme is increased by 34.7%. Figure 11 shows the results of two doubleobjective optimizations under Chengdu weather conditions. For convenience of display, the reciprocal of DA SD and UDI SD is still used to replace DA SD and UDI SD as the coordinate in the drawing. Compared with value obtained by the benchmark scheme, the value of DA av can be increased by at most 17.7%, the value of DA SD can be decreased by at most 87.7%, the value of UDI av can be increased by at most 32.5%, and the value of UDI SD can be decreased by at most 96.1%.
The above analysis shows that in terms of the single-objective optimization results, the difference in the DA av schemes in different light climate zones lies in the building orientation. In addition, although the annual average outdoor illuminance decreases from light climate zone I to light climate zone V, the indoor daylighting quality is not necessarily reduced due to the influence of the building daylighting structure. Different light climate zones exhibit great differences in the optimal scheme of UDI av , thus showing that when UDI av is taken as the optimization objective, the configuration of building daylighting-related parameters has higher flexibility.
As far as the glare of each typical scheme is concerned, the GIH of DA av optimal scheme is the highest, because only increasing the illuminance of the working face in the annual occupied period is considered in the DA av optimal scheme. The GIH of UDI av optimal scheme is the lowest, and its minimum value in this study is 0, while the maximum value is 66. This shows that UDI av is the most reasonable optimization objective without interior shading.
For the double-objective optimization results, although the daylighting quality (DA av ; UDI av ) is not as good as the single-objective optimal scheme, the uniformity of daylighting quality of most schemes is significantly higher. In addition, the number of Pareto solutions obtained by the optimization calculation used in this study is often lower than the population of the algorithm (50) because the daylighting design structure of the kindergarten classroom proposed in Section 2.2 is reasonable, so the consistency between the daylighting quality and the quality uniformity is high. In practical engineering applications, the minimum acceptable uniformity of daylighting quality can be set, and then single-objective optimization can be carried out with daylighting quality as the optimization objective.

Discussion
Section 3 studies the design optimization of a kindergarten classroom scheme that incorporates a south side window and a north skylight in five light climate zones in China. The overall optimization effect is significant, but the daylighting quality optimization effect of kindergarten classrooms in Kunming is relatively poor. Kunming is located in the level II light climate zone in China. The city's outdoor daylight design illuminance value reaches 16,500 lux (Standard for daylighting design of buildings 2013), and daylighting resources are very rich. However, in this study, the optimization effects of DA av and UDI av in Kunming are the lowest among the five cities, thus showing that the kindergarten classroom design structure proposed in this study has further optimization space in the application of Kunming. We will further explore this issue in follow-up research. As far as glare is concerned, the GIH of UDI av optimal scheme is the lowest, because the upper and lower limits of illuminance are strictly limited in this indicator. However, only the GIH of the optimal UDI av scheme in Kunming is 0, which indicates that the constraint of glare cannot be ignored in daylighting optimization.
In addition, the kindergarten classroom scheme proposed in this study is only applicable to singlestory kindergarten buildings. For multistory kindergarten buildings, due to the limited daylighting effect of one-sided windows, daylighting optimization should consider adding other side windows or using related technologies, such as courtyards and light guide tubes. In the actual project, the technical measures should be selected according to the specific situation.

Conclusions
This paper presents a method to optimize the daylighting design of kindergarten classrooms in China. In this method, first, according to the daylighting defects of the kindergarten classroom at present, a daylighting design structure that incorporates the south side window and north skylight of a kindergarten classroom is proposed. Then, this paper studies the application of the kindergarten classroom design structure in typical cities in five light climate zones in China and focuses on the singleobjective optimization effect of different daylighting quality evaluation indicators and the double-objective optimization effect while considering the daylighting quality and the uniformity of daylighting quality. In addition, the optimization method proposed in this paper uses ANN instead of physical model for optimization calculation, which saves a lot of calculation time. The main conclusions are as follows: (1) In the single-objective optimization, compared with the benchmark scheme, this study increases the DA av by 7.8%, 10.5%, 10.5%, 12.3% and 18.2% and increases the UDI av by 50.9%, 50.6%, 44.2%, 45.7% and 34.7% in the five light climate zones of China (level I -level V, respectively). In addition, the difference in the DA av optimal scheme in different light climate zones lies in the building orientation. The optimal scheme of UDI av varies greatly in different light climate zones, and the value of daylighting-related variables is more flexible.
(2) In the double-objective optimization with DA av and DA SD as the optimization objectives, compared with the benchmark scheme, this study can achieve maximum increases of 2.22%, 8.7%, 8.8%, 12.1%, and 17.7% in DA av and decreases of 81.8%, 72.7%, 82.5%, 83.7%, and 87.7% in UDI SD in the five light climate zones of China (level Ilevel V, respectively). (3) In the double-objective optimization with UDI av and UDI SD as the optimization objectives, compared with the benchmark scheme, this study can achieve maximum increases of 49.2%, 50.5%, 43.8%, 45%, and 32.5% in UDI av and decreases of 97.6%, 97.1%, 96%, 94.8%, and 96.1% in UDI SD in the five light climate zones of China (level I -level V, respectively).
The efficient optimization method proposed in this paper can be extended to optimization calculation in other fields, but attention should be paid to the ANN training and hyperparameter optimization, because the insufficient accuracy of ANN model will lead to deviation in the results of optimization calculation.