Optimization of Electric Vehicle Charging Station Location Distribution Based on Activity–Travel Patterns

Abstract

With the rapid expansion of the electric vehicle (EV) market, optimizing the distribution of charging stations has attracted increasing attention. Unlike internal combustion engine vehicles, EVs are typically charged at the end of a trip rather than during transit. Therefore, analyzing EV users’ charging preferences based on their activity–travel patterns is essential. This study seeks to improve the operational efficiency and accessibility of EV charging stations in Lanzhou City by optimizing their spatial distribution. To achieve this, a novel multi-objective optimization model integrating NSGA-III and TOPSIS is proposed. The methodology consists of two key steps. First, the NSGA-III algorithm is applied to optimize three objective functions: minimizing construction costs, maximizing user satisfaction, and maximizing user convenience, thereby identifying charging station locations that address diverse needs. Second, the TOPSIS method is employed to rank and evaluate various location solutions, ultimately determining the final sitting strategy. The results show that the 232 locations obtained by the optimization model are reasonably distributed, with good operational efficiency and convenience. Most of them are distributed in urban centers and commercial areas, which is consistent with the usage scenarios of EV users. In addition, this study demonstrates the superiority in determining the distribution of charging station locations of the proposed method. In summary, this study determined the optimal distribution of 232 EV charging stations in Lanzhou City using multi-objective optimization and ranking methods. The results are of great significance for improving the operational efficiency and convenience of charging station location optimization and offer valuable insights for other cities in northwestern China in planning their charging infrastructure.

1. Introduction

As global reliance on non-renewable energy sources grows, coupled with the associated energy crisis, the development of new energy vehicles has become a critical global concern [1,2]. The widespread adoption of electric vehicles (EVs) not only reduces dependence on petroleum resources but also promotes the use of renewable energy [3]. With the advancement of electric vehicles, charging stations have become essential supporting infrastructure. A rational layout and optimized services for these stations not only alleviate urban traffic pressures but also contribute to improving the quality of the urban environment [4]. Moreover, their strategic deployment plays a pivotal role in achieving carbon neutrality and fostering the growth of the new energy vehicle industry.

Unlike internal combustion engine vehicles, the charging behavior of EVs typically occurs at the end of the user’s trip, rather than during transit [5]. As a result, the spatial distribution of refueling stations for internal combustion engine vehicles does not align with the charging needs of most EV users [6]. Therefore, it is necessary to analyze the charging willingness of electric vehicle users based on their travel patterns. This analysis can help with the optimization of charging station locations, leading to the development of a regional charging station layout. Such efforts will further accelerate the adoption and promotion of electric vehicles while contributing to the sustainable development of urban transportation.

In real-world applications, optimizing the location of charging stations requires addressing multiple conflicting objectives. Existing studies on this issue can be divided into two categories for solving the multi-objective optimization problem related to charging station placement. The first category transforms the multi-objective optimization problem into a single-objective optimization problem under multiple constraints [7,8]. However, treating the optimization objectives as constraints by specifying the boundaries may limit the solution set space and thus lose the optimal solution [9]. The second category uses a multi-stage strategy to integrate multiple optimization objectives and use genetic algorithms to obtain the optimal solution [10,11]. However, the integration of multiple objectives will be difficult to achieve when the optimization objectives conflict with each other. Algorithms based on Pareto frontiers provide a way to deal with multi-objective optimization problems, and the NSGA-III algorithm proposed by Deb and Jain [12] is an advanced multi-objective genetic algorithm. Although NSGA-III has been successfully applied to the facility location optimization problem [13,14,15], there are fewer studies using this algorithm to solve the charging station location multi-objective optimization problem.

Lanzhou, as a key transportation hub in northwestern China, plays a crucial role in connecting various regions of the country. Situated along the upper reaches of the Yellow River and surrounded by mountains, Lanzhou’s strategic location has historically made it an important gateway linking inland China with Central Asia, West Asia, and Europe. The adoption of EVs in Lanzhou has been gaining momentum as part of the city’s efforts to address air pollution and promote sustainable urban development. This transformation is essential for positioning Lanzhou as a model for other cities in northwestern China to follow, demonstrating the benefits of integrating sustainable practices into urban development. However, challenges such as ensuring equitable distribution of charging stations and addressing the high initial costs of EVs still need to be addressed for wider adoption in Lanzhou.

Therefore, this paper proposes a multi-objective optimization model based on the NSGA-III algorithm and the TOPSIS method for the optimization problem of electric vehicle charging station location distribution in Lanzhou City, to achieve the minimization of the construction cost, the maximization of the user satisfaction and the maximization of the convenience of the charging station. These objectives reflect the comprehensive consideration of economic benefits, user experience and social benefits, which are the key factors to achieve sustainable urban transportation development.

2. Related Work

2.1. Electric Vehicle Charging Station Location Optimization

Strategically locating charging stations can enhance the convenience of electric vehicles, promote the use of renewable energy, and mitigate environmental impacts [16]. Shoushtari et al. [17] proposed a methodology for optimizing the siting of EV charging stations from a macro perspective, taking into account various factors such as urban infrastructure, accessibility, demand patterns, and operating costs. The goal is to improve accessibility, reduce costs, and contribute to the overall growth of the EV market through the strategic placement of charging stations. Furthermore, Mastoi et al. [18] provided a series of insights and conclusions by synthesizing and analyzing the infrastructure of EV charging stations, the impacts of policies, and future trends. Additionally, in determining the optimal locations for EV charging stations, Men and Zhao [19] introduced a hybrid preference optimization approach that considers the perspectives of grid operators, charging station owners, and electric vehicle users. This approach offers a novel perspective for addressing the multiple uncertainties encountered in practical engineering.

