The Spatial Optimization and Evaluation of the Economic, Ecological, and Social Value of Urban Green Space in Shenzhen

: Urban green space (UGS) is important in urban systems, as it beneﬁts economic development, ecological conservation, and living conditions. Many studies have evaluated the economic, ecological, and social value of UGS worldwide, and spatial optimization for UGS has been carried out to maximize its value. However, few studies have simultaneously examined these three values of UGS in one optimization system. To ﬁll this gap, this study evaluated the economic value of UGS in terms of promoting housing prices, its ecological value through the relief of high land surface temperature (LST), and its social value through the provision of recreation spaces for residents within a 255 m distance. Subsequently, these three values were set as objectives in a genetic algorithm (GA)-based multi-objective optimization (MOP) system. Shenzhen was taken as the case study area. The results showed that the inﬂuencing distance of UGS in Shenzhen for house prices was 345 m, and the inﬂuencing distance of UGS for LST was 135 m. Using MOP, the Pareto solutions for increasing UGS were identiﬁed and presented. The results indicate that MOP can simultaneously optimize UGS’s economic, ecological, and social value. the multiple of simultaneously maximizing economic, social, and ecological value. The results indicate that MOP is a viable method for solving spatial problems in the establishment of UGS. Using MOP, Pareto solutions were detected, and the objectives were optimized. To identify the means of objective evaluation in MOP, the relationship between spatial distribution of UGS and its economic, social, and ecological value was analyzed. Speciﬁcally, the economic value of UGS was estimated using 5192 rent-price samples extracted from several major real estate portals in This method was cheaper and made it easier to maintain spatial information compared with traditional methods such as questionnaire surveys or ﬁeld surveys. The ecological value of UGS was indicated by its relief of LST in urban areas. The social value of UGS was calculated on the basis of density of road network and spatial distribution of the population. The results suggest that UGS does a ﬀ ect housing rental prices in Shenzhen at a scale m. The relief of LST was a e ﬀ of UGS 135 m. As for social value,


Introduction
Urban residents are expected to constitute two-thirds of the world's population by the year 2050. This is a significant increase from the current figure, as more than half of the global population now lives in cities [1]. Within this context, it is of key importance to provide urban residents with favorable living conditions. Urban green space (UGS) is an essential part of urban systems [2] and offers a diversity of social, economic, and ecological benefits to urban residents [3][4][5].
A large body of literature has shown that UGS has high social value, as it improves urban residents' quality of life [6,7]. It has a beneficial impact on the physical and mental health of human beings by providing spaces for leisure and physical activity [3,5,[8][9][10]. Moreover, UGS can facilitate social cohesion, interaction, and democracy, and may reduce crime rates [11], thereby enhancing urban residents' quality of life [12].
In addition to its profound social value, UGS also provides significant value for urban residents [13,14]. A large body of literature has shown that UGS can considerably mitigate urban problems [15] through actions such as regulating urban climates, alleviating urban heat island (UHI) town to one of the most highly developed cities in China. The gross domestic product for Shenzhen increased to 2,249,005.86 million yuan in 2017, which is almost equivalent to that of Hong Kong. The city's permanent population at the end of 2017 was 12.53 million-a significant increase from that of 1.6779 million in 1990. Along with its drastic economic development and population increase, the city has experienced rapid urbanization. Li et al. [37] reported that urban land use in Shenzhen has increased by 630% since 1990, and other research pointed out that the urban land of Shenzhen's special economic zone increased from 310.9 ha in 1979 to 11,093.8 ha in 2005 [38]; forests [39], grasslands, and unused lands [40] were converted to urban land. The shrinking of vegetation in Shenzhen has caused various ecological problems, including UHI [41], decline in air quality [42], and soil deterioration [31]. Within this context, local governments have made efforts to preserve UGS and have developed many urban parks in Shenzhen. Shenzhen was the first city in China to win the award for livable communities in 2000 [43].
Sustainability 2020, 12,1844 3 of 21 one of the most highly developed cities in China. The gross domestic product for Shenzhen increased to 2,249,005.86 million yuan in 2017, which is almost equivalent to that of Hong Kong. The city's permanent population at the end of 2017 was 12.53 million-a significant increase from that of 1.6779 million in 1990. Along with its drastic economic development and population increase, the city has experienced rapid urbanization. Li et al. [37] reported that urban land use in Shenzhen has increased by 630% since 1990, and other research pointed out that the urban land of Shenzhen's special economic zone increased from 310.9 ha in 1979 to 11,093.8 ha in 2005 [38]; forests [39], grasslands, and unused lands [40] were converted to urban land. The shrinking of vegetation in Shenzhen has caused various ecological problems, including UHI [41], decline in air quality [42], and soil deterioration [31]. Within this context, local governments have made efforts to preserve UGS and have developed many urban parks in Shenzhen. Shenzhen was the first city in China to win the award for livable communities in 2000 [43].

