© X. Liu, Published by EDP Sciences, 2025

1 Introduction

As urbanization progresses at an increasing pace, the urban population density continues to rise, land resources are becoming increasingly scarce, and ecological and environmental problems are becoming more prominent [1,2]. During the actual urban construction process, the absence of scientific and systematic planning methods in the early stages has lead to an uneven distribution of park green spaces and incomplete service coverage, which not only affects the rationality of the urban spatial structure and the fairness of public services but also restricts the overall effectiveness of urban green infrastructure [3]. Traditional urban park green space planning mainly relies on experience, qualitative analysis, and static indicators. Although these standards can guide the distribution of park and green space to a certain extent, in the face of complex urban structure, diverse resident needs, and dynamic population and traffic routes, it often leads to an imbalanced configuration of planning and low space utilization rates [4]. Optimization models, as a technical means based on mathematical modeling and algorithmic solutions, are widely used in scheme configuration optimization. These models are guided by an objective function and constraints to further adjust the planning scheme of park green spaces and takes into account multiple variables associated with the planning of park green spaces to achieve the optimal objective. The principle of planning the layout of urban park green spaces in this paper is to transform the planning problem into an optimization problem that enables the function within the mathematical model to achieve the desired goal. The genetic algorithm (GA) was used to solve the mathematical model. The possible solutions of the green space planning scheme were regarded as chromosomes, and the function of the mathematical model was regarded as the fitness value of the chromosomes. Then, the population composed of multiple chromosomes imitated the genetic changes in nature. Through genetic operations such as selection, crossover, and mutation, the chromosomes within the population were updated, causing the fitness value of the population to change in the direction of the desired goal, and finally the optimal solution was obtained. This paper briefly introduces the park green space evaluation model based on supply and demand accessibility, the K-means algorithm for determining the number of new green spaces, and the improved GA for planning new green spaces. Moreover, a case analysis is presented. First, the K-means clustering algorithm was used to plan the number of new green spaces. Then, the improved GA was employed to optimize the green space planning scheme under the guidance of the supply-demand accessibility model. The contribution of this paper lies in using the GA to optimize the urban green space planning scheme and adopting adaptive genetic probabilities to improve the optimization performance of the algorithm, providing an effective reference for urban green space planning.

2 Literature review

Relevant studies are reviewed below. By using an improved urban park green space (UPGS) accessibility measurement approach with the smallest cluster unit (building) as the service demand point and UPGS entrance and exit as the service provision point, Li et al. [5] established a micro-scale evaluation framework for spatial equity considering the service radius and service quality of UPGS. Meng et al. [6] focused their research on Ningbo City and established a framework for the connection between accessibility research and urban planning practice. The research results indicated insufficient accessibility in areas where older adults gather and the periphery of the research area. Cheng et al. [7] explored the correlation between urban green spaces and psychological health for rural migrant workers in Wuhan. Moreover, they examined the quality and quantity of urban green spaces and the mediating role of perceived discrimination.

3 Methods and materials

3.1 Experimental data

This paper took the Yanta District nearby as the research subject. The Yanta District is located in the south-central part of Xi'an, Shaanxi Province, China, and is one of the core urban areas of Xi'an. As one of the main urban districts of Xi'an, Yanta District has a long history and rich cultural heritage. It has numerous cultural relics, historic sites, and modern urban facilities.

The data related to park green spaces and residential areas were derived from Gaode Map satellite images, on-site investigations, Xi'an Planning Bureau, and Anjuke website [8]. After investigation, the statistics of the existing urban park green spaces in Yanta District are displayed in Table 1. The number of residential communities was 899, and the relevant data of some communities are shown in Table 2.

3.2 Experimental methods

3.2.1 The evaluation model of urban park green space based on accessibility

Urban park green spaces provide green ecological services for urban residents. Therefore, the rationality of park green space planning can be evaluated from the perspective of whether urban residents can reach park green spaces quickly, i.e., accessibility. The travel time between residential areas and the nearest park is a relatively simple and feasible evaluation indicator, and it is also relatively simple in statistics. However, this indicator simply and crudely treats the needs of all residential areas equally, without considering the impact of the travel time required on residents' demand for green spaces. Therefore, this paper chooses to measure the accessibility of park green spaces from the perspective of the supply and demand of green spaces, i.e., the area that each park green space can provide for residential areas and the green space area required by each residential area.