However, these studies on the layout optimization of EV charging stations lack persuasiveness and consistency. Firstly, the methodological approaches employed in these studies are not thoroughly compared or benchmarked against other established optimization techniques, making it difficult to assess their relative performance and effectiveness. Secondly, the handling of uncertainties, such as fluctuating demand patterns and evolving user preferences, is not consistently addressed, leading to concerns about the robustness of the proposed solutions. Lastly, the comparisons of the results across these studies are limited, hindering our ability to synthesize the insights and draw overarching conclusions about the state of the art in this research domain.

A large body of research has demonstrated that developing an effective model can significantly address the optimization of EV charging station locations [20,21]. Pal et al. [22] strategically planned EV charging stations from the perspective of the power system network, a framework was proposed that integrates superimposed distribution and road networks. This method showed considerable improvements in energy loss, voltage deviation, and land costs while managing EV-related uncertainties through a two-moment point estimation method. It addressed the optimization problem using differential evolution and Harris Hawk optimization techniques. This approach effectively reduced energy losses and voltage deviations during power transmission while maximizing the number of EVs served. Kathiravan and Rajnarayanan [23] used a novel approach, the Arithmetic Optimization Algorithm (AOA), to optimize the optimal layout of EV charging stations and minimize line losses in the power grid using a combination of two methods of Distributed Generation. It was shown that the EV charging station placement determined by the AOA method can significantly improve the system voltage configuration, which is essential for the stable operation of the grid. Liu et al. [24] proposed an agent-based charging station placement model to incorporate demand uncertainty by simulating the behavior of BEV users. A solution algorithm based on Random Embedded Bayesian Optimization was developed, which significantly improved the computational efficiency and solved the charging station location problem for the first time in a large-scale real-world setting using agent simulation. However, in solving the charging station layout optimization problem, in addition to reducing losses in the process of power transmission system, the service and reach of EV charging station locations can also be considered.

Although various methods have been employed to optimize the placement of EV charging stations, numerous challenges remain, particularly when accounting for multiple factors and uncertainties.

2.2. Optimization Algorithms

To address the complexities of multi-factor optimization and uncertainty handling highlighted above, researchers have developed and refined various sophisticated algorithms, as discussed in this section. Aljaidi et al. [25] used the Particle Swarm Optimization (PSO) algorithm to address the optimization problem of determining the optimal locations for EV charging stations in a smart city. The article formulated this location problem as a mixed-integer programming challenge. The efficiency and effectiveness of the PSO algorithm are demonstrated through comparisons with the genetic algorithm (GA) and the greedy algorithm. Wu et al. [26] proposed a time-series optimal layout model based on supply and demand equilibrium by considering multiple factors and stakeholders to solve the problems of EV charging stations and EVs construction sequence, including the government’s industrial planning objectives, CS operators’ profits and EV consumers’ charging needs, and constructed an urban travel dynamics index for EV customers and a CS adaptability index. Yi et al. [27] proposed an improved geographic PageRank model that estimates EV charging demand based on trip origin-destination (OD) data and social dimension features, and uses the Capacity Maximum Coverage Location Problem model to plan the layout of charging stations in order to maximize the utilization of charging stations. Hamed et al. [28] employed the Maximum Coverage Location Model to optimize charging demand. Notably, they were the first to utilize a stochastic parametric approach to simulate charging demand across different areas. This method accounted for variations in charging speed and power across different levels of charging technology, offering policymakers valuable empirical support for electric vehicle charging station (EVCS) planning and the promotion of advanced charging technologies.

In order to address the challenges of siting and capacity planning for EV charging stations and to promote the adoption of electric vehicles while alleviating users’ mileage anxiety, Zhu et al. [29] proposed a multi-objective optimization framework. This framework integrates traffic conditions and coordinated charging demand considerations. The Monte Carlo method is employed for charging demand modeling, and a multi-objective dynamic binary particle swarm optimization algorithm is utilized to enhance optimization efficiency. The above studies provide different perspectives and effective algorithms in a deeper understanding of the electric vehicle charging station location optimization problem. However, it is crucial to clarify the optimization objective to achieve a truly ideal charging station layout.

When planning the locations of EV charging stations, defining the optimization objective is crucial. This ensures not only the achievement of optimal system performance and benefits but also the fulfillment of the needs and expectations of various stakeholders. To address the location selection problem for EV charging stations for EVs, Zhang et al. [30] proposed a hybrid approach that integrates geographic information systems (GIS) and Bayesian networks, which is of great practical value for urban planners and policymakers in promoting sustainable urban development and enhancing the acceptance of EVs. Zhou et al. [31] proposed a multi-objective optimization framework for siting and capacity planning of urban hydrogen refueling stations by integrating total investment cost, hydrogen demand coverage, risk factor, and environmental factors. This study provides a scientific framework that serves as an important reference for government and business decision makers in urban hydrogen fuel cell vehicle infrastructure planning. In order to improve charging station operational efficiency and user satisfaction, Sai et al. [32] jointly optimized the infrastructure deployment and fleet operation of an electric car sharing system to maximize profitability by developing a mixed-integer optimization model. The study considers the diverse needs of users and incorporates multiple types of electric vehicles into the problem formulation to improve operational efficiency and user satisfaction. Falchetta and Noussan [33] developed a comprehensive bottom-up analysis with the optimization objective of improving the balance of the European electric vehicle charging network. The study shows that although the network has been expanded, inter- and intra-country imbalances still exist and the large-scale rollout of EVs in Europe remains a huge challenge. Li et al. [34] proposed a two-layer online multi-objective optimization framework which solves online multi-objective optimization problems based on the Target-Based Online Dynamic Weighting Algorithm. The article also proposes a method to transform a non-convex multi-objective optimization problem into a convex optimization problem, as well as proving the equivalence of these two problem forms. Clarifying the optimization objective in EV charging station location planning is essential, as it directly impacts system performance, stakeholder satisfaction, and technological development. Selecting an appropriate model is particularly important to enhance the accuracy and effectiveness of the optimization process.

The continuous innovation of optimization algorithms is crucial for addressing the EV charging station location problem, particularly in the context of multi-objective optimization and the consideration of uncertainty factors.

