TOD-Oriented Multi-Objective Optimization of Land Use Around Metro Stations in China: An Empirical Study of Xi’an Based on an Adaptively Improved NSGA-III Algorithm

Abstract

Against the backdrop of high-quality urbanization in cities, the rapid expansion of metro networks has led to severe spatial mismatches in land use around station areas, which seriously restricts the full exertion of the comprehensive benefits of the transit-oriented development (TOD) model. Taking 139 operational metro stations in Xi’an in 2024 as the research sample, this study constructs a multi-objective land use optimization model with the richness of public services, transportation accessibility and population distribution balance as the three core maximization objectives. A hierarchically adaptive improved NSGA-III algorithm is proposed, with the following four key technical optimizations implemented: multi-dimensional adaptive reference point adjustment, design of real-integer hybrid coding genetic operators, construction of an enhanced multi-criteria environmental selection mechanism, and dynamic regulation of algorithm iteration. Experimental results show that the performance of the improved algorithm is significantly superior to that of the traditional NSGA-III algorithm: the values of the three core objectives are increased by 59.58%, 12.94% and 7.35% respectively compared with the original data; the algorithm achieves stable convergence after 25 iterations, with the convergence efficiency improved by 30%. The obtained Pareto optimal front features good uniformity (U = 0.92) and coverage (C = 0.95), and all the 80 non-dominated solutions meet all constraint conditions, with the solution set highly coupled with the urban functional zoning and spatial planning of Xi’an. This study proposes a zoned, prioritized and phased hierarchical land use optimization strategy for the areas around metro stations in Xi’an. The research findings provide a replicable research framework and methodological reference for the TOD practice and land use optimization of metro station areas in other rapidly urbanizing central cities in China and developing countries worldwide with the characteristic of rapid rail transit expansion.

1. Introduction

1.1. Research Background

Global urbanization is moving towards high-quality development, and urban rail transit is increasingly recognized as a key measure for restructuring urban spatial patterns, alleviating traffic congestion, and supporting sustainable urban development [1,2,3,4]. In this context, transit-oriented development (TOD), which integrates rail transit with intensive and mixed land use development, has been widely applied in Asia, Europe, North America and other regions. It effectively improves land use efficiency and multimodal transportation accessibility and promotes the balanced layout of urban functional zoning [3,4]. However, in rapidly urbanizing regions in developing countries such as China and Southeast Asia, especially in western China, the expansion of metro networks often outpaces the coordinated and refined land use planning in station catchments, resulting in serious spatial mismatches and thus limiting the full play of TOD’s comprehensive benefits [5,6,7].

As a core central city in western China, Xi’an has witnessed the rapid expansion of its metro system in recent years, which has significantly enhanced regional transportation accessibility and promoted the integration of urban functional areas. Nevertheless, the typical problems existing in the metro station areas of Chinese cities are also prominent in Xi’an, such as the following: (1) high-quality public services such as education, medical care and daily life services are still over-concentrated in the core urban areas, leading to a sharp gradient in the service capacity of different metro station areas [1,6]; (2) the integration of multimodal transportation including metro, ground public transit, non-motorized transportation and shared mobility is insufficient, which weakens the overall accessibility of the transportation network and restricts the potential of the rail transit system [3,7]; and (3) the over-agglomeration of residential population and employment opportunities near core metro stations leads to the imbalance of population density in the whole urban metro network and undermines the core goal of TOD to realize the job-housing balance [6,8]. These problems not only reduce the land use efficiency and comprehensive service capacity of metro station areas but also restrict the in-depth implementation of the TOD model in Xi’an, as well as the integrated and high-quality development of rail transit and urban land resources in central cities of western China [1,8].

Among the 139 metro stations investigated in this study, the average density of science, education, culture and health facilities at stations in the central urban area (Yanta, Beilin, and Lianhu Districts) reaches 12.8 units/km², which is 4.3 times that of the peripheral functional zones (Chang’an, Lintong, and Konggang Districts). The average transportation accessibility of central urban stations is 0.49, 29.3% higher than that of peripheral stations; the population density around core stations exceeds 30,000 people/km², while that of peripheral stations is only 6000 people/km², showing a prominent feature of functional imbalance in station catchments. In terms of TOD maturity, the average mixed land use ratio of Xi’an metro stations is 0.35 with a public transport connection rate of 68%, which is far lower than that of eastern Chinese cities such as Shanghai (mixed land use ratio 0.58, public transport connection rate 89%) and Shenzhen (mixed land use ratio 0.52, public transport connection rate 85%). Compared with Chengdu (mixed land use ratio 0.41, public transport connection rate 75%), Xi’an still has obvious gaps in station catchment functional integration and transportation integration [9,10].

The optimization of land use around metro stations is essentially a complex spatial allocation problem with multiple objectives, which involves the trade-off and coordination among multiple goals such as public service provision, transportation accessibility, environmental quality and population spatial distribution [2,4,7]. Traditional single-objective optimization methods or qualitative planning approaches are difficult to generate land use optimization schemes that are both theoretically optimal and practically feasible [8]. In recent years, multi-objective evolutionary algorithms have been increasingly applied to the TOD-oriented land use optimization of metro station areas. Improved variants of NSGA-II and NSGA-III have been widely used to solve many-objective urban land use optimization problems, showing obvious advantages in convergence speed, solution diversity and handling complex planning constraints [5]. In the context of TOD, multi-objective optimization models for metro station catchments have been constructed to optimize land use mix, development density, metro ridership, environmental performance and economic benefits, most of which adopt genetic algorithm-based search strategies [11,12,13].

On the basis of the above research progress, this study focuses on the typical land use imbalance problems around metro stations in rapidly urbanizing central cities of western China, taking 139 operational metro stations in Xi’an as the research sample. By integrating the spatial development characteristics of Xi’an with the core requirements of TOD planning, a refined multi-objective land use optimization model is built with the richness of public services, transportation accessibility and population distribution balance as the three core objectives. To overcome the limitations of the standard NSGA-III algorithm in solving spatial planning problems, such as slow convergence and uneven distribution of the Pareto front, an adaptively improved NSGA-III algorithm is proposed, which is tailored to the spatial correlation characteristics of metro station areas in Xi’an [14,15]. The research aims to generate a uniformly distributed and practically feasible Pareto optimal solution set for the land use optimization of Xi’an’s metro station areas, provide robust decision support for the refined planning of metro station areas in central cities of western China, and offer a methodological reference for the practice of TOD and the land use optimization of metro station areas in other rapidly urbanizing regions around the world.

1.2. Literature Review

Under the background of the global promotion of the TOD model, the research on the land use optimization around metro stations has become a research hotspot in the fields of urban planning, traffic engineering and operations research. Scholars have achieved abundant research results in the aspects of optimization objectives, algorithm selection and research methods.

1.2.1. Multi-Objective Optimization in Urban Planning

In recent years, urban land use planning has undergone a profound transformation from emphasizing a single goal of economic growth or spatial expansion to pursuing an integrated and multi-dimensional balance of social, economic and environmental benefits. The allocation of urban land resources is widely recognized as a typical spatial multi-objective optimization (MOO) problem, which requires the coordination of conflicting social, economic and environmental goals to support the sustainable and resilient development of cities [15,16,17,18]. Instead of maximizing a single objective, contemporary urban land use planning approaches seek to jointly improve social equity, ecological protection and economic benefits through the construction of multi-objective spatial optimization models [8,13]. With the increasing complexity of urban systems, multi-objective optimization has become a core tool for smart city land use planning, sustainability assessment and urban policy evaluation [14].

In the context of metro-oriented development, the focus of land use optimization has also shifted accordingly. Around rail transit or metro stations, the optimization models have moved beyond the simple control of the floor area ratio (FAR) and incorporated a comprehensive index system that takes into account the spatial efficiency of station areas, traffic volume or metro ridership, environmental quality and land use balance [12,13,14,15,16]. Such TOD-oriented multi-objective optimization frameworks help to coordinate land use intensity, functional mix and transportation performance, and support both the efficient operation of rail transit and the construction of a sustainable and high-quality urban living environment [17,18,19].

1.2.2. Improvement and Application of the NSGA-III Algorithm

In solving many-objective optimization problems, the NSGA-III algorithm exhibits strong convergence performance and solution diversity due to its unique reference-point-based selection mechanism [20,21,22]. In the field of geographic and spatial decision-making, NSGA-III is increasingly replacing the classic NSGA-II as a state-of-the-art tool for solving complex spatial allocation and land use planning problems [22,23]. Recent studies in urban planning have further improved the NSGA-III algorithm through dynamic reference point design and hybrid constraint handling strategies, which has significantly improved its performance in applications such as urban walkability optimization, where it is necessary to reconcile conflicting goals including traffic accessibility, environmental quality and spatial equity [23,24,25].

To mitigate the problem of relatively slow convergence commonly observed in many-objective evolutionary algorithms, some studies have coupled the Hopfield neural network with the NSGA-III algorithm. By utilizing the rapid reduction characteristic of the Hopfield energy function to prune inferior individuals in the population, the improved NSGA-III algorithm can accelerate the generation of high-quality Pareto fronts, with reports of efficiency gains of about 45% compared with the standard NSGA-III algorithm [24]. These methodological advances provide an important computational foundation for handling large-scale and data-intensive optimization tasks such as metro station area planning and other refined urban spatial allocation problems [25,26].

1.2.3. Research on Land Use in Metro Station Areas

Regarding transit-oriented development (TOD) around metro stations, research has increasingly shifted from macro-level conceptual planning to refined and data-driven quantitative optimization at the station scale. Existing research in Europe, North America and China focuses on optimizing the land use structure, transportation accessibility and operational efficiency around metro nodes, especially in high-density cities in China and developed cities such as Tokyo, New York and London.

Around metro stations, multi-objective optimization models and quantitative TOD evaluation indices are widely used to optimize land use layout, floor area ratio (FAR) and facility mix, so as to jointly improve metro ridership, land use efficiency and urban residents’ quality of life [1,9]. Studies in Shanghai and other megacities in China employ multi-source big data and multi-indicator evaluation frameworks to classify and optimize metro station areas and highlight the non-linear impacts of built environment factors such as FAR and functional mix on metro ridership and urban vibrancy [26,27,28]. Studies in Tokyo and London focus on the synergy between TOD and urban renewal and explore the land use optimization mode of metro station areas combined with historical and cultural protection [29]; research in Singapore and Hong Kong emphasizes the integration of TOD with high-density land use and ecological protection, forming a unique metro station area development model [30]. Research on high-density cities shows that the performance of TOD is strongly associated with the integration of multimodal transportation, particularly the coordination of metro, bus, shared bikes and walking [27]. Quantitative studies on TOD performance find that transportation accessibility indicators and pedestrian-oriented accessibility jointly shape metro ridership, while population density and employment density remain the key driving factors [26]. This research conclusion supports the formulation of differentiated TOD strategies adapted to the local urban development stage and the maturity of the rail transit network [28,29,30,31]. In recent relevant studies, the explainable DEA approach has been applied to the performance evaluation of public transport origin-destination (OD) pairs, clarifying the key influencing factors of station catchment transportation connection by decomposing efficiency values, which provides a new path for the accurate evaluation of TOD planning performance [32]. An empirical study in Nanjing has confirmed that the mixed land use layout and multi-modal transportation connection of station catchments under the TOD model can effectively promote the “early recovery” of metro ridership after the COVID-19 pandemic, revealing the intrinsic correlation between land use and ridership resilience [33]. Meanwhile, studies on the elastic regulation of land use mix and the nonlinear impact of the built environment on station catchment vitality have also provided new analytical perspectives for land use optimization of metro station catchments, emphasizing the importance of “rigid constraints + elastic adjustment” in planning.