Land-use Datasets and UGS in China
Land-use data for Shenzhen in 2017 were provided by The Global Ecosystems and Environment Observation Analysis Research Cooperation [44]. The land-use dataset was generated via remote sensing with high-resolution digital elevation models and night light data. The resolution was 30 m, with 10 land-use types. Eight types of land use in Shenzhen were identified: cropland, forest, grassland, shrubland, wetland, water, impervious surface, and bareland. Urban public green space includes parks and reserves, sporting fields, riparian areas such as streams and river banks, greenways and trails, community gardens, street trees, and nature conservation areas, as well as less conventional spaces such as green walls, green alleyways, and cemeteries [45]. In this study, UGS is defined as parks, wetlands, grasslands, and forests in Shenzhen. After identifying green spaces in Shenzhen with the land-use data, the Statistic Book for Green Parks in Shenzhen (May 2018 version; http://cgj.sz.gov.cn/zwgk/tjsj/zxtjxx/201805/t20180525_11941634.htm) was examined to extract the names, areas, and addresses of green parks [46]. Finally, the spatial boundaries or locations of listed green parks were drawn from OpenStreetMap (OSM) (https://www.openstreetmap.org/#map) and Amap (https://ditu.amap.com/). We searched for green parks listed in the Statistic Book for Green Parks in Shenzhen using OSM and Amap and identified their boundaries by altitude and longitude.

Land-use Datasets and UGS in China
Land-use data for Shenzhen in 2017 were provided by The Global Ecosystems and Environment Observation Analysis Research Cooperation [44]. The land-use dataset was generated via remote sensing with high-resolution digital elevation models and night light data. The resolution was 30 m, with 10 land-use types. Eight types of land use in Shenzhen were identified: cropland, forest, grassland, shrubland, wetland, water, impervious surface, and bareland. Urban public green space includes parks and reserves, sporting fields, riparian areas such as streams and river banks, greenways and trails, community gardens, street trees, and nature conservation areas, as well as less conventional spaces such as green walls, green alleyways, and cemeteries [45]. In this study, UGS is defined as parks, wetlands, grasslands, and forests in Shenzhen. After identifying green spaces in Shenzhen with the land-use data, the Statistic Book for Green Parks in Shenzhen (May 2018 version; http://cgj.sz.gov.cn/zwgk/tjsj/zxtjxx/201805/t20180525_11941634.htm) was examined to extract the names, areas, and addresses of green parks [46]. Finally, the spatial boundaries or locations of listed green parks were drawn from OpenStreetMap (OSM) (https://www.openstreetmap.org/#map) and Amap (https://ditu.amap.com/). We searched for green parks listed in the Statistic Book for Green Parks in Shenzhen using OSM and Amap and identified their boundaries by altitude and longitude. The boundaries for each green park were converted to points using ArcGIS, after which they were converted to polygons. Only some of the green parks maintained boundary information in OSM and Amap, while other green parks were presented as points to reflect their locations. UGS in Shenzhen, comprising wetlands, grasslands, and forests, is presented in Figure 2. The boundaries for each green park were converted to points using ArcGIS, after which they were converted to polygons. Only some of the green parks maintained boundary information in OSM and Amap, while other green parks were presented as points to reflect their locations. UGS in Shenzhen, comprising wetlands, grasslands, and forests, is presented in Figure 2.