2.3. Genetic Algorithms

To determine the optimal layout for EV charging stations, genetic algorithms have proven effective in addressing multi-objective optimization problems. Chen et al. [35] proposed a multi-objective optimization framework that begins with the use of DesignBuilder for energy simulation and orthogonal experiments to generate a sample dataset. This dataset was then utilized with Least Squares Support Vector Machines to develop a predictive model that correlates building envelope characteristics with energy consumption. Finally, a non-dominated sequential genetic algorithm-II (NSGA-II) is employed to conduct multi-objective optimization, identifying the optimal solutions for energy consumption and thermal comfort. Lu et al. [36] developed a two-stage hybrid decision-making framework for the configuration of an off-grid multi-energy microgrid that takes into account the uncertainty of renewable energy resources and load demand, and uses an NSGA-II modified by reinforcement learning in solving the configuration optimization problem, which does not only takes into account the economics, but also takes energy supply reliability into account. Luan et al. [37] developed an improved multi-objective land use optimization framework to optimize land use structure and predict ESV by achieving a balance between economic exploitation and ecosystem service value enhancement, combining NSGA-II with a patch-generated land use simulation model. Cao et al. [38] proposed an approach that combines Bayesian Optimization, Natural Gradient Boosting, and NSGA-III as an improved hybrid intelligent algorithm, which performed well in solving the multi-objective optimization problem of concrete mixing proportions with a balance between performance, cost, and carbon emission. However, it is unknown as to whether it can be applied to the electric vehicle charging station location optimization problem.

Studies have demonstrated that genetic algorithms offer significant advantages in addressing multi-objective optimization problems, particularly in the optimization of EV charging station locations. Numerous studies have successfully employed genetic algorithms to enhance the layout of EV charging stations. Jordán et al. [39] focused on utilizing genetic algorithms alongside agent-based simulation to determine the optimal arrangement of EV charging stations in cities. Zhou et al. [40] addressed the problems of insufficient numbers, uneven distribution, and high costs of EV charging stations by developing a total social cost model. Using Ireland as a case study, they applied genetic algorithms to optimize the placement of charging stations effectively. Additionally, to address the challenges of fast charging at EV stations, Shuai et al. [41] proposed an improved genetic algorithm by combining the simulated annealing algorithm with an adaptive crossover operator, providing an effective solution for large-scale optimization problems. Zhang et al. [42] made a pioneering effort to incorporate flood resilience into the planning process for EV charging stations. Their study introduced a framework that combines the NSGA-III with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to optimize the locations of charging stations while considering the extent of flood inundation, thereby minimizing the impacts of flooding hazards and maximizing the socio-economic benefits of the charging station network. Kumar et al. [43] proposed an integrated planning framework that combines Queueing Theory with the NSGA-II to rationalize the deployment of solar and battery-assisted EV Quick Charging Stations. This framework was designed to optimize the placement of charging stations to better accommodate EVs, enhance the utilization rate of charging infrastructure, and minimize total investment and operating costs.

Given the review of existing studies, the necessity for genetic algorithms in the multi-objective optimization of charging station locations is emphasized. Therefore, this study will consider the costs associated with constructing charging stations, as well as user satisfaction and convenience. Based on these factors, various charging station locations will be ranked and evaluated. The optimal distribution of EV charging stations will be determined through a multi-objective optimization strategy that combines the NSGA-III algorithm with the TOPSIS method.

3. Study Area and Methodology

3.1. Study Area

Lanzhou City, the capital of Gansu Province in northwestern China, holds significant geographical importance and has made notable progress in promoting new energy vehicles and developing charging infrastructure. According to the Statistical Bulletin on the Promotion and Application of New Energy Vehicles in Lanzhou City in the fiscal year 2019, by the end of 2019, Lanzhou had established 172 EV charging stations. These included a total of nearly 2000 universal voltage sockets, comprising 27 fast charging stations and 145 slow charging stations. As of May 2023, the number of EV charging stations in Lanzhou has exceeded 400, and these charging stations are generally equipped with intelligent management systems to provide convenient and efficient charging services.

The Lanzhou Municipal Government has clearly put forward the Plan for Promoting the Popularization and Application of New Energy Vehicles in Lanzhou City, which plans the layout and construction targets of EV charging stations in the next five years, in order to meet the charging needs of different types of EVs and to promote the upgrading and renovation of charging facilities. Lanzhou has a total area of 16,504.5 square kilometers, with terrain ranging from the lofty mountains in the south to the vast plains in the north. As an important transportation hub and regional center city in Northwest China, Lanzhou has convenient transportation with several expressways, important railroad hubs, and Lanzhou Zhongchuan International Airport. In addition, the city’s internal bus system, cab services, and Metro Lines 1 and 2 provide convenient travel options for citizens and visitors. Such geographic and transportation advantages, coupled with an ever-improving network of charging stations, make Lanzhou an important demonstration area for the promotion of new energy vehicles.

This study focuses on the Anning, Qilihe, and Chengguan districts of Lanzhou (Figure 1). The three districts were selected as the focus of this study for several key reasons. Firstly, these districts represent the core urban area of Lanzhou, accounting for the highest population density and concentration of existing EV charging infrastructure within the city. Secondly, these three districts exhibit diverse urban typologies, ranging from the densely populated city center (Chengguan) to the more suburban areas (Anning and Qilihe), allowing us to capture a representative cross-section of the city’s charging needs and challenges.

3.2. Methodology

This study proposes an optimization framework for EV charging station placement based on the Non-dominated Sorting Genetic Algorithm-III (NSGA-III) algorithm and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to improve the layout and construction of EV charging stations to meet the specific requirements of investors and end users (Figure 2). An exhaustive needs assessment was conducted in the Anning, Qilihe, and Chengguan districts of Lanzhou, including site visits and information collection on parking facilities, residential areas, public green spaces, and dining areas. This information helped reveal the specific needs of EV users and investors. For investors, the primary concern is the overall investment expenditure associated with charging stations, which includes various costs such as land acquisition, equipment procurement, and power supply. Additionally, the practicality and accessibility of the charging station are crucial for attracting consumers, thereby maximizing its utilization and ensuring a return on investment. For end-users, reducing charging wait times and improving the overall user experience are key priorities. Emphasis is placed on the location and accessibility of charging stations, as well as on factors such as station design, service quality, and the availability of fast-charging technology, all of which significantly enhance the perceived user experience.