1.2.4. Research Gaps

Although existing research has laid a certain theoretical and methodological foundation in the field of land use optimization in metro station areas in China and other countries, there are still many deficiencies to be made up for:

First, most studies focus on eastern coastal cities in China and mature developed cities in Europe and North America with mature development and balanced land use, and there is a lack of targeted research on cities with the characteristics of unbalanced spatial development and rapid expansion of rail transit, especially the central cities in western China and rapidly urbanizing cities in developing countries such as Southeast Asia and South America. Second, the existing optimization models fail to integrate the core development needs of cities and insufficiently consider the coupling relationship among the richness of public services, transportation accessibility and population distribution balance, resulting in poor practical applicability of the optimization results. Third, the traditional NSGA-III algorithm is directly used to solve the land use optimization problem of metro station areas without targeted improvement combined with the characteristics of the research object, which leads to problems such as slow convergence speed and uneven distribution of the Pareto front. Fourth, most studies attach importance to the construction of theoretical models and algorithm verification, but neglect the coupling with actual urban planning, resulting in weak operability and implementability of the proposed optimization strategies.

In view of the above deficiencies, this study takes 139 operational metro stations in Xi’an as the research object, combines the urban development characteristics with the core requirements of TOD planning, and constructs a refined multi-objective optimization model that integrates the coupling relationship of the three core objectives. An adaptively improved NSGA-III algorithm adapted to the spatial characteristics of metro station areas is proposed, and the optimization results are deeply combined with urban development planning to formulate hierarchical implementation strategies. This study aims to provide scientific decision support and a replicable research framework for the land use planning of metro station areas in other similar cities and promote the integrated and high-quality development of urban rail transit and land resources.

1.3. Paper Structure

This paper is divided into five sections, following the logical framework of “background laying—method design—result analysis—strategy suggestion—conclusion summary”. Section 1 is the introduction, which elaborates the research background, significance and literature review, and clarifies the research objectives and contents. Section 2 introduces data processing, the construction of the three core optimization objectives, and the design of the adaptively improved NSGA-III algorithm. Section 3 analyzes the characteristics of experimental data, the performance of the improved algorithm, and interprets the Pareto optimal solution set. Section 4 interprets the research findings, puts forward hierarchical optimization strategies and policy guarantees, and analyzes the research limitations and future prospects. Section 5 summarizes the research conclusions and theoretical and practical contributions and points out the application and promotion value of the research results.

2. Research Methods

2.1. Data Source and Preprocessing

2.1.1. Data Overview

As the core central city in western China, Xi’an has a municipal administrative area of 10,108 square kilometers and a permanent resident population of 13.16 million, with about 9.28 million permanent residents in the central urban area, forming a spatial development pattern of “one core, multiple centers and global synergy”. As of 2024, Xi’an’s metro system has 12 operational lines with a total operating mileage of 496 km, 139 operational stations, a daily average passenger volume of 3.85 million person-times, a peak hour headway of 2–3 min for core lines, and the metro accounts for 42.7% of the public transport travel share in the central urban area. The modal split of resident trips in Xi’an is characterized by non-motorized transportation as the main mode as follows: 45.2% for walking and shared bikes, 28.5% for public transport (metro + ground bus), 22.3% for private cars, and 4.0% for other travel modes. All the above basic data of Xi’an city and metro system are derived from Xi’an Statistical Yearbook 2024 [34] and Xi’an Annual Report on Urban Traffic Development 2024 [9], which provides the realistic urban and transportation background for the land use optimization of metro station areas in this study.

This study takes 139 operational metro stations in Xi’an in 2024 as the research sample and systematically collects multi-dimensional attribute data of the station areas to construct a comprehensive evaluation index system for land use optimization (Figure 1). The index system includes 5 core categories and 13 quantitative and categorical indicators, covering the following five dimensions: transportation infrastructure, population distribution, public services, spatial layout and basic station information, which fully reflects the actual characteristics and land use needs of Xi’an’s metro station areas. The specific composition, measurement units and data types of each indicator are shown in

Table 1. Data index system of Xi’an metro stations.

Indicator Category	Indicator Name	Unit	Data Type
Transportation Infrastructure	Road Density	km/km2	Continuous
	Minimum Transfer Times	Times	Continuous
	Minimum Transfer Distance	m	Continuous
	Bus Station Density	Number/km2	Continuous
	Daily Metro Ridership	Person/time	Continuous
Population Distribution	Residential Population	Person	Continuous
	Employment Population	Person	Continuous
Public Services	Density of Land for Science, Education, Culture and Health	Number/km2	Continuous
	Catering Density	Number/km2	Continuous
	Medical Land Density	Number/km2	Continuous
Spatial Layout	Distance to Central Business District (CBD)	m	Continuous
	Land Use Mix Index	Index	Continuous
Basic Information	Station Name	-	Categorical

.

The base map is generated based on the administrative division and land use planning data of Xi’an, with the spatial reference system of WGS84. The colored circles denote the 800 m graded catchment area of metro stations, in line with the TOD planning scope specified in Xi’an Rail Transit and Urban Integration Design Guidelines [35]. The color intensity (from dark to light) corresponds to the descending order of the station’s TOD maturity index, intuitively reflecting the spatial differentiation of TOD level in Xi’an’s metro station areas.

2.1.2. Data Preprocessing

To eliminate the influence of indicator dimension, data distribution and outliers on the operation of the subsequent optimization model and algorithm, a standardized data preprocessing process is carried out on the collected original data. All continuous indicators in the system are normalized to the interval [0, 1] by the min–max standardization method to eliminate the dimension differences among different indicators and ensure the comparability and additivity of the data. The calculation formula for min–max standardization is as follows:

$$x^{*}={\displaystyle \frac{x-x_{min}}{x_{max}-x_{min}}}$$

(1)

where $x^{*}$ is the normalized value of the indicator, $x$ is the original value of the indicator, and $x_{max}$ and $x_{min}$ are the maximum and minimum values of the indicator in the sample, respectively.

A comprehensive validity test is carried out on the entire data set, and the results show that there are no missing values in the 12 indicators of the 139 metro stations, so no additional missing value imputation or deletion is required. The 3σ principle (three times the standard deviation method) is used to detect outliers in the continuous indicator data, and the data points deviating from the mean by more than three times the standard deviation are defined as outliers. The detection results show that outliers account for 2.3% of the total data volume. The detected outliers are corrected by the winsorization method (replacing outliers with the maximum/minimum values within the 3σ range), which reduces the interference of outliers on the model results while retaining the integrity of the sample.

2.2. Construction of Optimization Objectives

Combined with the actual needs of land use optimization around Xi’an metro stations and the research connotation of urban rail transit integrated planning, the following three mutually restrictive and synergistic core optimization objectives are constructed: the richness of public services ($F_1(i)$), transportation accessibility ($F_2(i)$), and population distribution balance ($F_3(i)$). All objectives are set as maximization objectives. Parameters such as spatial attenuation coefficient, facility service level coefficient, and integrated residential-employment population are introduced to construct refined objective functions combined with the heterogeneity of Xi’an’s urban functional zones. The weight distribution of sub-indicators under each objective and the setting of core correction coefficients (α, β, λ, ω, μ, etc.) are determined based on the following three aspects: the latest urban planning guidelines of Xi’an, expert Delphi consultation results, and calibration with representative existing studies on TOD and metro station land use optimization [9,28,32,33,35]. The objective calculation model is constructed with normalized data as input. Meanwhile, multi-dimensional constraint conditions are set to ensure that the model is in line with actual planning. Among them, $i$ is the metro station number ($i=1,2,\dots ,139$), and $k$ is the type of functional zone (central urban area/emerging development zone/peripheral functional zone).

2.2.1. Richness of Public Services ($F_1(i)$)

The richness of public services is used to measure the comprehensive supply level and actual service efficiency of public service facilities in metro station areas, reflecting the ability of the station areas to meet the daily life and social service needs of residents and employees. Three core sub-indicators, including the density of land for science, education, culture and health, catering density, and medical land density, are selected to construct the evaluation model. The functional zone adaptation factor ${\alpha }_{k(i)}$, spatial attenuation factor $\beta (d_i)$, facility service level coefficient ${\lambda }_m$, and facility coupling correction term $\epsilon (·)$ are introduced to comprehensively reflect the facility grade, spatial heterogeneity, and the synergistic supply effect of science, education, culture, health and medical facilities. The calculation formula is as follows:

$$F_1(i)={\alpha }_{k(i)}·\beta (d_i)·\left[{\sum }_{m=1}^3 {\lambda }_m·{\omega }_m·S_m(i)+\epsilon (S_{edu}(i),S_{med}(i))\right]$$

(2)

Among them, the calculation formulas of the spatial attenuation factor and the facility coupling correction term are as follows:

$$\beta (d_i)=e^{-0.15d_i}$$

(3)

$$\epsilon (S_{edu}(i),S_{med}(i))=0.08·\sqrt{S_{edu}(i)·S_{med}(i)}$$

(4)

$S_m(i)$ is the normalized value of the indicator, calculated by the min–max standardization method, consistent with the data normalization formula in Section 2.1.2:

$$S_m(i)={\displaystyle \frac{S_{m,raw}(i)-S_{m,min}}{S_{m,max}-S_{m,min}}}$$

(5)

$d_i$: the straight-line distance from the $i$-th metro station to the core urban area of Xi’an (km);

${\alpha }_{k(i)}$ (functional zone adaptation factor): The division of Xi’an’s metro station functional zones is based on the Xi’an Rail Transit and Urban Integration Design Guidelines (2024) [35], which divides the research scope into central urban area, emerging development zone and peripheral functional zone according to urban spatial structure, public service resource layout and rail transit development maturity. The coefficient values (1.2 for central urban area, 1.0 for emerging development zone, and 0.8 for peripheral functional zone) are determined by Delphi consultation with 12 experts in the fields of Xi’an urban planning, traffic engineering and land resource management, and calibrated with the public service facility allocation standard in Xi’an 14th Five-Year Plan for the Development of the Public Service System (2022) [36], which is adapted to the differentiated public service supply needs of different functional zones;

${\lambda }_m$ (facility service level coefficient): the values (${\lambda }_{edu}=1.1$ for science, education, culture and health, ${\lambda }_{med}=1.2$ for medical care, and ${\lambda }_{food}=0.9$ for catering) are calibrated with the research results of Dong et al. [7] on TOD-oriented public service facility optimization and adjusted according to the actual demand of Xi’an residents for public services (medical and education resources are the core demand of residents, with higher service level weight);

${\omega }_m$ (basic weight of indicators): the weight distribution (${\omega }_{edu}=0.35$, ${\omega }_{med}=0.35$, ${\omega }_{food}=0.30$) is determined by the analytic hierarchy process (AHP) based on the Xi’an 14th Five-Year Plan for the Development of the Public Service System (2022) [36], taking into account the planning priority of core public service facilities (science, education, culture and health + medical care) in Xi’an, and verified by the correlation analysis of public service facility density and population demand in the research sample;

$S_{edu}\left(i\right),S_{med}\left(i\right), and S_{food}(i)$: the normalized values of the density of land for science, education, culture and health, medical land density, and catering density, respectively.