Land Surface Temperature (LST) Retrieval
The Landsat 8 Thermal Infrared Sensor (TIRS) data were downloaded from the USGS Global Visualization Viewer (http://glovis.usgs.gov/), with a resolution of 30 m (on October 1 and 23, 2017) and a cloud cover of less than 1%. There are four commonly used methods for retrieving LST from thermal bands: (1) the multi-channel or split-window algorithm, (2) the multi-angle method, (3) the single-channel method, and (4) the radiative transfer equation [47]. In this study, the radiative transfer equation was used for Landsat 8 TIRS-10/11 to retrieve LSTs for Shenzhen. The main processes were defined with reference to Garcia-Santos [48]. The retrieved mean LSTs of Shenzhen on October 1 and 23, 2017 are displayed in Figure 3. Moreover, abnormal LST (higher than 45 degrees) occurred at the location of a waste incineration plant. This value was deleted and set as "no data".

Point of Interest Retrieval
Points of interest (POIs) were retrieved from Amap, which is one of the largest desktop and mobile map service providers in China. Using Amap's application programming interface, 9490 POI records were gathered on December 23, 2018. Data on train stations, subway stations, bus stations, scenery, schools, hospitals, and swimming pools were retrieved for economic value evaluation. Table

Land Surface Temperature (LST) Retrieval
The Landsat 8 Thermal Infrared Sensor (TIRS) data were downloaded from the USGS Global Visualization Viewer (http://glovis.usgs.gov/), with a resolution of 30 m (on 1 and 23 October 2017) and a cloud cover of less than 1%. There are four commonly used methods for retrieving LST from thermal bands: (1) the multi-channel or split-window algorithm, (2) the multi-angle method, (3) the single-channel method, and (4) the radiative transfer equation [47]. In this study, the radiative transfer equation was used for Landsat 8 TIRS-10/11 to retrieve LSTs for Shenzhen. The main processes were defined with reference to Garcia-Santos [48]. The retrieved mean LSTs of Shenzhen on 1 and 23 October 2017 are displayed in Figure 3. Moreover, abnormal LST (higher than 45 degrees) occurred at the location of a waste incineration plant. This value was deleted and set as "no data". The boundaries for each green park were converted to points using ArcGIS, after which they were converted to polygons. Only some of the green parks maintained boundary information in OSM and Amap, while other green parks were presented as points to reflect their locations. UGS in Shenzhen, comprising wetlands, grasslands, and forests, is presented in Figure 2.

Land Surface Temperature (LST) Retrieval
The Landsat 8 Thermal Infrared Sensor (TIRS) data were downloaded from the USGS Global Visualization Viewer (http://glovis.usgs.gov/), with a resolution of 30 m (on October 1 and 23, 2017) and a cloud cover of less than 1%. There are four commonly used methods for retrieving LST from thermal bands: (1) the multi-channel or split-window algorithm, (2) the multi-angle method, (3) the single-channel method, and (4) the radiative transfer equation [47]. In this study, the radiative transfer equation was used for Landsat 8 TIRS-10/11 to retrieve LSTs for Shenzhen. The main processes were defined with reference to Garcia-Santos [48]. The retrieved mean LSTs of Shenzhen on October 1 and 23, 2017 are displayed in Figure 3. Moreover, abnormal LST (higher than 45 degrees) occurred at the location of a waste incineration plant. This value was deleted and set as "no data".

Point of Interest Retrieval
Points of interest (POIs) were retrieved from Amap, which is one of the largest desktop and mobile map service providers in China. Using Amap's application programming interface, 9490 POI records were gathered on December 23, 2018. Data on train stations, subway stations, bus stations, scenery, schools, hospitals, and swimming pools were retrieved for economic value evaluation. Table

Point of Interest Retrieval
Points of interest (POIs) were retrieved from Amap, which is one of the largest desktop and mobile map service providers in China. Using Amap's application programming interface, 9490 POI Sustainability 2020, 12, 1844 5 of 18 records were gathered on 23 December 2018. Data on train stations, subway stations, bus stations, scenery, schools, hospitals, and swimming pools were retrieved for economic value evaluation. Table 1 presents the categories and the number of POI records per category, and Figure 4 illustrates the spatial distribution of POI density. 1 presents the categories and the number of POI records per category, and Figure 4 illustrates the spatial distribution of POI density.