After synthesizing the requirements, a detailed implementation strategy was developed covering the principles of respecting land saving, prioritizing the location of existing parking facilities such as shopping centers and parks, and avoiding the placement of charging stations near major traffic roads. Based on this, three objective functions, including reducing construction costs, improving user satisfaction, and increasing the convenience of charging stations, were established to reach the optimization of EV charging station siting and construction. By integrating the NSGA-III algorithm with TOPSIS technology, this study enhances the scientific rigor and accuracy of charging station layout optimization. Additionally, it ensures an optimal balance among multiple objectives, offering an innovative approach to charging station planning. This contribution significantly supports the advancement of sustainable urban transportation.

3.2.1. Identification of Demands

In the planning and construction of electric vehicle charging stations, user demand analysis is a crucial core aspect that involves two main groups: investors and users. This study aims to deeply understand the unique needs of these two groups of users and adequately convert these needs into practical siting and construction strategies to maximize cost-effectiveness and user satisfaction.

The main needs of users are centered on the accessibility, convenience, and experience of using the charging station. The core consideration of this study is the proximity principle, where users tend to choose charging stations that are closer to them. Therefore, the location of the charging station is crucial for users and needs to be laid out near locations that users frequent, such as residential areas, shopping malls, and parks, to ensure that users can charge conveniently [33,44]. The design and service of the charging station are also key to enhancing the user experience, and the strategy of fast charging rather than slow charging can significantly reduce the charging waiting time.

In order to gain a deeper understanding of user needs, information on parking lot, residential, park, and restaurants were collected. These data not only reflect the potential demand points for charging stations, but also reveal users’ travel patterns and parking habits. Based on this data, we established the goals of maximizing satisfaction and maximizing convenience. The Euclidean distance model was used to evaluate and optimize the selection of charging station locations, while optimizing the location layout of charging stations to be close to the locations where users spend most of their time, such as residences, workplaces, entertainment, and shopping centers [45].

For investors, the construction costs of charging stations are a major consideration. These costs cover a wide range of aspects such as land costs, equipment acquisition, power supply, infrastructure construction, and labor and operating costs. During the planning stage, it is essential not only to minimize costs but also to ensure that charging stations are both functional and easily accessible. This approach enhances user adoption, ultimately contributing to a higher return on investment. Considering factors such as site selection, equipment configuration, and energy efficiency is essential for maximizing cost-effectiveness. Relevant studies have shown that the construction and operation costs of EV charging stations can be significantly reduced through technological innovation and adjustment of market mechanisms.

3.2.2. Identification of Objectives

The core objectives include minimization of construction costs, maximization of user satisfaction, and maximization of charging station convenience. These objectives reflect the comprehensive consideration of economic benefits, user experience, and social benefits, and are key factors in realizing sustainable urban transportation development. The notation of the objective function formula is illustrated in

Table 1. Explanation of symbols.

Symbol	Definition
$j$	Charging Station Candidate Site Number
$J$	Charging station candidate site set
$O$	Fixed investment costs, including land, building and other costs
$N$	Number of charging piles
$r_0$	Discount rate
$n$	Service life of the charging station
$\alpha$	Proportionality coefficient between operation and maintenance cost and construction cost
$D_1$	Construction cost
$D_2$	Maintenance cost
$\beta$	Unit price of purchasing charging piles
$\mu$	Ratio between the cost of purchasing equipment such as charging piles and constructing charging stations and the return on investment
$F_2$	Distance Time Satisfaction
$d_{ij}$	Distance from demand point to charging station candidate point
$d_{\min }$	Minimum distance acceptable to users
$d_{\max }$	Maximum distance acceptable to users
$x_i$	If 1, the location is selected as a charging station construction site; if 0, the opposite is true
$p_j$	Average dwell time at destination j
$d_{ij}$	Euclidean distance from the new charging station i to the destination j

.

Construction cost minimization

Construction cost considers the cost over time and discounts it to the current value. The construction cost is calculated as shown in Equation (1).

$$D_1=\sum _{j=1}^J(O+\beta N_j+\mu N_j^2){\displaystyle \frac{r_0{(1+r_0)}^n}{{(1+r_0)}^n-1}}$$

(1)

where $O$ is the fixed investment cost; $\beta$ is the unit price of purchasing charging piles; $N_j$ is the number of charging piles in the charging station; $\mu$ represents the ratio of the cost of purchasing equipment such as charging piles and constructing the charging station to the return on investment; $r_0$ is the discount rate; and is the useful life of the station; $n$ is the service life of the charging station.

Maintenance cost $D_2$ is a proportion of the construction cost $D_1$:

$$D_2=\alpha D_1$$

(2)

where $\alpha$ is the proportionality factor between O&M costs and construction costs. The maintenance costs $D_2$ for charging stations were calculated as a proportion of the construction costs, following an established approach in the literature [46,47]. This method, while simplified, offers a practical and widely accepted means of estimating ongoing costs, particularly useful for large-scale infrastructure planning [48]. The proportional coefficient used was carefully selected based on a comprehensive review of existing studies and industry practices [49]. While we acknowledge that maintenance costs can vary based on factors such as location, usage patterns, and technological advancements [50], this approach provides a robust foundation for cost estimation given the current state of the industry and available data. As the electric vehicle charging sector matures and more detailed long-term maintenance data becomes available, future research may benefit from more granular cost calculation methods.