2.2.2. Transportation Accessibility ($F_2(i)$)

Transportation accessibility evaluates the comprehensive traffic convenience and connection level of metro station areas, which is the core attribute of metro stations as urban transportation hubs. To reflect the actual travel demand in TOD planning, metro ridership (daily entry–exit passenger flow) is added as a core influence factor, and the indicator is incorporated into the objective function by coupling with public transport connection indicators. Four sub-indicators, including road density, bus station density, minimum transfer times, and comprehensive distance to urban multi-cores, are selected from the following three aspects: road network construction, public transport connection, ridership demand and spatial location. The road network connectivity correction term $\gamma (·)$, transfer efficiency coefficient $\eta (·)$, and public transport coupling term $\zeta (·)$ are introduced, and a ridership-weighted correction factor is embedded in the public transport coupling term to link infrastructure supply with actual passenger flow demand. Non-linear inverse processing is adopted for transfer times and distance to the core area to be more in line with the actual travel experience. The calculation formula is as follows:

$$\begin{array}{c}{F}_2(i)={\alpha }_{k(i)}·[0.32·\gamma (T_{road}(i))·T_{road}(i)+0.32·{\omega }_{rid}(i)·T_{bus}(i)+0.20·\eta (T_{trans}(i))·(1-T_{trans}(i){)}^{1.5}\\ +0.16·(1-T_{core}(i){)}^{1.2}+\zeta (T_{road}(i),T_{bus}(i))]\end{array}$$

(6)

Among them, the calculation formulas of each correction term and the normalized value of the comprehensive distance to urban multi-cores are as follows:

$$\gamma (T_{road}(i))=1+0.2·{\displaystyle \frac{T_{road}(i)-{\overline{T}}_{road}}{max(T_{road})-min(T_{road})}}$$

(7)

$$\eta (T_{trans}(i))=2-T_{trans}(i)$$

(8)

$$\zeta (T_{road}(i),T_{bus}(i))=0.06·T_{road}(i)·T_{bus}(i)$$

(9)

$$T_{core}(i)={\displaystyle \frac{d_{core}(i)-d_{core,min}}{d_{core,max}-d_{core,min}}}$$

(10)

${\mathit{\omega }}_{\mathit{r}\mathit{i}\mathit{d}}(\mathit{i})$: Ridership-weighted correction factor for bus station density, calculated as the normalized daily entry–exit ridership of the $i$-th metro station [9], with a value range of [0.1, 1.0]. The factor is positively correlated with actual metro ridership, meaning stations with higher passenger flow have a higher weight for bus station density, realizing the coupling of transportation infrastructure layout and actual travel demand in TOD planning.

${\alpha }_{k(i)}$ (functional zone adaptation factor): The coefficient values (1.0 for central urban area, 1.3 for emerging development zone, and 1.1 for peripheral functional zone) are formulated based on the Xi’an Rail Transit and Urban Integration Design Guidelines [35], which focuses on the transportation infrastructure improvement demand of emerging development zones and peripheral functional zones in Xi’an’s rail transit development stage. The values are verified by the regression analysis of transportation accessibility and urban development intensity of Xi’an metro stations and approved by the expert group of Xi’an Transportation Planning and Design Institute;

$T_{road}\left(i\right),T_{bus}\left(i\right), and T_{trans}(i)$: the normalized values of road density, bus station density, and minimum transfer times, respectively;

${\overline{T}}_{road}$: the mean value of the normalized road density of all metro stations;

$\gamma (T_{road}(i))$ is the road network connectivity correction term, and the higher the road network density, the larger the correction coefficient, reflecting the amplification effect of road network density on transportation accessibility;

$\eta (T_{trans}(i))$: transfer efficiency coefficient; the fewer the transfer times, the larger the coefficient, which gives a positive gain to transfer convenience;

$d_{core}(i)$: the weighted Euclidean distance from the $i$-th metro station to Xi’an’s urban multi-cores such as Bell Tower, Administrative Center, and Chanba Core (m); the weight of each core is determined based on the employment density and commercial activity of the core area, and $T_{core}(i)$ is its normalized value;

$\zeta (T_{road}(i),T_{bus}(i))$: road and bus station coupling term, reflecting the positive contribution of the synergistic layout of road network and bus facilities to transportation accessibility, and the coefficient 0.06 is calibrated with the research results of Zhao et al. [19] on Xi’an metro station transportation integration.

2.2.3. Population Distribution Balance ($F_3(i)$)

Population distribution balance measures the rationality of the spatial distribution of the integrated residential-employment population around metro stations, which is of great significance for alleviating the population agglomeration pressure in the central urban area, promoting the balanced development of urban space, and realizing the core demand of TOD for “job-housing balance”. Based on the information entropy theory, the single residential population is expanded to the integrated residential-employment population. The functional zone population carrying capacity coefficient ${\mu }_{k(i)}$, population–facility matching degree correction term $\theta (·)$, and spatial agglomeration inhibition term $\sigma (·)$ are introduced to map the objective value to the interval [0, 1]. A higher objective value indicates a more balanced population distribution in the metro station area. The calculation formula is as follows:

$$F_3(i)={\mu }_{k(i)}·\left[{\displaystyle \frac{-{\sum }_{i=1}^{139} P_i^{\prime }·ln(P_i^{\prime })}{ln(139)}}+\theta (F_1(i),P_i^{\prime })-\sigma (P_i^{\prime })\right]$$

(11)

Among them, the calculation formulas of the integrated residential-employment population, population proportion, population–facility matching degree correction term, and spatial agglomeration inhibition term are as follows:

$$P_i={\theta }_p·p_{res}(i)+(1-{\theta }_p)·p_{job}(i)$$

(12)

$$P_i^{\prime }={\displaystyle \frac{P_i}{{\sum }_{i=1}^{139} P_i}}$$

(13)

$$\theta (F_1(i),P_i^{\prime })=0.12·F_1(i)·(1-max(P_i^{\prime }-{\overline{P}}^{\prime },0))$$

(14)

$$\sigma (P_i^{\prime })=0.09·{\displaystyle \frac{(P_i^{\prime }-{\overline{P}}^{\prime }{)}^2}{{\overline{P}}^{\prime }}}$$

(15)

${\mu }_{k(i)}$ (functional zone population carrying capacity coefficient): The coefficient values (0.9 for central urban area, 1.2 for emerging development zone, and 1.3 for peripheral functional zone) are determined based on the Xi’an Municipal Master Plan of Territorial Spatial Development (2021–2035) [37], which aims to guide the population to disperse to non-core areas and adapt to the population carrying capacity and development positioning of different functional zones. The values are calibrated with the population density threshold of metro station catchment areas in TOD planning at home and abroad and adjusted according to the actual population distribution characteristics of Xi’an;

${\theta }_p$ (weight of residential and employment population): the weight value (0.6 for residential population $p_{res}(i)$ and 0.4 for employment population $p_{job}(i)$) is based on the Xi’an Municipal Master Plan of Territorial Spatial Development (2021–2035) [37], which is consistent with the characteristics of Xi’an’s urban residential and employment distribution (residential demand is dominant in metro station catchment areas), and verified by the correlation analysis of residential-employment population ratio and job-housing balance degree of Xi’an metro stations;

$P_i$: the integrated residential-employment population of the $i$-th metro station; $P_i^{\prime }$ is the proportion of the integrated population in the total integrated population of the 139 metro stations;

$\overline{P^{\prime }}$: the mean value of the integrated population proportion, $\overline{P^{\prime }}=1/139$;

$\theta (F_1(i),P_i^{\prime })$: population–facility matching degree correction term; the richer the public services and the smaller the population deviation from the mean, the larger the correction term, reflecting the adaptability of public services and population distribution; the coefficient 0.12 is determined by the regression analysis of public service richness and population distribution balance in the research sample;

$\sigma (P_i^{\prime })$: spatial agglomeration inhibition term; the higher the degree of population agglomeration, the larger the inhibition term, which makes a negative correction for excessive population agglomeration; the coefficient 0.09 is calibrated with the research results of Tong et al. [16] on land use optimization of Xi’an rail transit station areas.

2.2.4. Constraint Conditions of the Multi-Objective Optimization Model

To ensure that the model is in line with the actual planning needs of Xi’an’s land use, facility supply and transportation construction, and to avoid the optimization results from being divorced from reality, the following multi-dimensional constraint conditions are set:

$$\left\{\begin{array}{l}0\le F_1(i)\le 1.5, 0\le F_2(i)\le 1.5, 0\le F_3(i)\le 1.5\\ {\displaystyle \sum _{i=1}^{139}} S_m(i)·A(i)\le Q_m\\ T_{road}(i)\ge 0.1\\ 0.1\le {\omega }_{rid}(i)\le 1.0 \\ 0.005\le P_i^{\prime }\le 0.05\\ {\alpha }_{k(i)},\beta (d_i),{\lambda }_m\in (\mathrm{0,2})\end{array}\right.$$

(16)

Upper and lower limit constraints of objective values: restrict the value range of the three core objectives to avoid the objective values deviating from the actual situation excessively; the upper limit 1.5 is set based on the maximum improvement potential of each objective calculated from the original data of Xi’an metro stations, and approved by urban planning experts;

Total supply constraint of public service facilities: $A(i)$ is the planned land area of the $i$-th metro station area, and $Q_m$ is the upper limit of the total supply of public service facilities, ensuring that the facility layout matches the land planning and supply capacity [37];

Minimum road network density constraint: ensure the basic traffic capacity of metro station areas and avoid the impact of excessively low road network density on transportation accessibility; the threshold 0.1 is the minimum normalized road network density required for basic traffic operation of metro stations in Xi’an, formulated by Xi’an Transportation Planning and Design Institute;

Integrated population proportion constraint: avoid excessive sparseness or agglomeration of population in metro station areas and ensure the rationality of the spatial distribution of population; the range 0.005~0.05 is determined based on the population carrying capacity of metro station catchment areas (500 m–800 m) in TOD planning and combined with the actual population scale of Xi’an metro stations;

Value constraint of correction coefficients: restrict the value range of each correction coefficient to ensure the rationality and stability of the objective function calculation; the range (0, 2) is set based on the calibration results of existing studies and the actual variation range of coefficients in the research sample.

2.3. Design of the Improved NSGA-III Algorithm

Aiming at the defects of the traditional NSGA-III algorithm in solving the land use optimization problem of metro stations, such as slow convergence speed, uneven Pareto front distribution, insufficient solution diversity, and weak adaptability to discrete + continuous decision variables, this study proposes a hierarchical adaptively improved NSGA-III algorithm. On the basis of retaining the core framework of the traditional NSGA-III algorithm, the following four key improvements are carried out: multi-dimensional adaptive reference point adjustment, design of real-integer hybrid coding genetic operator, enhanced multi-criteria environmental selection mechanism, and dynamic regulation of algorithm iteration. The improved algorithm can adapt to the distribution characteristics of the multi-objective space and the type of decision variables for land use optimization of metro stations, effectively balance the convergence speed of the algorithm and the diversity of solutions, and improve the adaptability and optimization performance of the algorithm to practical problems.

2.3.1. Framework of the Traditional NSGA-III Algorithm

The traditional NSGA-III algorithm is a reference-point-based multi-objective evolutionary algorithm, which is an optimized improvement of NSGA-II for many-objective optimization problems. Its core framework consists of five basic steps, and the specific implementation process is as follows:

• Population initialization: randomly generate an initial population of a certain scale according to the problem constraints, and determine the range of decision variables and the coding method of solutions;
• Non-dominated sorting: perform non-dominated sorting on the individuals in the population according to the objective function values, and divide the population into different non-dominated fronts (F1, F2, F3…) according to the dominance relationship;
• Reference point setting: set a set of fixed reference points in the objective space to guide the search direction of the algorithm and maintain the diversity of solutions;
• Environmental selection: select excellent individuals from the non-dominated fronts to form the next generation population according to the correlation between individuals and reference points and the crowding distance;
• Genetic operation: perform selection, crossover and mutation operations on the selected population to generate offspring individuals and merge the parent and offspring populations for the next iteration.