Housing Rental Price Retrieval
In this study, the rental prices for residential houses were extracted from several real estate portals in China, including sz.fang.com, sz.zu.anjuke.com, www.sofang.com, sz.lianjia.com/zufang/, sz.ganji.com/wblist/zufang/, and sz.58.com/chuzu/, all of which had a large number of page views and visitors. We trawled 12,792 housing rental samples on December 18, 2018 and extracted the ID, location, rent price, area, number of bedrooms and halls, and whether the whole house or only a bedroom was being rented for each sample. To prepare the data for use, first, repeated samples from different portals were filtered to one record. Then, samples that were located outside of Shenzhen or that had nine or more bedrooms and halls were deleted. Third, samples with abnormal rent prices or with rent prices larger than or smaller than the mean ± 3std. of the total rent prices were deleted. Finally, samples with the same community name and type were combined into one sample by determining the average rent price per unit area (yuan/sq. m) and average area. After this process, 5192 samples remained. The remaining samples were converted to points according to their location information (see Figure 5).

Housing Rental Price Retrieval
In this study, the rental prices for residential houses were extracted from several real estate portals in China, including sz.fang.com, sz.zu.anjuke.com, www.sofang.com, sz.lianjia.com/zufang/, sz.ganji.com/wblist/zufang/, and sz.58.com/chuzu/, all of which had a large number of page views and visitors. We trawled 12,792 housing rental samples on 18 December 2018 and extracted the ID, location, rent price, area, number of bedrooms and halls, and whether the whole house or only a bedroom was being rented for each sample. To prepare the data for use, first, repeated samples from different portals were filtered to one record. Then, samples that were located outside of Shenzhen or that had nine or more bedrooms and halls were deleted. Third, samples with abnormal rent prices or with rent prices larger than or smaller than the mean ± 3std. of the total rent prices were deleted. Finally, samples with the same community name and type were combined into one sample by determining the average rent price per unit area (yuan/sq. m) and average area. After this process, 5192 samples remained. The remaining samples were converted to points according to their location information (see Figure 5).

Methods
The framework of this study is presented in Figure 6. The economic value evaluation, ecological value evaluation, social value evaluation, and optimization model are presented in this section. Multi-objective optimization was carried out using a genetic algorithm.

Evaluating Model
The hedonic prices model can be written as Equation (1) below: where P is housing rental prices or house prices, and 1 , 2 , …, are the factors that impact P. In Equation (1), f is the relationship between and P, where the linear model, semi-log model, and double-log model were in existing studies. The linear model was used [35,[49][50][51] in this study to evaluate the economic value of green spaces in Shenzhen.

Methods
The framework of this study is presented in Figure 6. The economic value evaluation, ecological value evaluation, social value evaluation, and optimization model are presented in this section. Multi-objective optimization was carried out using a genetic algorithm.

Methods
The framework of this study is presented in Figure 6. The economic value evaluation, ecological value evaluation, social value evaluation, and optimization model are presented in this section. Multi-objective optimization was carried out using a genetic algorithm.

Evaluating Model
The hedonic prices model can be written as Equation (1) below: where P is housing rental prices or house prices, and 1 , 2 , …, are the factors that impact P. In Equation (1), f is the relationship between and P, where the linear model, semi-log model, and double-log model were in existing studies. The linear model was used [35,[49][50][51] in this study to evaluate the economic value of green spaces in Shenzhen.

Evaluating Model
The hedonic prices model can be written as Equation (1) below: where P is housing rental prices or house prices, and x 1 , x 2 , . . . , x n are the factors that impact P. In Equation (1), f is the relationship between x and P, where the linear model, semi-log model, and double-log model were in existing studies. The linear model was used [35,[49][50][51] in this study to evaluate the economic value of green spaces in Shenzhen.

Dependent and Independent Variables
The average rent prices of the 5191 house samples were set as the dependent variables. Then, the characteristics of the house, including its type and area, were set as two independent variables (x 1 and x 2 , respectively). Specifically, the independent variables, the type of samples, were assigned positive integer values according to the number of bedrooms and halls of the sample (see Table 2). Following the work of previous studies [35,52], each sample's distance from a train station, distance from a subway station, density of schools, distance from a hospital, density of swimming pools, distance from scenery, distance from a river, distance from an urban park, rate of green space, and distance to a bus station were also selected as potential independent variables. All independent variables are listed in Table 3. Distance from river Euclidean distance from the sample point to the closest river. x 10 Distance from urban park Euclidean distance from the sample point to the closest urban park. x 11 Density of green space Density of green space at the location of the sample. x 12 Distance from bus station Euclidean distance from the sample point to the closest bus station.
The buffering tool in ArcGIS was used to extract the distance-independent variables, including x 3 , x 4 , x 6 , x 8 , x 9 , x 10 , and x 12 (see Figure 7). On the other hand, density-independent variables, including x 5 , x 7 , and x 11 , were calculated with MATLAB. Specifically, the density of schools and density of swimming pools were indicated according to the number of schools or swimming pools in a circle scale, which were calculated with a radius of 200 m, 500 m, and 1000 m. The correlation analysis suggested that a radius of 1000 m was reasonable for reflecting the impact of schools and swimming pools on housing rental prices. The spatial distributions of x 3 to x 10 and x 12 are presented in Figure 7. To determine the influence of distance of green space on rent prices, the density of green space (DGS) was calculated for square areas with a side length of 90 m, 150 m, . . . , and 1230 m. DGS was calculated according to Equation (2) below: where Area GS−dx is the area of green space in a square area and Area square −dx is the area of the square area. Consequently, 20 regression models were built with different densities of green space, calculated using Equation (2)