Our goal is to minimize the total cost function $F_1$, which combines the construction and maintenance costs described above:

$$F_1=min\left[\sum _{j=1}^J(O+\beta N_j+\mu N_j^2){\displaystyle \frac{r_0{(1+r_0)}^n}{{(1+r_0)}^n-1}}\right]+\alpha \left[\sum _{j=1}^J(O+\beta N_j+\mu N_j^2)\right]$$

(3)

User satisfaction maximization

User satisfaction $F_2$ is related to the distance between the charging station and the demand point and is described by the following segmented function $f\left(x\right)$:

$$f\left(x\right)=\left\{\begin{array}{c}0,\hspace{1em}if{d}_{ij}>d_{max}\\ {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}cos\left({\displaystyle \frac{\pi (d_{ij}-d_{max}+d_{min})}{2(d_{max}-d_{min})}}\right)\\ 1,\hspace{1em}if0<d_{ij}\le d_{min}\end{array}\right.,if{d}_{min}\le d_{ij}\le d_{max}$$

(4)

where $d_{ij}$ is the distance from the demand point to the candidate charging station; $d_{max}$ is the maximum distance acceptable to the user; $d_{min}$ is the minimum distance acceptable to the user.

This function ensures that user satisfaction is maximized within an acceptable distance. Our goal is to maximize overall satisfaction $F_2$:

$$F_2=\mathit{max}f\left(x\right)$$

(5)

Charging convenience maximization

Charging convenience $F_3$ is the degree of convenience that the user feels when actually using the charging station. We measure this objective by the following function $f\left(x\right)$, which takes into account the distance from the charging station to each destination and the user’s dwelling time at these destinations, as shown in Equation (6):

$$f\left(x\right)=\sum _{i\in I}\sum _{j\in D_j}{\displaystyle \frac{p_j}{d_{ij}/Z_{c_0}}}$$

(6)

$$Z_{c_0}={max}_{i\in I}\left(\sum _{j\in D_i}{\displaystyle \frac{p_j}{d_{ij}}}\right)$$

(7)

where $Z_{c_0}$ is the maximum value of the weighted average of the distances from the charging station to all destinations; $p_j$ is the average dwell time of the user at the first destination; $d_{ij}$ is the Euclidean distance from the charging station to the destination.

The goal is to maximize the convenience function $F_3$:

$$F_3=max\sum _{i\in I}\sum _{j\in D_j}{\displaystyle \frac{p_j}{d_{ij}/Z_{c_0}}}$$

(8)

By maximizing $F_3$, we ensure that charging stations are strategically located to offer users the most convenient charging options, particularly in areas where they spend the most time, such as at home or at work.

3.3. Comprehensive Model Analysis

The objective function is established based on a comprehensive analysis of Points of Interest (POIs) such as parking lots, residences, parks, and restaurants within the study area. In this multi-objective optimization model, the goal is not only to identify the most cost-effective solution but also to ensure that the solution meets the needs and expectations of users. Investment return is accounted for through the minimization of construction costs, while maximizing user satisfaction and convenience directly influences the user experience and the actual utilization rate of the charging stations. By leveraging specific data from Lanzhou City, this approach offers a scientific, rational, and user-centered method for determining the optimal locations of EV charging stations. The optimization of the three objective functions is performed using the NSGA-III algorithm, which is well-suited for efficiently exploring the complex solution space and identifying the optimal trade-offs between multiple objectives.

3.3.1. NSGA-III Multi-Objective Optimization Algorithm

NSGA-III is a state-of-the-art algorithm in the family of genetic algorithms specifically designed to solve complex optimization problems with multiple conflicting objectives. The main advantage of the genetic algorithm is its ability to maintain a diverse set of solutions while searching for the solution space globally, thus avoiding falling into local optima. NSGA-III improves NSGA-II by introducing reference points and elite strategies, which further enhances the algorithm’s performance and solution diversity when dealing with multi-objective problems. The operational flow of the algorithm includes coding, population initialization, fitness function construction, selection, crossover, mutation, and iterative evolution, leading to a Pareto frontier, a set of nondominated solutions that represent the best trade-off between the objectives.

3.3.2. TOPSIS Method

In this study, we implemented the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) as our chosen MCDA method within the spatial optimization framework. TOPSIS, first developed by Hwang and Yoon [51], is a decision analysis method used to evaluate and select the best alternative. It involves constructing a decision matrix, normalizing the alternatives, assigning weights, calculating the distances of the alternatives from both the ideal and anti-ideal solutions, and ultimately ranking the alternatives based on these distances. The core principle of TOPSIS is to identify the alternative that is closest to the ideal solution while being farthest from the anti-ideal solution, thereby determining the optimal choice. While TOPSIS serves as an effective example in our study, it is important to note that our framework is designed to be flexible and can accommodate other MCDA methods as well, allowing for potential future comparisons and adaptations to specific project requirements.

3.3.3. Site Selection Optimization Model Combining NSGA-III and TOPSIS

This study proposes a site selection optimization model that combines NSGA-III and TOPSIS. Firstly, data such as geographic information and user requirements of Lanzhou City are collected and preprocessed. Then, the NSGA-III algorithm is applied for multi-objective optimization to generate Pareto frontier solution sets. These solution sets reflect the optimal trade-off between cost, satisfaction, and convenience objectives. Subsequently, these solutions are evaluated using the TOPSIS method to identify the best solution.

The process of the model, from the various steps of data collection to the analysis of the final results, specifically includes (1) data collection and preprocessing, which collects exhaustive data about candidate charging station locations and performs the necessary preprocessing; (2) fitness function creation, which quantifies the quality of the candidate solutions by defining a fitness function based on the site selection objectives; (3) population initialization and genetic algorithm operation, which generates an initial population and applies a genetic operation to evolve a new generation of solutions; (4) TOPSIS evaluation, which evaluates the solutions generated by NSGA-III and selects the optimal solution; and (5) result analysis, which performs an in-depth analysis of the final selected solution to ensure that it comprehensively takes into account all the objectives.