2.3.2. Key Improvements of the Algorithm

Aiming at the problems of the traditional NSGA-III algorithm in the application of land use optimization of metro stations, such as the reference points cannot adapt to the dynamic distribution of the objective space, the genetic operator has low adaptability to discrete + continuous variables, the environmental selection does not fully consider the feasibility and spatial correlation of solutions, and the algorithm is prone to premature convergence and oscillation, four targeted improvement strategies are proposed, with the specific implementation details as follows:

• Multi-dimensional adaptive reference point adjustment

The core problem of the traditional NSGA-III algorithm is that the preset fixed reference points cannot adapt to the dynamic distribution characteristics of the solution set in the objective space, which is easy to lead to uneven distribution of the Pareto front and loss of optimal solutions in some areas. The multi-dimensional adaptive reference point adjustment strategy proposed in this study sets 10 reference points ($r=1,2,\dots ,10$) in the objective space, introduces objective dimension layering, spatial correlation weight ${\rho }_{ij}$ and dynamic scaling of reference points. According to the density distribution of the current population solutions in the objective space and the spatial correlation between metro stations, the position and number of reference points are dynamically adjusted in each iteration while keeping the total number of reference points unchanged. The specific implementation steps are as follows:

Step 1: Reference point layering: Set $F_1/F_2/F_3$ as the main objective layer and the sub-indicators of each objective as the secondary objective layer. The reference points of the main objective layer account for 70% and those of the secondary objective layer account for 30%, which takes into account the optimization of core objectives and the refinement of indicators, and improves the refinement degree of the algorithm search;

Step 2: Calculation of spatial correlation density: introduce the spatial correlation weight between metro stations ${\rho }_{ij}=e^{-0.08d_{ij}}$ ($d_{ij}$ is the straight-line distance between station $i$ and station $j$), and calculate the spatial correlation solution density of the reference point area to reflect the spatial distribution characteristics of solutions and the correlation between metro stations:

$${\rho }_r={\sum }_{i\in {\Omega }_r} {\sum }_{j\in {\Omega }_r} {\rho }_{ij}·x_i$$

(17)

Among them, ${\Omega }_r$ is the associated solution set of reference point $r$, and $x_i$ is the validity coefficient of solution $i$ (1 if all constraint conditions are satisfied, 0 otherwise);

Step 3: Splitting and merging of reference points: Calculate the average spatial correlation density $\overline{\rho }$ of all reference point areas. For the reference point areas with high solution density (${\rho }_r>1.2\overline{\rho }$), perform regional splitting, divide the reference point into 2 sub-reference points, and the positions of the sub-reference points are dynamically generated based on the gradient of the objective space to improve the search accuracy in high-density areas; for the reference point areas with low solution density (${\rho }_r<0.3\overline{\rho }$), perform regional merging, merge it with the adjacent low-density reference point, and the position of the merged reference point is the weighted center of the two (the weight is their respective spatial correlation density) to avoid the waste of search resources;

Step 4: Dynamic scaling and normalization of reference points: according to the objective space range of the Pareto front in each iteration $R_t=[min(F_m(t)),max(F_m(t))]$, scale and adjust the reference points according to the scaling coefficient ${\xi }_t=R_t/R_{t-1}$ ($R_{t-1}$ is the objective space range of the previous generation), so that the reference points always fit the evolutionary characteristics of the objective space; re-normalize the adjusted reference points to ensure that the reference points are evenly distributed in the objective space and maintain the guiding role of the reference points.

• Real-Integer Hybrid Coding Genetic Operator

Genetic operator is the core of the algorithm’s evolutionary search, which directly affects the convergence speed of the algorithm and the quality of solutions. Aiming at the problems of low search efficiency and easy destruction of excellent gene segments of the traditional genetic operator in solving the discrete + continuous decision variable problem of metro station land use optimization, a real-integer hybrid coding genetic operator is designed, including a hierarchical adaptive crossover operator and a multi-strategy controlled mutation operator, which takes into account the diversity of solutions, the retention of excellent genes and the adaptability to different types of decision variables.

Hybrid coding is employed to match the variable types of metro station land-use optimization, ensuring a one-to-one mapping between chromosomes and decision variables.

According to the type of decision variables for metro station land use optimization, a real-integer hybrid coding method is adopted to ensure the one-to-one correspondence between coding and decision variables. The specific coding rules are as follows:

Integer coding: for discrete decision variables (such as land use type, number of bus station layouts, and number of public service facility constructions), 8-bit integer coding is adopted, with the value range of $[0,N_{max}]$ ($N_{max}$ is the maximum number of facility layouts);

Real coding: for continuous decision variables (such as facility density, road network density, and land use mix index), 6-bit real coding is adopted, with the value range of [0, 1], matching the normalized value of indicators;

Coding length of solution: $L=8\times N_d+6\times N_c$ ($N_d$ is the number of discrete variables, $N_c$ is the number of continuous variables), and each solution corresponds to the land use optimization decision combination of 25 metro stations.

The selection of 25 metro stations as a single optimization unit (one decision chromosome) is grounded in practical planning principles, technical feasibility analysis, and alignment with Xi’an’s actual metro station land use planning and management units, with the key justifications as follows:

Matching corridor-level planning: In line with Xi’an Rail Transit TOD Planning Guideline (2024), Xi’an’s rail transit is developed in corridor clusters of 20~30 spatially and functionally correlated stations. A 25-station unit aligns with this scale, bridging algorithm optimization and practical planning for direct application in corridor-level land use planning;

Adapting to spatial correlation: Adjacent metro stations in Xi’an show strong spatial correlation in land use, public services and population distribution. Calculation of the spatial autocorrelation coefficient (Moran’s I = 0.78, 95% significance) identifies 25 stations as the optimal scale, avoiding local optimization in single-station analysis and enabling integrated land use optimization for correlated station clusters;

Balancing algorithm efficiency and solution refinement: Sensitivity analysis of solution scales (5 to 30 stations) on convergence speed, Pareto front quality and feasibility shows that <20 stations causes severe local optimization (C < 0.75), while >30 stations leads to sharp growth in decision variables, slow convergence (>40 iterations) and low feasibility (<85%). The 25-station unit achieves the optimal balance, ensuring high convergence efficiency and reflecting both corridor-level integrated planning and station-level refined adjustment;

Conforming to land use control units: Per Xi’an Municipal Master Plan of Territorial Spatial Development (2021–2035) [37], the city’s “street + corridor” dual land use control system designates corridor-level units (8~10 street-level units, covering 20~30 stations) as the core control scale. A 25-station unit is fully consistent with this standard, ensuring optimization results can be integrated into statutory planning and land use adjustment measures are practically implementable.

Hierarchical adaptive crossover operator is designed to enhance the search efficiency of the algorithm.

A set-based crossover method is adopted to ensure that the scale of the solution remains unchanged after crossover. The crossover probability is dynamically adjusted according to the similarity of parent individuals, and layered crossover is carried out according to variable types to avoid the destruction of gene segments during the crossover of discrete/continuous variables. Meanwhile, a retention mechanism for excellent gene segments is set. The specific design is as follows:

Calculate the multi-objective similarity of two parent individuals to reflect the similarity of parent individuals in the objective space:

$$S_{pq}=1-{\displaystyle \frac{{\sum }_{m=1}^3 |F_m(p)-F_m(q)|}{3}}$$

(18)

Among them, $p,q$ are two parent individuals, and $F_m\left(p\right), F_m(q)$ are the $m$-th objective function values of parent individuals $p,q$ respectively.

Dynamically adjust the crossover probability within the range of [0.6, 0.9] according to the multi-objective similarity as follows: for parent individuals with high similarity ($S_{pq}>0.8$), set a high crossover probability (0.85~0.9) to improve the diversity of offspring; for parent individuals with moderate similarity ($0.5\le S_{pq}\le 0.8$), set a moderate crossover probability (0.7~0.85); and for parent individuals with low similarity ($S_{pq}<0.5$), set a low crossover probability (0.6~0.7) to retain the excellent gene segments of parents.

Layered crossover: the discrete variable layer adopts order crossover (OX) to ensure the validity and rationality of discrete variables after crossover; the continuous variable layer adopts simulated binary crossover (SBX) to take into account the diversity and continuity of solutions.

Retention of excellent gene segments: set retention marks for the excellent gene segments of the top 20% of the objective function values in the parents, which do not participate in gene exchange during crossover to ensure the effective transmission of excellent characteristics.

Multi-strategy controlled mutation operator is applied to maintain population diversity and avoid local optima. Limit the number of mutation nodes of a single solution to avoid the loss of excellent characteristics of the parent solution and the slowdown of the algorithm’s convergence speed caused by excessive mutation. A performance-based mutation priority strategy is adopted, introducing mutation direction guidance and multi-strategy mutation, and carrying out mutation validity test. The specific design is as follows:

Limit the number of mutation stations for each solution to 1~3 and fix the mutation probability to 0.08 after sensitivity analysis to balance the exploration and development capabilities of the algorithm.

Mutation node screening: adopt a performance-based mutation priority strategy, and give priority to mutating the nodes with short board objective performance (the sum of the three objective values is in the bottom 30% of the solution) and constraint boundary nodes (the indicator value is close to the upper and lower constraint limits) in the solution, so that the algorithm focuses on optimizing the weak links of the solution and improves the search efficiency.

Mutation direction guidance: based on the objective gradient direction of the Pareto front in the current generation $\nabla F_m=(F_m^{max}-F_m^{min})/L_m$ ($F_m^{max},F_m^{min}$ are the maximum and minimum values of the $m$-th objective respectively; $L_m$ is the solution distribution length of objective $m$), guide the mutation to the direction of objective value improvement to avoid invalid mutation.

Multi-strategy mutation: the discrete variable layer adopts neighborhood mutation, and the mutation value is the neighborhood integer of the original value to ensure the rationality of discrete variables; the continuous variable layer adopts Gaussian mutation, and the mutation value obeys the normal distribution to improve the search accuracy of continuous variables:

$$x_{new}=x_{old}+N(\mu ,{\sigma }^2), \mu =x_{old},\sigma =0.05$$

(19)

Among them, $x_{old}$ is the variable value before mutation, $x_{new}$ is the variable value after mutation, $\mu$ is the mean value, and $\sigma$ is the standard deviation.

Mutation validity test: Conduct constraint condition test on the solution after mutation. If the constraint conditions are violated, perform reverse mutation (restore the original value and fine-tune) to ensure the feasibility and rationality of the solution.

• Enhanced Multi-Criteria Environmental Selection Mechanism

The environmental selection mechanism of the traditional NSGA-III algorithm mainly selects individuals based on the non-dominated front and the correlation between individuals and reference points, ignoring the diversity of reference point areas, the feasibility and spatial correlation of solutions, which is easy to lead to the lack of solutions in some areas and invalid solutions entering the next generation population. The enhanced multi-criteria environmental selection mechanism proposed in this study constructs a four-criterion multi-dimensional evaluation system, optimizes the selection rules of the last incomplete non-dominated front, and ensures the diversity, feasibility, spatial adaptability and integrity of the solution set while guaranteeing the convergence of the algorithm. The specific implementation rules are as follows:

Step 1: select all individuals of the complete non-dominated fronts in turn to join the next generation population until adding the next front will exceed the set population scale;

Step 2: For the last incomplete non-dominated front, construct a multi-criteria evaluation system with the solution feasibility coefficient $\phi (x)$, reference point area priority, spatial correlation degree $\rho (x)$, objective balance coefficient $\psi (x)$ and crowding distance as the core, and sort all individuals in the front. The calculation formulas of each evaluation coefficient are as follows:

$$\phi (x)=\left\{\begin{array}{ll}1,& \mathit{Satisfy} \mathit{all} \mathit{constraints}\\ 0.7,& \mathit{Violate} 1 \mathit{constraint}\\ 0,& \mathit{Violate} 2 \mathit{or} \mathit{more} \mathit{constraints} (\mathit{eliminated} \mathit{directly})\end{array}\right.$$

(20)

$$\psi (x)=1-{\displaystyle \frac{\sigma (F_1,F_2,F_3)}{\mu (F_1,F_2,F_3)}}$$

(21)

$$\rho (x)={\sum }_{i\in x} {\sum }_{j\in x} {\rho }_{ij}$$

(22)

Among them, $\phi (x)$ is the solution feasibility coefficient, which directly eliminates invalid solutions that violate 2 or more constraints; $\psi (x)$ is the objective balance coefficient, calculated based on the coefficient of variation, and a larger coefficient indicates a more balanced development of the three objectives of the solution; $\rho (x)$ is the spatial correlation degree of the solution, reflecting the spatial correlation of the metro station combination corresponding to the solution, and a larger coefficient is more in line with the integrity of urban spatial planning; and ${\rho }_{ij}$ is the spatial correlation weight between metro stations;

Step 3: Sort the individuals of the last incomplete front in the order of $\phi (x)\to$ reference point area priority $\to \rho (x)\to \psi (x)\to$ crowding distance. First, give priority to selecting individuals in the reference point areas with a small number of associated individuals to ensure that there is at least one solution in each reference point area; then, for individuals in the same reference point area, select individuals with larger spatial correlation degree, objective balance coefficient and crowding distance to maintain the diversity and spatial adaptability of the solution set in the area;

Step 4: select individuals from the sorted last incomplete front in turn to fill the next generation population until the population scale reaches the set value and the environmental selection is completed.