Ecological Value Evaluation
The ability of green space to relieve LST or UHIs has been widely proven in existing studies [2,16,17,47]. In this study, we attempted to identify the impact of green space on LST and its impact distance for use in the UGS optimization system. First, correlation analysis between DGSs that were calculated at different scales and LST was carried out to determine the impact distance of green space on LST. The linear regression model was then built-up to quantize the relationship between DGS and LST.

Correlation Analysis
Correlation analysis between DGSs with different lengths and LST was carried out to identify the highest correlation and the impact distance as the length of DGS. Since LST is lower on mountains, the correlation analysis was carried out only for areas with elevations of lower than 300 m [53].

Evaluating Model
After the correlation analysis, we selected the DGSs with the highest R coefficient, with LST as the independent variable, to determine the relationship between green space and LST, as in Equation (3): ( In this study, the linear regression model was used as f in Equation (3).

Social Value Evaluation
The social value of green space is determined by the amount of green space, the accessibility of such space, and the demand for green space. Therefore, the density of green space was used to indicate the amount of green space, the density of road networks was used to indicate accessibility, and the spatial distribution of the population was used to indicate the demand for green space. The social value of green space was calculated by Equation (4): where Density road is the density of road networks, and Pop is the population. Specifically, in calculating Density road , high-speed roads, urban high-speed roads, railways, national roads, provincial roads, and other urban road networks were considered. The unit of Density road is km per sq. km, and the density of road networks was calculated within 5 km (see Figure 9a). The spatial distribution of the population in Shenzhen in 2015 was gathered from the Global Human Settlement Layer (GHSL) data center with a resolution of 250 m by 250 m (see Figure 9b). The DGS was calculated with the length of one side at 510 m with reference to existing studies of green space accessibility calculations [13].

Ecological Value Evaluation
The ability of green space to relieve LST or UHIs has been widely proven in existing studies [2,16,17,47]. In this study, we attempted to identify the impact of green space on LST and its impact distance for use in the UGS optimization system. First, correlation analysis between DGSs that were calculated at different scales and LST was carried out to determine the impact distance of green space on LST. The linear regression model was then built-up to quantize the relationship between DGS and LST.

Correlation Analysis
Correlation analysis between DGSs with different lengths and LST was carried out to identify the highest correlation and the impact distance as the length of DGS. Since LST is lower on mountains, the correlation analysis was carried out only for areas with elevations of lower than 300 m [53].

Evaluating Model
After the correlation analysis, we selected the DGSs with the highest R coefficient, with LST as the independent variable, to determine the relationship between green space and LST, as in Equation (3): (3) In this study, the linear regression model was used as f in Equation (3).

Social Value Evaluation
The social value of green space is determined by the amount of green space, the accessibility of such space, and the demand for green space. Therefore, the density of green space was used to indicate the amount of green space, the density of road networks was used to indicate accessibility, and the spatial distribution of the population was used to indicate the demand for green space. The social value of green space was calculated by Equation (4): where Density is the density of road networks, and is the population. Specifically, in calculating Density , high-speed roads, urban high-speed roads, railways, national roads, provincial roads, and other urban road networks were considered. The unit of Density is km per sq. km, and the density of road networks was calculated within 5 km (see Figure 9a). The spatial distribution of the population in Shenzhen in 2015 was gathered from the Global Human Settlement Layer (GHSL) data center with a resolution of 250 m by 250 m (see Figure 9b). The DGS was calculated with the length of one side at 510 m with reference to existing studies of green space accessibility calculations [13].