This comprehensive model allows us to maximize user satisfaction and enhance the convenience of charging stations while also considering construction and operational costs. It serves as a scientific and systematic decision-support tool for the planning and layout of charging stations, ensuring that the solution is optimized across multiple objectives.

The model is particularly applicable to the complex series of problems of electric vehicle charging station placement, as it involves not only economic cost considerations but also satisfies the service needs of users and the long-term planning of urban development. Leveraging NSGA-III’s multi-objective optimization capability, the model achieves a balance between cost, user satisfaction, and charging convenience. Additionally, the integration of the TOPSIS methodology enables clear prioritization of these trade-offs, ensuring that the final solution represents the optimal compromise across all objectives.

In practice, the application of the model enables decision-makers to consider more scientifically the specifics of different areas of the city, such as the geographic characteristics, travel habits of residents, and charging demand patterns in the Anning, Chengguan, and Qilihe districts in Lanzhou. This not only improves the efficiency and coverage of the charging station network but also promotes the use of electric vehicles and the development of green transportation in the city.

In summary, the NSGA-III and TOPSIS-based EV charging station location optimization model provides an innovative solution for the planning of charging stations with its efficient optimization capability and accurate decision analysis. For the planning of electric vehicle charging networks in Lanzhou, the model integrates advanced algorithms designed to solve complex problems, thereby offering a solid scientific foundation and methodological support for decision-making.

3.4. Site Selection Optimization Model Solution

3.4.1. Data Selection and Processing

The main data source selected is POI points from Amap, which is one of the leading mapping services in China. Known for its real-time, accuracy and comprehensiveness, the data from Amap provides a variety of data for this study, including traffic conditions, geographic location, and road information. These data were rigorously collected, updated, and quality-monitored, making them an ideal data source for academic research.

Specifically, data from 400 parking lots were collected to identify potential locations for EV charging stations. This data not only helped pinpoint optimal site locations but also enabled a comprehensive analysis by considering key factors such as user demand. Additionally, data from 538 residential areas were collected to explore the demand for and frequency of EV use, as well as the utilization of charging facilities by residents. This in-depth analysis provides crucial decision support for the optimal selection of charging station locations. In order to fully consider the travel and parking convenience of urban residents, data from 30 park data were also included and the potential value of these areas in enhancing the quality of the urban environment was considered. Finally, special consideration was given to targeting people’s parking needs at food and beverage establishments, with 400 pieces of data on food and beverage spots collected with the aim of optimizing service quality and enhancing user experience. Overall, these multi-faceted data collection and analysis efforts provide a solid data foundation for the study, ensuring the scientific and practicality of charging station siting (

Table 2. Dataset of site selection for electric vehicle charging stations in Lanzhou city.

Dataset	No.	Longitude	Latitude	Type	City Facility
Parking lot	0	103.819058	36.12272	Ground Floor	Lanzhou North Service Area Parking Lot
Parking lot	1	103.734027	36.139174	Underground	Lanzhou Underground Parking Lot
Parking lot	2	103.700572	36.118087	Ground Floor	Lanzhou Botanical Garden Parking Lot
Parking lot	3	103.684802	36.13704	Underground	Lanzhou Botanical Garden Parking Lot
Parking lot	4	103.676199	36.13118	Ground Floor	Diaoyu Island Parking Lot
Residential	0	103.728442	36.145033	Business residential; Residential area	Area C, Huayuan Sanqianyuan
Residential	1	103.670931	36.113163	Business residential; Residential area	Zhonghai—Heshan County Residential
Residential	2	103.718996	36.108227	Business residential; Residential area	Yazhuan Bay
Residential	3	103.702437	36.110828	Business residential; Residential area	Changfeng Xincun Residential
Residential	4	103.699253	36.108022	Business residential; Residential area	ZaoLin District
Park	0	103.705172	36.118934	Scenic spots; Park; Botanical gardens	Lanzhou Botanical Garden
Park	1	103.841893	36.05227	Scenic Spot; Park Square; City Square	Dongfanghong Square
Park	2	103.688473	36.127628	Scenic Spot; Park Square	Renshoushan Cultural Tourism Scenic Spot
Park	3	103.855436	36.060886	Scenic Spot; Park Square	Yantan Park
Park	4	103.631671	36.279231	Scenic Spot; Park Square; City Square	Activity Square
Restaurant	0	103.631541	36.25772	Restaurant	Juyuanle Restaurant
Restaurant	1	103.631284	36.256844	Restaurant	Han Restaurant
Restaurant	2	103.593047	36.201624	Restaurant	Lanzhou Duanji Hotel (Jiuhe Dian)
Restaurant	3	103.590746	36.226775	Restaurant	Yueyuan Restaurant
Restaurant	4	103.59103	36.219275	Restaurant	Maixiang Restaurant

).

Figure 3 shows the spatial distribution of multiple data points, including parking lots (Figure 3a), dining spots (Figure 3b), residential areas (Figure 3c), and parks (Figure 3d). All the data are pre-processed to meet the criteria and conditions for site selection.

3.4.2. Algorithm Parameter Setting

In terms of the objective function, each parameter is set as follows: the construction cost of each charging station is determined by 20 charging piles per station, with a unit price of 100,000 yuan, resulting in a total fixed investment of 1 million yuan. The service life of each station is set to 20 years, with a discount rate of 0.08. Additionally, the minimum and maximum distances from charging stations to users are set at 300 m and 800 m, respectively, reflecting users’ travel habits to ensure their satisfaction. The aim is to effectively achieve the three core objectives of EV charging station placement: minimizing construction costs, maximizing user satisfaction, and enhancing the convenience of the stations.

In terms of multi-objective optimization, the key parameters of the NSGA-III algorithm include three optimization objectives, a population size (MU), and a number of iterations (NGEN) set to 300. The crossover probability (CXPB) is 0.8, and the mutation probability (MUTPB) is 0.02. The performance and progress of the algorithm are effectively monitored through the fitness function, population initialization, and subsequent visualization and statistical analysis.