• Dynamic Regulation Mechanism of Algorithm Iteration

To avoid the problems of premature convergence and oscillation in the algorithm iteration process and improve the robustness and stability of the algorithm, a convergence dynamic monitoring index $\delta (t)$ and parameter adaptive regulation rules are introduced to monitor the convergence state of the algorithm in real time and dynamically adjust the algorithm parameters according to the monitoring results to realize the self-regulation and optimization of the algorithm. The specific implementation is as follows:

Calculate the convergence dynamic monitoring index, which reflects the change rate of the objective function value in the recent 5 iterations and measures the convergence state of the algorithm:

$$\delta (t)={\displaystyle \frac{{\sum }_{m=1}^3 |{\overline{F}}_m(t)-{\overline{F}}_m(t-5)|}{{\sum }_{m=1}^3 {\overline{F}}_m(t-5)}}$$

(23)

Among them, $\delta (t)$ is the convergence monitoring index of the $t$-th generation, ${\overline{F}}_m(t)$ is the mean value of the $m$-th objective function value of the $t$-th generation, and ${\overline{F}}_m(t-5)$ is the mean value of the $m$-th objective function value of the $t-5$-th generation;

Parameter adaptive regulation rules: dynamically adjust parameters such as crossover probability, number of mutation nodes, and reference point splitting ratio according to the value of the convergence monitoring index to adapt to different convergence stages of the algorithm:

If $\delta (t)>0.05$ (the algorithm converges rapidly): keep the current crossover/mutation probability, and appropriately increase the reference point splitting ratio to 70% to strengthen the diversity of solutions and avoid premature convergence of the algorithm;

If $0.01\le \delta (t)\le 0.05$ (the algorithm converges steadily): keep all parameters unchanged to maintain the stability and optimization efficiency of the algorithm;

If $\delta (t)<0.01$ (the algorithm is close to convergence/premature convergence): increase the crossover probability by 0.05, adjust the number of mutation nodes to 2~4, and perform random disturbance (random gene exchange) on 5% of the solutions to activate the search ability of the algorithm and explore a better solution space.

2.3.3. Algorithm Flow Chart

The improved NSGA-III algorithm takes the preprocessed metro station data as input, takes the three maximization objectives of $F_1(i)$, $F_2(i)$ and $F_3(i)$ as the optimization direction, and iteratively searches for the Pareto optimal solution set for the land use optimization around Xi’an metro stations. The complete execution process of the algorithm takes population initialization → solution pre-screening → hierarchical non-dominated sorting → multi-dimensional adaptive reference point adjustment → hybrid coding genetic operation → enhanced multi-criteria environmental selection → dynamic convergence monitoring → dynamic parameter regulation → refined Pareto solution screening → convergence judgment as the core main line, reflecting the dynamic iteration and self-regulation process of the algorithm (Figure 2).

2.3.4. Algorithm Parameter Setting

To ensure the optimal performance of the improved NSGA-III algorithm in solving the land use optimization problem of Xi’an metro stations, a systematic sensitivity analysis is carried out on the key algorithm parameters (population size, number of iterations, solution scale, crossover rate, mutation rate, number of reference points, hybrid coding parameters, dynamic regulation parameters, etc.). The analysis method is as follows: fix other parameters unchanged, change the value of a single parameter, evaluate the algorithm performance from three dimensions of convergence speed, Pareto front quality and solution feasibility, and finally determine the optimal parameter combination adapted to the research problem in this study. The specific parameter settings are shown in

Table 2. Optimal parameter settings of the improved NSGA-III algorithm.

Parameter Category	Parameter Name	Setting Value/Value Range
Basic Population Parameters	Population Size	80
	Number of Iterations	40
	Solution Scale (Number of Stations per Solution)	25
Genetic Operator Parameters	Crossover Rate	0.6~0.9 (Adaptive)
	Mutation Rate	0.08 (Fixed)
	Number of Mutation Nodes per Solution	1~3 (Dynamically Regulated to 2~4)
	Retention Ratio of Excellent Gene Segments	20%
Reference Point Parameters	Total Number of Reference Points	10
	Proportion of Reference Points in Main/Secondary Objective Layers	70%/30%
	Reference Point Splitting/Merging Threshold	$1.2\overline{\rho }$$/0.3\overline{\rho }$
Multi-Criteria Selection Parameters	Feasibility Coefficient Elimination Threshold	$\phi (x)=0$ (Eliminated Directly)
	Gaussian Mutation Standard Deviation	0.05
Dynamic Regulation Parameters	Convergence Monitoring Index Threshold	$\delta (t)=0.01/0.05$
	Random Disturbance Ratio	5% (Triggered in Case of Premature Convergence)
Hybrid Coding Parameters	Integer Coding Bits	8 bits
	Real Coding Bits	6 bits

.

2.3.5. Software and Analysis Tools

All data preprocessing, descriptive statistics and correlation analysis were conducted using SPSS 26.0 and Python 3.9 (Pandas, NumPy libraries). The adaptively improved NSGA-III algorithm was coded and implemented based on Python 3.9 (DEAP, Scikit-opt libraries), and the algorithm iteration and multi-objective optimization were run on the Anaconda 3 platform. The visualization of experimental results (convergence curve, 3D Pareto front, and objective value distribution) and spatial mapping were completed using Matplotlib 3.7, Seaborn 0.12 and ArcGIS 10.8.

3. Experimental Results and Analysis

This section carries out a comprehensive analysis of the experimental results obtained based on the multi-objective land use optimization model of Xi’an metro stations and the improved NSGA-III algorithm.

3.1. Analysis of Original Objective Data

3.1.1. Descriptive Statistics of Optimization Objectives

Descriptive statistical analysis was conducted on the original values of the three core optimization objectives (public service richness $F_1(i)$, transport accessibility $F_2(i)$, and population distribution balance $F_3(i)$) for the 139 metro stations in Xi’an, with the results presented in

Table 3. Descriptive statistics of the original optimization objectives.

Optimization Objective	Mean	Standard Deviation	Minimum	Maximum	Median
$\mathrm{Public} \mathrm{Service} \mathrm{Richness} (F_1(i)$)	0.2192	0.1877	0.0000	0.8128	0.1950
$\mathrm{Transport} \mathrm{Accessibility} (F_2(i)$)	0.3586	0.0812	0.0952	0.5713	0.3579
$\mathrm{Population} \mathrm{Distribution} \mathrm{Balance} (F_3(i)$)	0.7879	0.1492	0.3191	0.9956	0.7917

, including the mean, standard deviation, minimum, maximum and median of each objective. The statistical results quantitatively reflect the overall level and dispersion of each objective across the research sample, laying a foundation for evaluating the subsequent optimization effects of the algorithm.

As shown in Table 3, the three objectives exhibit distinct distribution characteristics in the original data:

Public service richness has the lowest mean (0.2192) and the largest standard deviation (0.1877), with a minimum value of 0 and a maximum of 0.8128, indicating a severe imbalance in the supply level of public service facilities around Xi’an’s metro stations and a significant gap between stations with high-quality and low-efficiency service provision. Transport accessibility shows a slightly wider distribution range (standard deviation 0.0812) compared with the original single infrastructure evaluation, which more truly reflects the actual difference in transportation service capacity between stations—core stations with high ridership have higher accessibility values, while peripheral low-ridership stations show lower accessibility, which is more in line with the actual TOD planning evaluation demand. Population distribution balance has the highest mean (0.7879) and a moderate degree of dispersion, with more than half of the stations recording a balance value higher than 0.7917, meaning the overall distribution of residential population around Xi’an’s metro stations is relatively balanced, with only a few stations suffering from severe population agglomeration or sparsity.

3.1.2. Correlation Analysis of Optimization Objectives

To explore the linear correlation and potential conflicts among the three core optimization objectives, a bivariate correlation analysis of the objective values was conducted using the Pearson correlation coefficient, yielding a correlation matrix (Figure 3). The Pearson correlation coefficient ranges from −1 to 1: a value close to 1 indicates a strong positive linear correlation, a value close to −1 indicates a strong negative linear correlation, and a value close to 0 indicates a weak or no linear correlation. The significance of all correlation coefficients was tested at the 95% confidence level ($p<0.05$).

The correlation coefficient between public service richness and transport accessibility is 0.312, showing a moderate positive linear correlation (an increase from the original weak correlation). This means that the improvement of transport accessibility (coupled with ridership demand) around metro stations is accompanied by a more obvious increase in public service richness, which conforms to the actual law of urban development where high-passenger flow transportation hubs are more likely to agglomerate high-quality public service facilities. The correlation coefficient between public service richness and population distribution balance is −0.110, presenting a weak negative linear correlation, indicating that the excessive agglomeration of public service facilities in individual station areas may lead to population distribution imbalance to a certain extent, and there is a slight conflict between the two objectives. The correlation coefficient between transport accessibility and population distribution balance is 0.178, showing a weak positive linear correlation, reflecting that the improvement of traffic convenience (matching actual ridership) has a more obvious promoting effect on the balanced distribution of population, which further verifies the rationality of incorporating ridership factors into the accessibility evaluation.

The three objectives still show an overall low correlation (the absolute value of all correlation coefficients is <0.35), indicating that there is no obvious linear constraint relationship between them, and the improvement of a single objective will not significantly drive or inhibit the changes in other objectives. This characteristic fully proves the necessity of adopting a multi-objective optimization method for land use optimization around metro stations.

3.1.3. Spatial Distribution Characteristics of Optimization Objectives

The spatial distribution laws of the three core optimization objectives were analyzed from the perspective of data distribution forms, and the frequency distribution characteristics of each objective value were visualized (Figure 4).

Public service richness presents a right-skewed distribution (skewness > 0), with the objective value of most metro stations (about 78%) lower than the mean (0.2192), and only a few stations in the central urban area having a high level of public service facilities. This distribution characteristic indicates that public service resources around Xi’an’s metro stations are highly agglomerated in the core area, and peripheral station areas face a severe shortage of resources. Transport accessibility shows an approximately normal distribution (skewness ≈ 0), with the objective value of most stations concentrated in the range of 0.30~0.45, and the number of stations gradually decreasing from the mean to both sides. This distribution reflects that the construction of transportation infrastructure around Xi’an’s metro stations has formed a relatively uniform layout, and the gaps between stations are mainly reflected in the refined adjustment of local road networks and public transport connections. Population distribution balance shows a left-skewed distribution (skewness < 0), with more than 82% of the stations having an objective value higher than the mean (0.7879), and most stations concentrated in the range of 0.70~0.95. This distribution means that the distribution of residential population around most metro stations in Xi’an is in a relatively balanced state, and the few stations with low balance values are mainly concentrated in the urban emerging development zones and the edge of the central urban area with severe population agglomeration.

3.2. Convergence Performance Analysis of the Improved NSGA-III Algorithm

Convergence performance is one of the core indicators for evaluating the effectiveness of evolutionary algorithms, reflecting the ability of the algorithm to approach the true Pareto optimal front with the increase in iteration generations. Taking the number of iteration generations as the abscissa and the mean value of the three objective values of the Pareto front solutions in each generation as the ordinate, the convergence curve of the improved NSGA-III algorithm was plotted (Figure 5). Convergence analysis was carried out based on the change trend of the objective mean values in 40 iterations to verify the convergence characteristics and stability of the algorithm.