The two-step mobile search technique is used to evaluate the accessibility of park green space in terms of supply and demand, and the calculation formula is:

$$\{\begin{array}{l}{R}_j=\frac{S_j}{{\displaystyle \sum _{i\in \{d_{ij}\le d_o\}}^k}{D}_i\cdot G(d_{ij},d_o)}\\ G(d_{ij},d_o)=\frac{\exp (\frac{-d_{ij}}{2d_o})-\exp (-\frac{1}{2})}{1-\exp (-\frac{1}{2})}\\ A_i={\displaystyle \sum _{j\in \{d_{ij}\le d_o\}}^k}{R}_j\cdot G(d_{ij},d_o)\\ E_i=\frac{A_i}{A_o}\end{array}\text{,}$$(1)

where R_j is the green space supply and demand ratio of park j, expressed by per capita green space area, S_j is the area of green space that the park can provide, D_i indicates the number of people in residential area i [9], i ∈ { d_ij ≤ d_o } indicates that residential area i is within service radius d_o of park j, G(d_ij, d_o) is a Gaussian function based on distance decay within the range of d_o [10], j ∈ { d_ij ≤ d_o } indicates that park j is within accessible radius d_o of the residential area i, A_i is the per capita green space area available to residential area i, E_i is the accessibility of green space supply and demand in residential area i, and A_o is the standard value of green space supply and demand, i.e., the minimum per capita green space area that a residential area can obtain during the local construction process.

3.2.2 Urban park green space planning based on an optimization algorithm

The overall process of planning new park spaces is as follows: first determine the quantity of new park spaces and then optimize the coordinates of new park spaces to make the supply and demand accessibility of the park space in the selected residential area optimal [11]. The basic flow is shown in Figure 1.

The specific steps are as follows.

• Relevant data on park green spaces and residential areas within the study area are collected. Then, the availability of green space supply and demand in each residential area is calculated through equation (1). Residential areas where the availability of green space supply and demand is less than the set threshold are selected.

• The K-means clustering algorithm [12] is employed to cluster the selected residential areas. The average distance between residential areas and park green spaces in the clustering results is compared under different K values, i.e., the number of new park green spaces added. The appropriate number of new green spaces added is determined based on the average distance.

• After obtaining the appropriate number using the K-means clustering algorithm, a GA is employed to plan the location of the new green spaces. First, the genetic population is initialized to generate initial chromosomes [13], with each chromosome representing a planning scheme. The chromosomes are encoded in a two-dimensional form, with each column representing a gene locus, i.e., the coordinates of a new green space; each row represents the value of each new green space on one coordinate axis.

• The fitness value is calculated:

  $$f={\displaystyle \sum _{l=1}^n}{D}_l\times \min (d_{l1},d_{l2},\cdots ,d_{lK})\text{,}$$(2)

  where D_l is the number of residents in the l-th residential area where the supply and demand accessibility of green spaces is smaller than the set threshold, n indicates the number of residential areas where the supply and demand accessibility of green spaces is smaller than the set threshold, d_lK is the distance between the l-th residential area where the supply and demand accessibility is less than the set threshold and newly added green space K, and f is the fitness value.

• Whether the optimization continues is determined. If the number of optimization iterations reaches the preset number or the fitness convergence change is less than 10⁻⁸, the optimization stops, and the optimal chromosome within the population is output and decoded to obtain the planning scheme. Otherwise, proceed to the next step.

• Genetic manipulations are performed on the population [14]. Selection manipulation involves directly replicating the best few chromosomes within a population into offspring chromosomes. Single-point crossover and single-point variation operations are employed, and adaptive crossover and variation probabilities are used. The probability formulas are:

  $$\{\begin{array}{l}{P}_c=\{\begin{array}{cc}\hfill \frac{k_1(f_{\max }-f)}{f_{\max }-f_{\sigma }}\hfill & \hfill f\ge f_{\sigma }\hfill \\ \hfill k_2\hfill & \hfill f<f_{\sigma }\hfill \end{array}\\ P_m=\{\begin{array}{cc}\hfill \frac{k_3(f_{\max }-f)}{f_{\max }-f_{\sigma }}\hfill & \hfill f\ge f_{\sigma }\hfill \\ \hfill k_4\hfill & \hfill f<f_{\sigma }\hfill \end{array}\end{array}\text{,}$$(3)

  where P_c and P_m are the crossover probability and the mutation probability respectively, k₁, k₂, k₃, k₄ are constants between 0 and 1, f_max is the maximum fitness value within the current population, f is the fitness value of chromosomes for crossover and mutation, and f_σ is the current average fitness value [15].