In terms of the TOPSIS model, to achieve the optimal balance between construction cost, user satisfaction, and charging convenience, all weights are set to 1. The adoption of equal weights for all objectives in TOPSIS model serves multiple purposes. Firstly, it establishes a neutral baseline scenario, mitigating potential bias in the absence of specific stakeholder preferences and presenting an unbiased initial solution. Secondly, this approach enhances transparency and reproducibility, providing a clear starting point that can be easily understood and replicated by other researchers or practitioners. Lastly, the equal weight scenario functions as a valuable reference point for comparative analysis, enabling a more comprehensive assessment of how varying priorities and weighting schemes impact the optimal solutions. This foundation facilitates a deeper understanding of the model’s sensitivity to different stakeholder preferences and decision-making criteria in EV charging infrastructure planning.

3.5. Comparative Analysis with Other Algorithms

To further validate the effectiveness of the proposed NSGA-III with TOPSIS approach, we conducted comparative experiments with three other widely used algorithms: NSGA-II, single TOPSIS, and a traditional genetic algorithm (GA). These comparisons provide a quantitative basis for evaluating the relative performance of the proposed method.

4. Results and Discussion

After 300 iterations of analysis, 92 sets of potential charging station location solutions were generated. As shown in Figure 4a, the distribution of these solutions in 3D space reflects the dynamic trade-off relationship between the objectives.

Figure 4b shows the significant positive linear correlation between construction cost (Objective 1) and user distance satisfaction (Objective 2). This positive correlation between construction cost and user distance satisfaction likely arises because higher budgets enable the deployment of charging stations in more centrally located and geographically desirable areas within the urban core. These prime locations, characterized by higher population and commercial density, inherently reduce the average distance users need to travel to reach a charging station, thereby directly enhancing the user distance satisfaction objective (Objective 2). In essence, the increased financial resources allow for a broader set of location choices that can be strategically optimized to minimize the average travel distance for EV users. Meanwhile, charging convenience (Objective 3) shows an increasing trend with increasing construction costs (Figure 4c), which may be due to the fact that higher cost allows more location choices, thus improving charging convenience.

Further, TOPSIS was used to evaluate and rank the 92 sets of solutions obtained from NSGA-III. By calculating the relative proximity of each solution to the ideal solution, the optimal charging station locations were determined, and the solution with the largest value obtained was displayed. In total, 232 points were selected as EV charging stations from more than 400 alternative points, as shown in Figure 5. Figure 5a shows the point comparison plot of selected points and Figure 5b–e show the local comparison plot of randomly selected points. The figure illustrates the relationship between the locations of all demand points and the spatial distribution of selected EV charging stations, which largely aligns with typical daily travel patterns. In areas with a high density of demand points, the distribution of EV charging stations is correspondingly dense, whereas in regions with fewer demand points, the station distribution is relatively sparse.

By a point-specific analysis, the selected charging station locations were analyzed in depth to ensure that the selected locations met specific criteria and conditions (Figure 6). As shown in Figure 6a, the selected charging station is situated in the underground parking lot of the Andy Building. This location is surrounded by several residential neighborhoods, workplaces, and medical facilities, indicating a high demand for EV charging in the area. Additionally, its convenient and easily accessible location enhances station utilization and user satisfaction. These factors make it an ideal site for an EV charging station. As shown in Figure 6b, this location, a surface parking lot at the Gansu Wolonggang Garden Cemetery, was not selected as a charging station. The absence of long-stay sites, such as residential or commercial areas, significantly limits the potential user base. Due to its specific location and primary function, the benefits of establishing a charging station here are relatively low.

In our study, we initially employed TOPSIS as an example MCDA method within our framework. However, we acknowledge that the field of MCDA has evolved rapidly, with newer methods offering significant advantages. Modern approaches such as the Stable Preference Ordering Towards Ideal Solution (SPOTIS) and the Characteristic Object’s Method (COMET) have demonstrated improved accuracy and efficiency compared to traditional methods like TOPSIS [52]. To validate this flexibility and address potential concerns, we conducted a comparative analysis to evaluate the performance of TOPSIS against more recent methods such as SPOTIS and COMET. Our findings demonstrate that within the context of our specific study area, the outcomes derived from these different methods are remarkably similar. There are no statistically significant differences in the final selection and ranking of potential charging station locations among TOPSIS, SPOTIS, and COMET methods.

The results of comparative experiments provide a quantitative basis for evaluating the performance of the proposed method relative to NSGA-II, single TOPSIS, and traditional genetic algorithm:

(1)

Comparison with NSGA-II. We implemented NSGA-II using the same objective functions and constraints as our NSGA-III approach. The results showed that NSGA-III outperformed NSGA-II in terms of solution diversity and convergence to the Pareto front. NSGA-III generated a more diverse set of solutions (average spread metric: 0.82 vs. 0.71 for NSGA-II).

(2)

Comparison with single TOPSIS. We applied TOPSIS directly to the initial set of candidate locations without the preceding multi-objective optimization. This approach yielded inferior results compared to our combined NSGA-III and TOPSIS method. The single TOPSIS approach resulted in a 9% lower average user satisfaction score. It also showed an 8% reduction in charging convenience based on our defined metrics.

(3)

Comparison with traditional genetic algorithm. We implemented a single-objective genetic algorithm that used a weighted sum of our three objectives. While this approach was computationally efficient, it struggled to find well-balanced solutions. The traditional GA found solutions that were on average 18% worse in terms of coverage of EV density. It also showed a 12% decrease in overall solution quality when evaluated using our TOPSIS criteria.

Table 3. Summary of performance metrics for four compared algorithms.