Fast initial convergence speed: In the first 15 iterations, the mean values of the three core optimization objectives showed a significant rapid growth trend. Public service richness increased from the original mean of 0.2192 to about 0.3125, transport accessibility from 0.3586 to about 0.3912, and population distribution balance from 0.7879 to about 0.8264. This indicates that the improved NSGA-III algorithm can quickly search for high-quality solution areas in the early stage of iteration, which benefits from the multi-dimensional adaptive reference point adjustment and the real-integer hybrid coding genetic operator, endowing the algorithm with strong global search capability.

Stable and smooth convergence: After 25 iterations, the objective mean values of the Pareto front tended to be stable, and the growth rate of the objective values in each subsequent generation was less than 0.5% without obvious fluctuations. This shows that the algorithm has basically converged to a stable Pareto optimal front at this stage, and the search capability of the algorithm has shifted from global exploration to local exploitation. The dynamic regulation mechanism of algorithm iteration effectively avoids the premature convergence and oscillation of the traditional algorithm.

High convergence level: At the 40th iteration (the termination generation of the algorithm), the mean values of the three objectives of the final Pareto front solutions reached a stable optimal level as follows: 0.3468 for public service richness, 0.4052 for transport accessibility, and 0.8458 for population distribution balance. Compared with the original mean values, the three objectives increased by 59.58%, 12.94% and 7.35% respectively, fully verifying the effectiveness of the improved NSGA-III algorithm in realizing the synergistic improvement of multiple objectives for land use around metro stations—the transport accessibility objective achieved a higher growth rate due to the incorporation of ridership factors, which makes the algorithm more sensitive to the optimization of actual transportation service capacity matching passenger flow demand.

3.3. Characteristic Analysis of the Pareto Optimal Front

The Pareto optimal front obtained by the improved NSGA-III algorithm after 40 iterations is a set of non-dominated solutions in the three-dimensional objective space (public service richness $F_1(i)$, transport accessibility $F_2(i)$, and population distribution balance $F_3(i)$), and all solutions satisfy the multi-dimensional constraint conditions in Section 2.2.4, with practical planning feasibility. A three-dimensional scatter plot was constructed to visualize the Pareto optimal front (Figure 6), with the three coordinate axes representing the three core optimization objectives and the red triangles representing the adaptively adjusted reference points. The characteristics of the Pareto optimal front were analyzed from the following four core dimensions—continuity, uniformity, coverage and feasibility—to comprehensively evaluate the solution quality of the improved algorithm and its adaptability to practical problems.

Good continuity and integrity: The solutions on the Pareto front form a continuous and complete surface in the three-dimensional objective space without obvious solution gaps or discontinuous areas. This characteristic benefits from the gradient guiding effect of the multi-dimensional adaptive reference point adjustment, enabling the improved algorithm to comprehensively search all non-dominated solution areas in the objective space. Urban planners can select continuous decision solutions from the front surface according to different optimization priorities (e.g., prioritizing the improvement of public services in the central urban area, improving transportation in emerging development zones, and regulating population balance in peripheral functional zones), ensuring the flexibility and connectivity of planning strategies.

Excellent spatial distribution uniformity: The solutions on the Pareto front are evenly distributed in the objective space without the phenomenon of solution agglomeration in individual areas and sparse solutions in other areas, completely solving the core problem of uneven solution distribution of the traditional NSGA-III algorithm. Through the calculation of the spatial correlation density of reference point areas, the algorithm realizes the targeted allocation of search resources—splitting reference points in high-density areas to improve search accuracy and merging reference points in low-density areas to avoid resource waste, making the solution distribution highly matching the characteristics of the objective space and ensuring that high-quality non-dominated solutions can be obtained under different optimization directions.

Effective and practical reference point guidance: The adaptively adjusted reference points are evenly distributed in the objective space and closely associated with the Pareto front solutions, with corresponding non-dominated solutions for each reference point and no reference point invalidation or disconnection between solutions and reference points. At the same time, the hierarchical setting of reference points (70% for the main objective layer + 30% for the secondary objective layer) enables the algorithm to focus on the synergistic optimization of the three core objectives while taking into account the refined adjustment of each sub-indicator, making the guiding effect of reference points more in line with the actual needs of land use optimization in metro station areas and effectively avoiding the algorithm from falling into local optimal solutions.

All non-dominated solutions have high performance and feasibility: All solutions on the Pareto front are non-dominated solutions, that is, for any solution on the front, it is impossible to improve one objective value without reducing at least one other objective value. After the feasibility test of the enhanced multi-criteria environmental selection, all solutions meet the actual constraint conditions such as land use, facility supply and transportation construction, with no invalid solutions. Each solution has its own advantages in different objectives: for example, some solutions focus on the improvement of public service richness, some on the optimization of transport accessibility, and some on the regulation of population distribution balance. This provides a diversified, highly adaptive and implementable optimal decision choice for land use optimization around metro stations, which can accurately match the differentiated planning needs of different urban areas and functional zones in Xi’an.

3.4. Comparative Performance Analysis of the Improved and Traditional NSGA-III Algorithms

To evaluate the performance improvement of the improved NSGA-III algorithm through a combination of quantitative and qualitative methods, a comparative experiment was conducted between the improved algorithm and the traditional NSGA-III algorithm under exactly the same experimental conditions (the same data set, identical hardware environment, and consistent evaluation criteria). A comprehensive comparison was made from the following four core dimensions: the growth rate of objective function values, the quality of the Pareto front, the convergence efficiency of the algorithm, and the feasibility of solutions. The growth rate of objective function values was calculated as the percentage increase in the objective mean values of the Pareto front obtained by the improved algorithm relative to the traditional algorithm (Figure 7). The quality of the Pareto front was quantitatively evaluated using the uniformity index $U$ and the coverage index $C$, and the convergence efficiency was measured by the number of iterations required for the algorithm to reach stable convergence.

3.4.1. Quantitative Improvement of Objective Function Values

The experimental results show that compared with the traditional NSGA-III algorithm, the improved NSGA-III algorithm has achieved a significant quantitative improvement in all three core optimization objectives, and all objective improvements are based on the premise of satisfying actual constraint conditions. The specific growth rates are as follows:

Public service richness: the mean value of the Pareto front obtained by the improved algorithm is 0.3468, and that by the traditional algorithm is 0.3235, with a growth rate of 7.2%;

Transport accessibility: the mean value of the improved algorithm is 0.4052, and that of the traditional algorithm is 0.3701, with a growth rate of 9.5%;

Population distribution balance: the mean value of the improved algorithm is 0.8458, and that of the traditional algorithm is 0.8017, with a growth rate of 5.8%.

The average growth rate of the three objectives reaches 7.5%, fully verifying the superiority of the improved algorithm in the optimization effect of objective function values. Among them, transport accessibility has a further increased growth rate (from 8.3% to 9.5%) because the hybrid coding genetic operator of the improved algorithm has high adaptability to both continuous variables (e.g., road density, bus station density) and discrete variables (e.g., number of transfer stations) related to transportation infrastructure, and the incorporation of the ridership weighted correction factor makes the algorithm more targeted in optimizing the coupling of transportation infrastructure and actual passenger flow demand, thus achieving a better optimization effect for the transportation accessibility objective. The improvement of public service richness and population distribution balance benefits from the hierarchical guidance of reference points and the synergistic optimization of population–facility matching degree, making the algorithm take into account the spatial adaptability of facility layout and population distribution while improving the objective values.

3.4.2. Quantitative and Qualitative Improvement of Pareto Front Quality

The uniformity index $U$ and coverage index $C$ were used to quantitatively evaluate the quality of the Pareto front, where a value of $U$ closer to 1 indicates a more uniform distribution, and a value of $C$ closer to 1 indicates a wider coverage range. The experimental results show that the improved algorithm has $U=0.92$ and $C=0.95$, while the traditional algorithm has $U=0.65$ and $C=0.71$, indicating that the improved algorithm has achieved a qualitative improvement in front quality. Combined with the visualization results, the qualitative analysis of the front quality differences between the two algorithms is as follows:

Uniformity: The Pareto front obtained by the traditional NSGA-III algorithm has an obvious solution agglomeration phenomenon in the objective space, with a large number of solutions concentrated in the low-to-medium objective value area and sparse even missing solutions in the high objective value area. In contrast, the solutions on the Pareto front of the improved algorithm are evenly distributed, with sufficient non-dominated solutions in the high, medium and low objective value areas, ensuring decision choices under different optimization needs.

Coverage: The coverage range of the Pareto front of the improved algorithm is significantly larger than that of the traditional algorithm, covering the entire objective space from low to high values, and forming a continuous solution surface in the high-value range of the three objectives. However, the solution set of the traditional algorithm only covers a small part of the objective space, with obvious solution gaps in the high objective value area, which cannot provide effective decision references for high-priority optimization needs.

3.4.3. Significant Improvement in Algorithm Convergence Efficiency

The comparison results of convergence efficiency show that the traditional NSGA-III algorithm requires about 35 iterations to converge to a stable state, and there are still slight fluctuations after convergence; in contrast, the improved NSGA-III algorithm achieves stable convergence after 25 iterations, reducing the convergence time by 30%, with no fluctuation in the objective mean values after convergence and excellent stability.

The improvement in the convergence efficiency of the improved algorithm stems from the following two core factors: first, the adaptive crossover and multi-strategy mutation of the hybrid coding genetic operator improve the evolutionary search efficiency of the algorithm, enabling it to quickly lock in high-quality solution areas in the early stage of iteration; second, the real-time monitoring and parameter adjustment of the iterative dynamic regulation mechanism avoid invalid search and premature convergence of the algorithm, allowing the algorithm to approach the Pareto optimal front in a more efficient manner.

3.4.4. Substantial Improvement in Solution Feasibility

The feasibility of solutions was evaluated by counting the proportion of solutions on the Pareto front that satisfy the constraint conditions in Section 2.2.4 for both algorithms: 100% of the non-dominated solutions obtained by the improved algorithm satisfy all constraint conditions with no invalid solutions; in contrast, only 68% of the non-dominated solutions obtained by the traditional algorithm satisfy all constraint conditions, and 32% of the solutions violate constraints such as the total supply of facilities and the minimum road network density, lacking practical planning feasibility.

The core reason for the difference in solution feasibility is that the improved algorithm introduces solution pre-screening and feasibility verification of the enhanced multi-criteria environmental selection, which strictly controls the feasibility of solutions from two stages—population initialization and environmental selection—and completely eliminates invalid solutions. This makes the obtained Pareto optimal solution set directly connect with urban planning practice, solving the problem that the optimization results of the traditional algorithm are divorced from actual planning.

In summary, the improved NSGA-III algorithm is significantly superior to the traditional algorithm in the following four dimensions: objective value optimization, front quality, convergence efficiency and solution feasibility. The four key improvement strategies form a synergistic optimization effect, enabling the algorithm to solve the multi-objective land use optimization problem around Xi’an’s metro stations more accurately, efficiently and practically.

3.5. Analysis of the Pareto Optimal Solution Set

The Pareto optimal solution set obtained by the improved NSGA-III algorithm includes 80 non-dominated solutions that satisfy all constraint conditions, and each solution is a land use optimization combination of 25 metro stations. This section conducts an in-depth analysis of the optimal solution set from the following three aspects: the identification and characteristic analysis of the global optimal solution, the distribution characteristics of the optimal solution set, and the functional zoning adaptability of the solutions, to explore the intrinsic laws and practical planning value of the solution set and provide direct decision-making basis for the formulation of subsequent hierarchical optimization strategies.

3.5.1. Identification and Characteristic Analysis of the Global Optimal Solution

From the Pareto optimal solution set, the global optimal solution of this study was identified with the comprehensive evaluation criteria of the highest mean value of the three core optimization objectives, the smallest coefficient of variation among objectives, and the highest spatial correlation degree. This global optimal solution is a combination of 25 metro stations, which realizes the synergistic optimal improvement of the three objectives, and the solution has strong spatial correlation and is highly coupled with Xi’an’s urban spatial planning. It is the core reference solution for the overall land use optimization around Xi’an’s metro stations and can be used as the basic blueprint for the overall land use planning of Xi’an’s metro station areas.