• After performing genetic manipulations on the population, go back to step (4).

Fig. 1 The planning flow of urban park green spaces.

3.2.3 Parameter setting

First, a park green space evaluation model based on supply and demand accessibility was employed to calculate the supply and demand accessibility of green spaces in different communities. The supply and demand accessibility [16] was divided into five levels: Level 1, E_i ∈ [0, 0.5), the supply and demand are lacking in community i ; Level 2, E_i ∈ [0.5, 0.75), the supply and demand of green space in community i is relatively insufficient; Level 3, E_i ∈ [0.75, 1.25), the supply and demand is balanced; Level 4, E_i ∈ [1.25, 2), the supply and demand are sufficient; Level 5, E_i ∈ [2, + ∞), the supply and demand are saturated. Among the five levels mentioned above, communities at Levels 1, 2, and 5 are unfair in terms of supply and demand. Levels 1 and 2 are unfair due to the lack of supply and demand, while Level 5 is unfair to other communities due to the saturation of supply and demand.

After calculating the accessibility of green space supply and demand in different communities, the communities with insufficient or lacking green space supply and demand (i.e., levels 1 and 2) were selected. The K-means clustering algorithm was used. The K value of the clustering algorithm was set to integers ranging from 1 to 20 respectively, and the average distance between the communities and the newly added green space under different K values was calculated. Then, the appropriate K value was determined, i.e., the number of newly added green spaces.

After determining the number of new green spaces, an improved GA was used to plan the locations of the new green spaces. The relevant parameters of the improved GA are as follows. The population size was 20 chromosomes. The selection operation within the population reserved two optimal chromosomes. The probability-related parameters k₁ and k₂ for crossover operations were 0.7 and 0.8, respectively. The probability-related parameters k₃ and k₄ for mutation operations were 0.1 and 0.2, respectively.

In addition, the particle swarm optimization (PSO) algorithm and traditional GA were used to plan the locations of new green spaces for comparison. The relevant parameters of the particle swarm algorithm are as follows. The particle swarm size was 20 particles. The inertia weight was set to 0.6. The learning factor was 0.1. The maximum number of iterations was 100. The relevant parameter settings of the traditional GA were nearly the same as those of the improved GA, but the only difference was that the crossover probability was fixed at 0.8 and the mutation probability was fixed at 0.2.

4 Results

The evaluation model based on supply and demand accessibility was used to calculate the supply and demand accessibility of green spaces in the residential area of Yanta District. The distribution of the supply and demand accessibility levels for green spaces in the residential areas is shown in Figure 2. It can be seen that the majority of residential areas were concentrated at Levels 3 and 4, i.e., the supply and demand were balanced and sufficient. Moreover, only a few residential areas reached saturation in their supply and demand accessibility for green spaces. The remaining 192 residential areas were at Level 2 (lack of supply and demand), and 91 residential areas were at Level 1 (insufficient supply and demand). That is to say, a total of 283 residential areas were at the level of insufficient supply and demand of green spaces, highlighting the need for additional green spaces.

From the Yanta District, residential areas at Levels 1 and 2 were selected, and the K-means clustering effect of these residential areas under different K values was tested. The results are shown in Figure 3. As the K value increased, the average distance between the residential area and the newly added green spaces gradually decreased and eventually converged to a stable state. This phenomenon occurs because an increase in the number of newly added green spaces provides residential areas with more options to access closer green spaces. Once a certain threshold was reached, the number of options for residential areas to access nearer green spaces became saturated, making it difficult to significantly shorten the distance, regardless of the chosen option. Therefore, the reduction in average distance became negligible and stabilized. Considering that an increase in the number of green spaces would result in a rise in the expense of new construction, the final number of new green spaces was set at nine.

After determining the number of new green spaces, the locations of these new green spaces were planned using the PSO algorithm, the traditional GA, and the improved GA, respectively. After planning, a park green space evaluation model based on supply and demand accessibility was used again to calculate the distribution of accessibility levels in the residential areas after the new green spaces were added. The results are shown in Figure 4. Compared with the distribution of accessibility levels before the addition of the green spaces, the distribution changed after planning by the three optimization algorithms. Overall, the number of residential areas at Levels 1 and 2 decreased, while the number of residential areas at Levels 3 and 4 increased. The change caused by the PSO algorithm was the smallest, while the change caused by the traditional GA was medium. The improved GA caused the largest change.