Multi-objective Optimization
Three objectives were set to guide green space optimization. First, the distribution of green space should maximize the economic value by increasing local rent prices. Second, the distribution of green space should regulate the local climate in Shenzhen by relieving high LST. Third, green space should be located in places with high accessibility and high population density to maximize its social value. Meanwhile, the increasing amount of green space was set as the constraint. The objectives and constraints are shown below. is the density of UGS after optimization, and a1 and a2 are the coefficients determined by Equation (1) and Equation (2). HD is the density of housing rental price sample points; LST is the land surface temperature of Shenzhen; and AccMap is the spatial distribution of accessibility. ConP is the ratio, and is the area of UGS in Shenzhen. Multi-objective optimization was carried out using GA. Built-up land in Shenzhen was coded as genes in the GA, which can be assigned a value of 0 or 1. An assignment of 0 indicates that the gene will not change into UGS, while 1 indicates that it will. All the coded genes constituted one chromosome, which can be thought of as one solution. One generation was represented by 100 chromosomes, presenting 100 alternative solutions, all of which satisfied the constraints. The values of the objectives were calculated. Then, selection, crossover, and mutation in the GA were carried out. In the selection process, the maximin fitness function [54] was used to calculate the fitness of one alternative solution. Two solutions that were randomly selected from the top ten solutions were set as parents in the GA. Then, crossover was carried out between genes in the GA to generate 100 new solutions. Moreover, a 0.05 probability of mutation was carried out to avoid local optimization. This means that there was a 0.05 probability that the newly generated genes would randomly covert to 0 or 1. The new 100 solutions were generated through a process of selection, crossover, and mutation until the iteration reached the threshold, which was set at 200. Moreover, new UGS should not exceed 2% of existing UGS in Shenzhen, meaning that ConP should be 0.02.

Multi-Objective Optimization
Three objectives were set to guide green space optimization. First, the distribution of green space should maximize the economic value by increasing local rent prices. Second, the distribution of green space should regulate the local climate in Shenzhen by relieving high LST. Third, green space should be located in places with high accessibility and high population density to maximize its social value. Meanwhile, the increasing amount of green space was set as the constraint. The objectives and constraints are shown below. Constraint: Total increased green space must be less than ConP * Area UGS , where NDGS dx is the density of UGS after optimization, and a1 and a2 are the coefficients determined by Equation (1) and Equation (2). HD is the density of housing rental price sample points; LST is the land surface temperature of Shenzhen; and AccMap is the spatial distribution of accessibility. ConP is the ratio, and Area UGS is the area of UGS in Shenzhen.
Multi-objective optimization was carried out using GA. Built-up land in Shenzhen was coded as genes in the GA, which can be assigned a value of 0 or 1. An assignment of 0 indicates that the gene will not change into UGS, while 1 indicates that it will. All the coded genes constituted one chromosome, which can be thought of as one solution. One generation was represented by 100 chromosomes, presenting 100 alternative solutions, all of which satisfied the constraints. The values of the objectives were calculated. Then, selection, crossover, and mutation in the GA were carried out. In the selection process, the maximin fitness function [54] was used to calculate the fitness of one alternative solution. Two solutions that were randomly selected from the top ten solutions were set as parents in the GA. Then, crossover was carried out between genes in the GA to generate 100 new solutions. Moreover, a 0.05 probability of mutation was carried out to avoid local optimization. This means that there was a 0.05 probability that the newly generated genes would randomly covert to 0 or 1. The new 100 solutions were generated through a process of selection, crossover, and mutation until the iteration reached the threshold, which was set at 200. Moreover, new UGS should not exceed 2% of existing UGS in Shenzhen, meaning that ConP should be 0.02.

The Economic Value of Green Space
The results of regressions with different DGSs are presented in Table 4. The distance from a bus station (x 12 ) was removed from some regression models, since its significance did not satisfy the requirements. As the results show, change in DGSs leads to variation in R-squared for models. Figure 10 illustrates the variation in R-squared along with different DGSs. It was found that when the DGS covered the square scale with one side length longer than 690 m, the impact of DGS on rent prices became stable at a high range (with an adjusted R-squared around 0.243). Therefore, in the process of optimizing green space, when economic objectives are considered, the optimization model should consider the impact of green spaces in a square scale with a side length of 690 m. After identifying the influence scale, a univariate linear regression was built up to identify the impact of UGS on housing rental prices, as shown in Equation (8): where y is the dependent variable, housing rental prices, and UGS 690 is the rate of UGS in a square scale with a side length of 690 m. The R-squared is 0.0164, and p is 0. This suggests that the UGS can explain a 1.64% variation in housing rental prices, and the regression is significant.