• Objective Value Level of the Global Optimal Solution

The three objective values of the global optimal solution are all in the high-level range of all sample stations, and the development among the objectives is balanced with no obvious shortcomings as follows: public service richness is 0.6823 (ranking in the top 5% of the 139 stations), transport accessibility is 0.5269 (ranking in the top 7%), and population distribution balance is 0.9135 (ranking in the top 12%). The coefficient of variation among the objectives is 0.08, far lower than the coefficient of variation of 0.32 for all original solutions, fully reflecting the research goal of multi-objective synergistic optimization—the transport accessibility value is further improved due to the matching of high ridership and perfect infrastructure, which is more in line with the actual high-quality development demand of TOD model.

• Core Characteristics of the Global Optimal Solution

Complementary station combination: The global optimal solution selects a combination of stations with outstanding performance in a single objective and balanced performance in multiple objectives. For example, it includes Jixiangcun Station with the top-level public service richness, Shuangzhai Station with the highest transport accessibility, Sanqiao Station with the optimal population distribution balance, and also incorporates stations with excellent comprehensive performance such as Beidajie Station and Wulukou Station. This realizes the complementary advantages of different stations and promotes the synergistic improvement of the three core objectives.

Layout in line with urban spatial structure: The 25 metro stations in the global optimal solution are evenly distributed in Xi’an’s central urban area, emerging development zones and peripheral functional zones, accounting for 40%, 36% and 24% respectively. This is highly consistent with Xi’an’s spatial development planning of “optimization and upgrading of the core area, key expansion of emerging areas, and improvement of supporting facilities in peripheral areas”, ensuring the spatial adaptability and planning operability of the solution.

Layout logic of job-housing balance and facility synergy: All stations in the solution achieve a reasonable ratio of residential and employment population, and the layout of public service facilities is highly matched with the population scale, with no excessive agglomeration of facilities or spatial mismatch between population and facilities. This fully reflects the core connotation of the TOD model of “job-housing balance and facility synergy”.

• Core Metro Stations in the Global Optimal Solution

The core metro stations in the global optimal solution are divided into the following four categories according to functional positioning: public service core nodes, transportation hub core nodes, population balance core nodes, and comprehensive optimization core nodes. The representative stations and core characteristics of each category are as follows:

Public service core nodes: Jixiangcun Station, Wulukou Station; Jixiangcun Station is the station with the highest public service richness (0.8128) in the sample, with the density of science, education, culture, health, medical and catering facilities all at the top level, serving as the core benchmark for the improvement of public services in Xi’an;

Transportation hub core nodes: Shuangzhai Station, Yujiazhai Station; Shuangzhai Station is the station with the highest transport accessibility (0.5664) in the sample, with a high road network density, a perfect metro–bus transfer system, and a moderate distance to urban multi-cores, being the core hub of Xi’an’s rail transit network;

Population balance core nodes: Sanqiao Station, Hangtiandadao Station; Sanqiao Station is the station with the highest population distribution balance (0.9956) in the sample, with a reasonable ratio of residential and employment population, perfect supporting facilities, and no population agglomeration or sparsity, being a typical node of population distribution balance in Xi’an;

Comprehensive optimization core nodes: Beidajie Station, Zhonglou Station; Beidajie Station is the station with the best comprehensive performance in the sample (all three objectives rank in the top 3%), realizing the synergistic development of public services, transport accessibility and population distribution balance, and serving as the core benchmark for the comprehensive land use optimization of Xi’an’s metro station areas.

3.5.2. Distribution Characteristics of the Optimal Solution Set

A comparative analysis of the objective value distribution of the Pareto optimal solution set and all original solutions was conducted (Figure 8), and the following four characteristic indicators of the two sets of solutions were calculated: objective mean value, coefficient of variation, spatial correlation degree and feasibility proportion. The distribution characteristics of the optimal solution set were revealed from the following five aspects: objective value level, balance among objectives, solution diversity, spatial adaptability and feasibility, with the results shown in

Table 4. Comparison of characteristic indicators between the Pareto optimal solution set and the original solutions.

Characteristic Indicator	Pareto Optimal Solution Set	All Original Solutions	Improvement/Improvement Amplitude
Mean of Public Service Richness	0.3468	0.2192	59.58%
Mean of Transport Accessibility	0.4052	0.3586	12.94%
Mean of Population Distribution Balance	0.8458	0.7879	7.35%
Coefficient of Variation Among Objectives	0.11	0.32	65.63% reduction
Average Spatial Correlation Degree	0.87	0.52	67.31%
Feasibility Proportion	100%	76%	31.58%

.

Combined with Table 4 and the visualization results, the distribution characteristics of the optimal solution set can be summarized as follows:

Leapfrog improvement in objective value level: The mean values of the three objectives of the Pareto optimal solution set are significantly higher than those of all original solutions, among which the public service richness has the most significant improvement with an amplitude of 59.58%, effectively solving the core problem of the unbalanced distribution of public service facilities around Xi’an’s metro stations. Transport accessibility achieved a higher growth rate (12.94%) after incorporating ridership factors, which effectively optimizes the matching degree between transportation infrastructure layout and actual passenger flow demand, and solves the problem of insufficient consideration of travel demand in the original transportation accessibility evaluation. Population distribution balance has also achieved steady improvement, reflecting the effectiveness of the improved algorithm in multi-objective synergistic optimization.

Greatly improved balance among objectives: The coefficient of variation among the objectives of the optimal solution set is only 0.11, a 65.63% decrease compared with the original solutions, indicating that all solutions in the optimal solution set have achieved the balanced development of the three objectives without extreme solutions with an extremely high single objective value and extremely low other objective values. This characteristic fully reflects the core idea of multi-objective optimization and is also in line with Xi’an’s urban planning demand of “balanced development and synergistic improvement”.

Rich solution diversity and strong spatial adaptability: The optimal solution set includes 80 diversified non-dominated solutions, and the average spatial correlation degree of all solutions reaches 0.87, a 67.31% increase compared with the original solutions. According to different optimization priorities, the optimal solution set can be divided into the following three subsets: public service priority subset, transport accessibility priority subset and population distribution balance priority subset. Each subset has a clear optimization focus, and the spatial layout of the solutions is highly matched with the positioning of different functional zones in Xi’an, providing sufficient decision choices for differentiated planning.

3.5.3. Functional Zoning Adaptability Analysis of the Solutions

According to the functional zoning positioning of Xi’an’s urban spatial planning, the research area is divided into the following three categories: central urban area (Yanta, Beilin, and Lianhu), urban emerging development zones (Weiyang, Chanba, and Qujiang) and urban peripheral functional zones (Chang’an, Lintong, and Konggang). Combined with the three solution subsets of the Pareto optimal solution set, the adaptability of the solutions to functional zoning was analyzed, and the results show the following:

Public service priority subset: Including 28 non-dominated solutions, with the core optimization objective of public service richness. The stations in the solutions are mainly concentrated in Xi’an’s central urban area, which is highly adapted to the functional positioning of the central urban area of “optimizing the layout of public service facilities and improving service levels”;

Transport accessibility priority subset: Including 25 non-dominated solutions, with the core optimization objective of transport accessibility. The stations in the solutions are mainly concentrated in the urban emerging development zones, which is highly adapted to the functional positioning of emerging development zones of “improving transportation infrastructure and strengthening rail transit connection”;

Population distribution balance priority subset: Including 27 non-dominated solutions, with the core optimization objective of population distribution balance. The stations in the solutions are mainly concentrated in the urban peripheral functional zones, which is highly adapted to the functional positioning of peripheral functional zones of “undertaking the population migration from the central urban area, improving supporting facilities and realizing the balanced distribution of population”.

To enhance the practical applicability of the optimization results, this study further classifies metro stations into three typical types (CBD core stations, residential-oriented stations, and comprehensive transfer hubs) based on land use functions and TOD positioning (Xi’an Rail Transit and Urban Integration Design Guidelines (2024)), and selects representative stations to illustrate differentiated land use adjustment directions, with key before-and-after optimization indicators summarized as follows (

Table 5. Key optimization measures by station type.

Station Type	Representative Station	Before Optimization (Key Indicators)	Core Land Use Adjustment Measures	After Optimization (Key Indicators)
CBD Core Station	Zhonglou Station	Public service richness: 0.6215; population distribution balance: 0.7236; commercial land ratio: 65%; public service land ratio: 12%	1. Reduce commercial land ratio to 55%, increase public service land to 20%; 2. add community medical and cultural facilities; 3. optimize pedestrian connection between commercial complexes and metro entrances	Public service richness: 0.7892 (↑ 27%); population distribution balance: 0.8561 (↑ 18.3%); transportation accessibility: 0.5235 (↑ 2.5%)
Residential-Oriented Station	Qujiangchi XI Station	Public service richness: 0.1896; transportation accessibility: 0.3015; residential land ratio: 78%; public service land ratio: 8%	1. Reduce residential land ratio to 70%, increase public service land to 15%; 2. add primary school and community medical center; 3. improve bus station density and non-motor vehicle facilities	Public service richness: 0.4218 (↑ 122.5%); Transportation accessibility: 0.3987 (↑ 32.2%); Population distribution balance: 0.9105 (↑ 2.0%)
Comprehensive Transfer Hub	Shuangzhai Station	Public service richness: 0.2568; population distribution balance: 0.7512; transportation land ratio: 45%; commercial service land ratio: 15%	1. Reduce transportation land ratio to 35%, increase commercial service land to 25%; 2. add catering, retail and leisure facilities; 3. arrange affordable housing to balance residential-employment population	Public service richness: 0.4897 (↑ 90.7%); population distribution balance: 0.8693 (↑ 15.7%); transportation accessibility: 0.5789 (↑ 2.2%)

):

The Pareto optimal solution set provides targeted land use optimization schemes for different types of stations. CBD core stations focus on balancing commercial functions and public services; residential-oriented stations prioritize supplementing supporting facilities and improving transportation convenience; and comprehensive transfer hubs emphasize land use intensification and functional diversification. All measures are compatible with Xi’an’s urban planning constraints and have strong operability for practical planning implementation.

4. Discussion

This section conducts an in-depth interpretation of the core experimental results, combines the research findings with the actual background of land use planning around Xi’an’s metro stations and the core connotation of the TOD model, and clarifies the theoretical and practical implications of the research. On this basis, based on the characteristics of the Pareto optimal solution set and its functional zoning adaptability, a targeted and operable hierarchical land use optimization strategy for Xi’an’s urban planning practice is proposed according to optimization priorities, implementation timelines and functional zones. Meanwhile, a multi-dimensional policy guarantee system is formulated to ensure the effective implementation of the optimization strategy. Finally, the inherent limitations of the current research are systematically analyzed, and feasible future in-depth research directions are proposed to provide a more comprehensive scientific basis for the integrated development of urban rail transit and land use.

4.1. Core Research Findings

4.1.1. Necessity and Intrinsic Logic of Multi-Objective Optimization for Metro Station Land Use

There is a weak positive correlation between transportation accessibility and population distribution balance, yet the driving effect of the former is limited. This is because the supporting public services and employment facilities in emerging development zones and peripheral functional zones have not been improved in a synchronous manner, meaning that the enhancement of transportation conditions fails to effectively guide the population to disperse to non-core areas. Single-objective optimization will give rise to a series of urban development problems. Only by adopting a multi-objective optimization method to balance the mutual restriction and synergy among the three core objectives can we realize the coordinated improvement of public service supply, transportation convenience and the spatial distribution of population, which is also an inevitable choice for the scientific optimization of land use around metro stations in Xi’an and other rapidly urbanizing central cities in western China. The intrinsic logic of multi-objective optimization is not to pursue the extreme improvement of a single objective, but to achieve the synergistic balance and spatial adaptability among all objectives. Through the optimal layout of land use, the improvement of transportation accessibility is turned into a driving force for the agglomeration of public services, and the synergistic development of public services and transportation serves as a guiding force for the rational distribution of the population. Ultimately, the spatial coupling and synergistic development of the “transportation-facilities-population” system is realized, which is highly consistent with the core connotation of the TOD model featuring “public transport orientation, job-housing balance and facility synergy”.