Fig. 2 Distribution of green space supply and demand accessibility levels in residential areas within Yanta District.

Fig. 3 Clustering effects under different numbers of new green spaces (K value).

Fig. 4 Distribution of green space supply and demand accessibility levels in residential areas before and after the addition of green space under the three optimization algorithms.

5 Discussion

With the accelerated progress of the global urbanization, the population density in cities is constantly rising, and the pressure on the ecological environment is gradually increasing. Urban green spaces play an ecological regulatory role in this context. Moreover, they also have multiple functions such as leisure and entertainment, cultural display, fitness and sports, and are crucial for the construction of urban livability. However, at present, the layout of park green spaces in most cities has problems such as uneven distribution, insufficient service coverage radius, imbalance between supply and demand, and low space utilization rate. In order to scientifically and reasonably plan the layout of park green spaces in the limited urban space, this paper conducted the layout planning of urban park green spaces based on an optimization model. During the planning process, the K-means clustering algorithm is first used to determine the number of green spaces to be added. Then, the improved genetic algorithm is employed to plan the locations of the newly added green spaces. The quality of the planning scheme is evaluated by a park green space evaluation model based on supply-demand accessibility. Subsequently, an empirical analysis is conducted with Yanta District in Xi'an as the subject.

The reason for choosing the K-means clustering algorithm to set the number of newly added green spaces is that, compared with other clustering algorithms, it can actively set the number of categories. The purpose of clustering residential areas in need of green spaces is not to classify the residential areas, but to analyze the appropriate number of newly added green spaces. By assuming the number of newly added green spaces to set the K value for clustering, the distance between residential areas and green spaces under different numbers of newly added green spaces can be analyzed.

The green space layout plan under the improved GA was the best. The reason is that when the PSO algorithm optimized and iterated the planning plan, it was easy to fall into the local optimal solution. During the optimization process, the traditional GA used the mutation operation to jump out of the local optimal solution. Therefore, the green space plan under its planning was better. The improved GA adjusted the crossover probability and mutation probability to make them adaptively adjustable. When the fitness value of the population was quite different from the optimal value, it changed faster. When the gap was small, the change was slower, avoiding excessive adjustment.

Based on the above analysis, the following suggestions are put forward: (1) Give priority to building park green spaces in service blind areas; (2) Optimize the functional configuration of newly built park green spaces to improve the utilization efficiency; (3) Establish a dynamic evaluation mechanism for green spaces and regularly update the optimization model. The limitation of this paper lies in that it only conducted a planning analysis of the urban green spaces in Yanta District, Xi'an, and only compared with some optimization algorithms, making the analysis results restrictive and not universal enough. Therefore, the future research direction is to expand the research scope and compare with more other optimization algorithms.

6 Conclusions

This paper briefly introduces a park green space evaluation model based on supply and demand accessibility, the K-means algorithm for determining the number of new green spaces, and an improved GA for planning new green spaces. Then, a case study was conducted on the Yanta District of Xi'an City. The analysis revealed that the majority of residential areas was concentrated in Levels 3 and 4, indicating a balanced and sufficient supply and demand. A very small number of residential areas experienced saturated supply and demand. The remaining 192 residential areas were at Level 2 (lack of supply and demand), and 91 residential areas were at Level 1 (insufficient supply and demand). As the K value increased, the average distance between residential areas and new green spaces gradually decreased, eventually converged, and remained stable after exceeding nine. Considering that an increase in the number of green spaces would increase new construction costs, the final number of new green spaces was set at nine. After the optimization algorithms' planning, the overall number of residential areas at Levels 1 and 2 decreased, and the number of residential areas at Levels 3 and 4 increased. The PSO algorithm caused the smallest change, while the improved GA caused the largest change.

Funding

No funding received.

Conflicts of interest

The author declares no conflict of interests.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contribution statement

Xiaojie Liu designed research, performed research, analyzed data, and wrote the paper.

References

All Tables

All Figures

	Fig. 1 The planning flow of urban park green spaces.
In the text

	Fig. 2 Distribution of green space supply and demand accessibility levels in residential areas within Yanta District.
In the text

	Fig. 3 Clustering effects under different numbers of new green spaces (K value).
In the text

	Fig. 4 Distribution of green space supply and demand accessibility levels in residential areas before and after the addition of green space under the three optimization algorithms.
In the text