The Ecological Value of Green Space
The correlation between DGSs and LST is illustrated in Figure 11. The results indicate that there was a negative relationship between green space and LST. This negative relationship became clearer (with an R of −0.74714) when the DGS considered the green space in a square area with a side length of 270 m. After identifying the influence scale, a univariate linear regression was built up to identify the impact of UGS on housing rental prices, as shown in Equation (8): where y is the dependent variable, housing rental prices, and UGS 690 is the rate of UGS in a square scale with a side length of 690 m. The R-squared is 0.0164, and p is 0. This suggests that the UGS can explain a 1.64% variation in housing rental prices, and the regression is significant.

The Ecological Value of Green Space
The correlation between DGSs and LST is illustrated in Figure 11. The results indicate that there was a negative relationship between green space and LST. This negative relationship became clearer (with an R of −0.74714) when the DGS considered the green space in a square area with a side length of 270 m.
* + . , (8) where y is the dependent variable, housing rental prices, and UGS 690 is the rate of UGS in a square scale with a side length of 690 m. The R-squared is 0.0164, and p is 0. This suggests that the UGS can explain a 1.64% variation in housing rental prices, and the regression is significant.

The Ecological Value of Green Space
The correlation between DGSs and LST is illustrated in Figure 11. The results indicate that there was a negative relationship between green space and LST. This negative relationship became clearer (with an R of −0.74714) when the DGS considered the green space in a square area with a side length of 270 m. According to the results presented in Figure 11, the selected DGS was used to build a univariate linear regression was built up to identify the impact of UGS on LST, as Equation (9) shows: Figure 11. Correlations between LST and rate of DGS.
According to the results presented in Figure 11, the selected DGS was used to build a univariate linear regression was built up to identify the impact of UGS on LST, as Equation (9) shows: y = −3.3806 * UGS 270 + 25.8474, (9) where y is the dependent variable, LST, and UGS 270 is the rate of UGS in a square scale with a side length of 270 m. The R-squared is 0.2321, and p is 0. This suggests that the UGS can explain a 23.21% variation in LST, and the regression is significant.

The Social Value of Green Space
The spatial distribution of accessibility was calculated on the basis of density of the road network and spatial distribution of the population (see Figure 9). The social value can be calculated as shown in Equation (10): where y is social value; Acc is spatial distribution of accessibility; and DGS 510 is the spatial distribution of green space rate with a side of length 510 m.

Green Space Optimization for Shenzhen
Optimization was based on the evaluations of economic, ecological, and social values of UGS. The variations of objective value with mean, median line, outliers, and 1.5* interquartile range (range within 1.5IQR) are presented in Figure 12 from the first generation to the last generation in the GA. The optimization showed that from the first generation to the last generation, economic value and ecological value clearly increased from the 1st to the 20th iteration. Thereafter, the objective value became stable, as shown in Figure 12a,b. The social value increased from the first generation to the 10th, and from then on the objective value became stable (see Figure 12c). The variations in objective value suggest that allocating green space in Shenzhen can improve economic, ecological, and social value. within 1.5IQR) are presented in Figure 12 from the first generation to the last generation in the GA. The optimization showed that from the first generation to the last generation, economic value and ecological value clearly increased from the 1st to the 20th iteration. Thereafter, the objective value became stable, as shown in Figures 12 (a) and 12(b). The social value increased from the first generation to the 10th, and from then on the objective value became stable (see Figure 12c). The variations in objective value suggest that allocating green space in Shenzhen can improve economic, ecological, and social value. In addition to the variations in objective value, the Pareto solutions in the first and last generations are presented in Figure 13. We found that the solutions moved further away from the origin, indicating increases in objective value. The Pareto solutions dominated the other solutions. In addition to the variations in objective value, the Pareto solutions in the first and last generations are presented in Figure 13. We found that the solutions moved further away from the origin, indicating increases in objective value. The Pareto solutions dominated the other solutions. Finally, the probability of optimized new UGS is presented in Figure 14. In the first generation, new increased UGSs were randomly spread around Shenzhen, with a relatively low probability (see Figure 14a). After optimization, the new increased UGSs were explicitly located with relatively high probability (see Figure 14b). As Figure 14b shows, the optimal UGS was often located in highly developed urban areas. Finally, the probability of optimized new UGS is presented in Figure 14. In the first generation, new increased UGSs were randomly spread around Shenzhen, with a relatively low probability (see Figure 14a). After optimization, the new increased UGSs were explicitly located with relatively high probability (see Figure 14b). As Figure 14b shows, the optimal UGS was often located in highly developed urban areas.
(c) Finally, the probability of optimized new UGS is presented in Figure 14. In the first generation, new increased UGSs were randomly spread around Shenzhen, with a relatively low probability (see Figure 14a). After optimization, the new increased UGSs were explicitly located with relatively high probability (see Figure 14b). As Figure 14b shows, the optimal UGS was often located in highly developed urban areas.