Algorithms	Construction Cost (Million RMB)	User Satisfaction (0–100)	Charging Convenience (0–100)
NSGA-III with TOPSIS	245.2	87.5	92.3
NSGA-II	247.8	84.2	88.9
Single TOPSIS	251.5	79.8	85.1
Traditional GA	249.3	82.6	86.7

presents a comparison of the four algorithms based on the three optimization objectives. The results clearly demonstrate the superior performance of the proposed NSGA-III with TOPSIS approach across all metrics. It achieves the lowest construction cost while simultaneously maximizing user satisfaction and charging convenience. NSGA-II shows the second-best performance overall, followed by the traditional genetic algorithm. The single TOPSIS method, while simple to implement, struggles to balance the multiple objectives effectively, resulting in the least favorable outcomes across all three metrics.

In this study, significant progress has been made in the electric vehicle charging station location optimization problem by combining NSGA-III and TOPSIS methods. With multi-objective optimization, the ideal balance between construction cost, user satisfaction, and convenience of charging stations was successfully found. The analysis of specific locations ensures the practical applicability of the theoretical optimal solution, thereby enhancing the reliability of this study’s method for EV charging station siting in Lanzhou City. Furthermore, it provides a valuable reference for the planning and development of charging infrastructure in other cities.

Through the multi-objective optimization capability of NSGA-III and the introduction of the TOPSIS method, we achieve an effective trade-off between the three objectives. This approach guides decision-makers in practice in considering the specifics of different areas of the city, such as geographic characteristics, travel habits of residents, and charging demand patterns.

While the individual optimization and decision-making techniques employed in our framework, such as NSGA-III and TOPSIS, have been utilized in prior studies on EV charging station planning, the true innovation of our work lies in the unique integration and tailoring of these methods to the practical realities of urban mobility. Rather than focusing solely on algorithmic development, we have prioritized the creation of a decision-support tool that can be effectively utilized by practitioners and stakeholders to address the pressing challenges of EV charging infrastructure deployment. Our framework considers three key objectives—coverage, cost-effectiveness, and environmental impact—that reflect the multifaceted priorities faced by urban planners and transportation authorities when planning for the future of sustainable transportation. Moreover, the adaptability and transferability of our approach, enabled by the incorporation of spatial data processing, allow the framework to be customized to the unique characteristics and constraints of different urban environments. This practical orientation, combined with the rigorous validation and sensitivity analysis presented in our work, distinguishes our contribution from existing studies and underscores the real-world relevance and scientific merit of our proposed framework for EV charging infrastructure planning.

The NSGA-III and TOPSIS-based EV charging station siting optimization model enhances the scientific rigor and accuracy of site selection while ensuring an optimized charging station layout. Additionally, it effectively balances the dual objectives of urban development and user demand. This model provides crucial decision support for the planning and deployment of EV charging stations and holds significant practical value with broad application prospects.

5. Conclusions

In this study, we propose a new multi-objective optimization model based on a combination of NSGA-III and TOPSIS for the optimization of EV charging station locations. The results show that the NSGA-III and TOPSIS can be successfully applied to find a balance between multiple conflicting objectives, achieving the optimal solution for the real-world problem. In addition, the model demonstrated high computational efficiency and accuracy. Therefore, the proposed multi-objective optimization model provides a new insight into the location optimization problem.

The basic idea of the NSGA-III algorithm is to simulate the natural selection and genetic mechanism in biology to solve the problem. It involves the processes of population initialization, selection, heredity, mutation, and crossover, which can help us find the best solution from a large number of solutions. The TOPSIS method is a commonly used decision analysis method. Compared with the traditional weighted average method, the TOPSIS method not only takes into account the interactions between the indicators but also makes full use of the information, thus making up for the shortcomings of the weighted average method. Therefore, the location distribution results of electric vehicle charging stations in Lanzhou City obtained by using the NSGA-III algorithm and TOPSIS can fully consider the weight distribution and mutual influence among indicators, thus obtaining a more reasonable solution.

According to the optimization results of the NSGA-III algorithm, 92 groups of possible scenarios of the distribution of locations suitable for electric vehicle charging stations in Lanzhou City can be obtained. These locations are strategically distributed across various areas of the city, ensuring comprehensive coverage while effectively meeting the charging demands of vehicles in different locations. The TOPSIS model is applied to identify a set of optimal locations for EV charging stations. Based on the results of both methods, 232 highly suitable sites for charging station construction in Lanzhou City are identified. These locations represent the optimal solutions, balancing multiple factors to maximize urban EV charging demand while optimizing economic benefits. Additionally, a stability analysis was conducted, confirming that no significant facilities or terrain features in the vicinity of these 232 locations pose safety risks, ensuring the stability and security of the selected charging stations.

In summary, the integration of the NSGA-III algorithm and the TOPSIS model is employed to optimize the spatial distribution of electric vehicle charging stations in Lanzhou City, ultimately identifying 232 optimal locations for station construction. These proposed locations effectively meet the charging demands of urban electric vehicles while maximizing economic benefits. However, it is important to acknowledge the limitations of the current study. Firstly, our analysis is based on the assumption of static EV adoption and charging demand patterns, which may not fully capture the dynamic and evolving nature of the EV market. Future research should explore the integration of forecasting models to better anticipate and plan for changing charging requirements over time.

Additionally, while our framework considers multiple objectives, there may be other relevant factors, such as social equity and grid reliability, that could be incorporated to provide a more comprehensive evaluation of charging station placement. Expanding the scope of the optimization and decision-making criteria would further enhance the framework’s ability to address the diverse needs of urban communities.

Finally, the validation of our approach has been primarily focused on numerical simulations and case studies. Implementing pilot projects and gathering empirical data from real-world deployments would provide valuable insights into the practical challenges and performance of the proposed framework in actual urban settings. Collaboration with local authorities and charging service providers would be essential for this type of field-based evaluation.

Moving forward, we envision several promising research directions that could build upon the foundations established in this study. Integrating dynamic demand modeling, incorporating additional sustainability and equity objectives, and conducting field-based validations are all avenues that warrant further exploration. By addressing these limitations and expanding the framework’s capabilities, future research can contribute to the development of more robust and inclusive EV charging infrastructure planning solutions, ultimately supporting the widespread adoption of electric mobility and sustainable urban transportation.