4.1.2. Effectiveness and Core Mechanism of the Improved NSGA-III Algorithm

The improved NSGA-III algorithm has achieved a 5.8%~8.3% increase in objective function values compared with the traditional algorithm and has also made significant improvements in Pareto front quality, convergence efficiency and solution feasibility, which fully verifies the scientificity and effectiveness of its four key improvement strategies. These four strategies form a synergistic and progressive core mechanism that jointly drives the improvement of algorithm performance. The multi-dimensional adaptive reference point adjustment acts as the “direction navigation” of the algorithm, which solves the defect that the fixed reference points of the traditional algorithm cannot adapt to the dynamic distribution of the objective space, provides an accurate search direction for the algorithm, and ensures the uniformity and coverage of solution distribution. The real-integer hybrid coding genetic operator is the “power core” of the algorithm, which is designed for the discrete + continuous decision variable characteristics of metro station land use optimization, greatly improving the algorithm’s search efficiency and the optimization effect of objective values. The enhanced multi-criteria environmental selection serves as the “screening gate” of the algorithm, constructing a multi-dimensional screening system that completely eliminates invalid solutions based on feasibility and screens out high-quality, implementable and spatially adaptive solutions, solving the problem that the optimization results of the traditional algorithm are divorced from actual planning. The dynamic regulation of algorithm iteration is the “intelligent regulation” module of the algorithm, which grasps the algorithm’s convergence state in real time through the convergence monitoring index and dynamically adjusts parameters, effectively avoiding premature convergence, oscillation and invalid search, and realizing the balance between the algorithm’s “global exploration” and “local exploitation”. The four improvement strategies perform their respective functions and form a synergistic effect, comprehensively improving the algorithm’s performance from the following four dimensions: direction guidance, evolutionary search, solution quality control and stability guarantee. This makes the algorithm not only have theoretical innovation in the framework of multi-objective evolutionary algorithms but also have strong practical applicability and operability in solving practical urban planning problems. It can be extended to the multi-objective optimization research of land use around metro stations in other cities and also provide an algorithm reference for other multi-objective optimization problems in the field of urban planning.

4.1.3. High Coupling Between Optimization Results and Xi’an’s Urban Spatial Planning

The spatial distribution characteristics of the Pareto optimal solution set, the layout of core stations and the functional zoning adaptability of the solution subsets obtained in this study are all highly consistent with Xi’an’s urban development planning, spatial layout features and functional zoning positioning, which highlights the strong practical value and spatial adaptability of the research results and also verifies the scientificity of the constructed multi-objective optimization model and improved algorithm. The supplementary type-based typical cases and optimization indicator comparison further refine the application scenarios of the Pareto solution set, making the theoretical optimization results directly applicable to station-specific land use adjustment and effectively bridging the gap between model output and planning practice. This high coupling is reflected in the following three aspects: first, the core stations are consistent with key planning areas, as all core stations in the optimal solution set are key development nodes clearly defined in Xi’an’s urban planning, which is highly matched with Xi’an’s spatial development pattern of “one core, multiple centers and global synergy”; second, the solution subsets are consistent with functional zoning positioning, where the public service priority subset, transport accessibility priority subset and population distribution balance priority subset correspond to Xi’an’s central urban area, emerging development zones and peripheral functional zones respectively, which is highly consistent with the core development needs of each functional zone and can be directly used as a decision reference for land use optimization in the corresponding areas; third, the optimization directions are consistent with Xi’an’s TOD planning, and the three core optimization objectives of the research are highly unified with the core content of Xi’an’s metro TOD planning, providing it with quantitative, accurate and implementable decision support and making up for the lack of quantitative optimization models and algorithm support in the current TOD planning.

4.1.4. Core Path of Land Use Optimization Around Xi’an’s Metro Stations Under the TOD Model

Combined with the core research findings and the essential connotation of the TOD model, the core path for land use optimization around Xi’an’s metro stations can be summarized as taking the improvement of transport accessibility as the foundation, the synergistic layout of public service facilities as the core, and the job-housing balance and the spatial balanced distribution of population as the goal, so as to realize the spatial coupling and synergistic development of the “transportation-facilities-population” system. This path is not only suitable for Xi’an but also provides a reference for other central cities in western China with unbalanced urban spatial development and rapid rail transit expansion and can be used for reference by rapidly urbanizing cities in developing countries with similar characteristics after appropriate local adaptation. Instead of simply increasing road network density, it prioritizes improving the multi-modal transportation connection of “metro + ground bus + non-motorized vehicles”, optimizing the transportation links between stations and urban multi-cores, and enhancing the connectivity and transfer efficiency of the road network, thus making transportation improvement the foundation of land use optimization. The core level centers on the synergistic layout of public service facilities. Based on transport accessibility, it carries out the intensive layout and grade upgrading of public service facilities in accordance with the population scale and functional positioning of each station, creating an integrated development model of “transportation hub + public service center”. Meanwhile, it promotes the extension of public service resources to emerging development zones and peripheral functional zones to avoid the excessive agglomeration of resources in the core area. The target level aims at job-housing balance and the spatial equilibrium of population. It guides the dispersion of residential and employment population to non-core areas through the synergistic development of transportation and public services and optimizes the layout of residential and commercial land according to the population carrying capacity of each region to avoid excessive population agglomeration or sparsity, ultimately achieving the spatial balanced distribution of population. This path not only conforms to the core connotation of the TOD model of “public transport orientation” but also fits the actual development of Xi’an. It clarifies the implementation ideas for land use optimization around the city’s metro stations and lays a foundation for the formulation of subsequent hierarchical optimization strategies.

4.2. Targeted Land Use Optimization Suggestions for Metro Stations

4.2.1. Hierarchical Land Use Optimization Strategy

Combined with the characteristics of the Pareto optimal solution set, the classification of core optimized stations and the functional zoning adaptability of the solutions, this study proposes a **zoned, prioritized and phased** hierarchical land use optimization strategy for the areas around Xi’an’s metro stations. The research area is divided into the following three sectors: the public service improvement zone, the transport accessibility improvement zone, and the population distribution balance regulation zone. Adhering to the principle of “focusing on key priorities, implementing classified measures and advancing in phases”, the strategy is highly aligned with Xi’an’s urban planning positioning of “optimization of the core area, expansion of emerging areas and population bearing of peripheral areas”. For each zone, clear definitions of core functional positioning, optimization objectives, core stations, specific measures and implementation timelines are provided, while also ensuring the synergistic improvement of multiple objectives to avoid the negative impacts of single-objective optimization. The public service improvement zone serves as Xi’an’s core public service area, with core stations in the central urban area as optimization objects and maximization of public service richness as the core objective. It aims to create a 15 min living/medical service circle by intensively arranging science, education, culture and health, medical and living service facilities and synergistically optimizing the integration of public services and transportation and is implemented as a short-term optimization priority with a 1–2 year timeline. The transport accessibility improvement zone is the core area for Xi’an’s urban spatial expansion, centered on stations in emerging development zones with the maximization of transport accessibility as the core objective. It focuses on improving the road network, deepening the integration of rail transit and public transport, coordinating transportation infrastructure construction with land use, and building an intelligent transportation system, and is implemented as a medium-term optimization priority with a 2–3-year timeline. The population distribution balance regulation zone acts as Xi’an’s core population bearing area, with stations in peripheral functional zones as the main objects and the maximization of population distribution balance as the core objective. It promotes job-housing balance and undertakes population migration from the core area by optimizing the mixed layout of residential, commercial and industrial land, synchronously constructing supporting public service facilities, continuously improving transportation conditions, and balancing population agglomeration with ecological protection, and is implemented as a long-term optimization priority with a 3–5-year timeline.

4.2.2. Policy Guarantee Measures for the Implementation of Optimization Strategies

To ensure the smooth implementation of the hierarchical land use optimization strategy around Xi’an’s metro stations and the long-term effectiveness and stability of the optimization results, this study establishes a sound policy guarantee system from the following four dimensions: planning coordination, investment and financing, monitoring and evaluation, and policy support, forming a promotion mechanism with multi-department linkage and whole society participation to facilitate the integrated development of Xi’an’s metro and land use. First, a multi-department collaborative planning and implementation mechanism is established. A leading group for the integrated planning of metro and land use, led by Xi’an municipal government and participated by multiple functional departments, is set up to break departmental planning barriers. The optimal solution set and optimization strategy of the research are incorporated into statutory planning, departmental responsibilities are clarified and included in the assessment system to ensure the implementation of the planning. Second, diversified investment and financing channels for public service and transportation facilities are expanded. The model of “government-led + social capital participation” is adopted, the PPP and REITs models are introduced with preferential policies, and the comprehensive development model of “metro + land” is explored to realize a virtuous circle of metro construction, land development and facility supporting. Third, a long-term monitoring and dynamic evaluation system for optimization effects is constructed. A real-time monitoring platform for land use around metro stations is built to integrate multi-source data for real-time monitoring of the implementation effect of the optimization strategy. A dynamic evaluation index system centered on the three core objectives is established for annual evaluation, forming a closed-loop management mechanism of “monitoring—evaluation—adjustment”. Fourth, targeted land and industrial policy support is issued. The supply of various core land around metro stations is prioritized and the land supply process is optimized. Fiscal, tax and talent policy support is given to industries introduced in emerging and peripheral functional zones, and population agglomeration incentive policies are launched to enhance the population attractiveness of peripheral functional zones, providing policy support for the implementation of the optimization strategy.

5. Conclusions

This study takes 139 operational metro stations in Xi’an in 2024 as the research object, focusing on prominent problems such as the unbalanced distribution of public services, insufficient transportation connection, uneven population density, and the disconnection between land use and urban planning around metro stations in rapidly urbanizing central cities in western China. Combining the urban development characteristics of Xi’an and the core requirements of TOD planning, a refined multi-objective land use optimization model with public service richness, transport accessibility and population distribution balance as the three core objectives is constructed, with parameters such as functional zone adaptation factors, spatial attenuation factors and integrated residential-employment population introduced, and multi-dimensional practical planning constraints set. Aiming at the defects of the traditional NSGA-III algorithm, a hierarchical adaptively improved NSGA-III algorithm with the following four key improvements is proposed: multi-dimensional adaptive reference point adjustment, real-integer hybrid coding genetic operator design, enhanced multi-criteria environmental selection, and dynamic regulation of algorithm iteration. The improved algorithm is applied to solve the multi-objective optimization problem, and a Pareto optimal solution set with uniform distribution, good coverage and 100% feasibility is obtained. Based on the optimal solution set, targeted and operable hierarchical land use optimization strategies and supporting policy guarantee measures are proposed, which provide scientific and targeted decision support for the land use optimization of Xi’an’s metro station areas and the integrated development of urban rail transit and land resources in Xi’an. More importantly, the research framework and methodological system constructed in this study provide a replicable and promotable reference for the TOD practice and land use optimization of metro station areas in other rapidly urbanizing central cities in China and can be used for reference by rapidly urbanizing cities in developing countries worldwide with the characteristic of rapid rail transit expansion after local adaptation and adjustment.

This study achieves targeted results in TOD-oriented land use optimization of Xi’an’s metro stations, but there are still limitations to be improved:

The research sample is limited to 139 operational stations in 2024, excluding under-construction and planned stations; single-year cross-sectional data fail to reflect the dynamic evolution of land use with metro network expansion. The optimization objective system focuses on public services, transportation accessibility and population balance, without incorporating ecological protection and economic benefit indicators. The improved NSGA-III algorithm is tailored to Xi’an’s characteristics, and its adaptability to ultra-large-scale samples and cross-city application needs further verification.

Future research will focus on the following three directions: first, expand the sample to include planned stations and multi-period data to build a dynamic optimization model; second, enrich the objective system by adding ecological and economic indicators to meet sustainable development needs; and third, optimize the algorithm for cross-city verification and strengthen the combination of model results and practical planning projects.