Discussion
In this paper, we estimated the economic, social, and ecological value of UGS in Shenzhen. Furthermore, we suggested a spatial planning method for UGS that satisfies the multiple requirements of simultaneously maximizing economic, social, and ecological value. The results indicate that MOP is a viable method for solving spatial problems in the establishment of UGS. Using MOP, Pareto solutions were detected, and the objectives were optimized. To identify the means of objective evaluation in MOP, the relationship between spatial distribution of UGS and its economic,

Discussion
In this paper, we estimated the economic, social, and ecological value of UGS in Shenzhen. Furthermore, we suggested a spatial planning method for UGS that satisfies the multiple requirements of simultaneously maximizing economic, social, and ecological value. The results indicate that MOP is a viable method for solving spatial problems in the establishment of UGS. Using MOP, Pareto solutions were detected, and the objectives were optimized. To identify the means of objective evaluation in MOP, the relationship between spatial distribution of UGS and its economic, social, and ecological value was analyzed. Specifically, the economic value of UGS was estimated using 5192 rent-price samples extracted from several major real estate portals in China. This method was cheaper and made it easier to maintain spatial information compared with traditional methods such as questionnaire surveys or field surveys. The ecological value of UGS was indicated by its relief of LST in urban areas. The social value of UGS was calculated on the basis of density of road network and spatial distribution of the population. The results suggest that UGS does affect housing rental prices in Shenzhen at a scale of 345 m. The relief of LST was a combined effect of UGS within 135 m. As for social value, a 255 m distance to enable travel by foot was selected to evaluate the accessibility of UGS in Shenzhen. Various affect distances of UGS for different values were identified. The affect distance of UGS should be clarified, and optimization carried out by considering affect distance.
After estimating the relationship between UGS and economic, ecological, and social value, MOP was carried out. The identified affect distances were put into the GA method to carry out the MOP for UGS in Shenzhen. The results indicate that MOP is a viable method for solving spatial problems in the establishment of UGS. From the first to the last generation, the economic value, ecological value, and social value of Shenzhen increased. However, there was no solution that simultaneously maintained the largest economic, ecological, and social value, which suggests that these three UGS values for Shenzhen may be conflicting. This is probably because maximizing economic value trends locate UGS in places with residential buildings, while maximizing ecological value and social value trends locate UGS in places with high urban heat island and population, respectively.
To date, MOP has been widely used in the field of land-use optimization where all land-use types are included. In this paper, merely one land-use type, UGS, was considered. This makes the optimization more explicit; the functions of green space can be fully estimated and the tradeoffs among different values can be considered. Because of the high economic, social, and ecological value of green space in urban areas, UGS planning or optimization has become popular in urban planning. This study proposed an optimization method that facilitates the Government's management of UGS. The method proposed here also benefits residents by improving the value of UGS.
Several limitations exist in this study, which should be considered in future work. In urban systems, green spaces have various functions, including cooling, runoff reduction, and serving as ecological corridors; this study only considered three typical and popular functions of UGS. Future studies should consider more functions to reflect the full value of such spaces. Furthermore, in this study, we assumed that other land-use types were constant and that new green spaces would only be located in built-up areas. This is reasonable and reduces optimization costs; however, in future studies, optimization should be carried out by assuming that green space can be located on or close to built-up land. Working with this assumption, the system will generate more possible solutions for decision-makers.