A Hierarchical Spatio-Temporal Framework for Sustainable and Equitable EV Charging Station Location Optimization: A Case Study of Wuhan

Abstract

Deploying public EV charging infrastructure while balancing efficiency, equity, and implementation feasibility remains a key challenge for sustainable urban mobility. This study develops an integrated, grid-based planning framework for Wuhan that combines attention-enhanced ConvLSTM demand forecasting with a trajectory-derived, rank-based accessibility index to support equitable network expansion. Using large-scale charging-platform status observations and citywide ride-hailing mobility traces, we generate grid-level demand surfaces and an accessibility layer that helps reveal structurally connected yet underserved areas, including demand-sparse zones that may be overlooked by utilization-only planning. We screen feasible grid cells to construct a new-station candidate set and formulate expansion as a constrained three-objective optimization problem solved by NSGA-II: maximizing demand-weighted neighborhood service coverage, minimizing the Group Parity Gap between low-accessibility populations and the citywide population, and minimizing grid-connection friction proxied by road-network distance to the nearest power substation. Practical deployment plans for 15 and 30 sites are selected from the Pareto set using TOPSIS under an explicit weighting scheme. Benchmarking against random selection and single-objective greedy baselines under identical candidate pools, constraints, and evaluation metrics demonstrates a persistent coverage–equity–cost tension: coverage-driven heuristics improve demand capture but worsen parity, whereas equity-prioritizing strategies reduce gaps at the expense of coverage and feasibility.

1. Introduction

With the global energy transition and carbon-neutrality targets, the electric car market has expanded rapidly. In 2024, global electric car sales surpassed 17 million units, raising the worldwide share of electric cars in new-car sales to over 20% [1]. China remained the largest market, with over 11 million electric cars sold in 2024; in the domestic market, electric cars accounted for almost half of all new car sales in China that year [1]. The International Energy Agency projects that global electric car sales will exceed 20 million units in 2025, representing more than one-quarter of cars sold worldwide [2]. However, the deployment of public charging infrastructure has not kept pace with this rapid adoption. According to [2], by the end of 2024, more than 75% of the European highway network had chargers at most 50 km apart, whereas only 35% of the U.S. interstate highway system achieved the same level of coverage. In the United States, total non-home charging deployment increased from about 151,000 in mid-2023 to 204,000 in 2024 [3].

In this context, the scientific accuracy and precision of charging station location optimization decisions have a direct impact on the development of the electric vehicle industry and the effectiveness of energy system transformation. Research demonstrates that optimized siting can reduce total system costs by 30–40%, increase charging station utilization rates by 60–80% compared to suboptimal locations, and reduce transmission losses by 6.4% [4]. Charging station location optimization has become a critical technical issue for promoting the sustainable development of the electric vehicle industry.

Early studies typically formulated charging station placement using facility location models and heuristic algorithms. For example, p-median and related formulations have been used to minimize travel distance and improve accessibility, but they often rely on static or simplified demand representations and thus struggle to capture short-term spatio-temporal dynamics [5]. Hybrid approaches combining location optimization with simulation can better reflect behavioral responses but may become computationally expensive for city-scale deployment [6]. Metaheuristics such as genetic algorithms, simulated annealing hybrids, and particle-swarm variants have also been widely adopted to handle non-convex search spaces and complex constraints [7,8,9,10]. However, many of these approaches focus on a single objective (or collapse multiple objectives into a single score), which can obscure the tensions among competing planning goals.

Multi-objective evolutionary algorithms have consequently gained popularity in charging infrastructure planning. NSGA-II and related methods have been used to jointly optimize coverage, cost, and other performance metrics, and comparative studies frequently report NSGA-II as a strong baseline for approximating Pareto-optimal trade-offs [11,12,13]. Beyond NSGA-II, multi-objective particle swarm optimization and other evolutionary designs have been applied to bi- or tri-objective charging station problems that consider electricity costs, emissions, or grid-oriented performance measures [14,15]. Despite these advances, two limitations remain common. First, many multi-objective siting studies still rely on coarse demand proxies (e.g., static POIs, aggregate travel indicators, or historical averages) rather than planning-ready spatio-temporal forecasts, which can lead to hotspot misallocation under demand sparsity. Second, the objectives and feasibility terms are often parameterized by assumptions that are difficult to verify at a city scale, which can weaken interpretability and transferability for practical planning.

Recent work has begun to incorporate richer mobility evidence and data-driven prediction to better match real-world charging dynamics. Activity-based and mobility-informed approaches can better reflect where charging opportunities are structurally needed beyond observed utilization alone [16,17,18]. Complementing these mobility-informed approaches, GIS-enabled multi-criteria screening frameworks have been used to synthesize heterogeneous spatial layers (e.g., land-use constraints, walk/cycle catchments, population exposure, and proximity to grid assets) into interpretable suitability surfaces or ranked zones, providing a transparent pre-planning step for narrowing candidate areas before detailed optimization [19,20]. In parallel, spatio-temporal deep learning has emerged as a promising tool for forecasting charging demand, including graph-based models and recurrent variants that better capture temporal dependence and spatial spillovers [21,22,23]. However, these components are often studied in isolation: forecasting is evaluated primarily by generic error metrics rather than planning-relevant hotspot fidelity, and mobility representations are rarely integrated into an end-to-end decision framework that explicitly balances efficiency, equity, and feasibility through constrained multi-objective optimization. As a result, planners still lack a unified workflow that (1) produces robust demand signals under extreme sparsity, (2) complements realized charging demand with citywide mobility structure to avoid overlooking demand-sparse but strategically important areas, and (3) yields transparent, constraint-feasible trade-off portfolios rather than a single opaque “optimal” solution.

To address these gaps, this study develops a hierarchical spatio-temporal planning framework that integrates demand forecasting, mobility representation learning, and constrained multi-objective siting within a unified grid-based decision system. First, a ConvLSTM-based forecasting module with attention is trained to produce short-term grid-level demand surfaces, and performance is evaluated in a planning-relevant manner under demand sparsity by reporting hotspot-oriented and system-level indicators. Second, to complement realized charging demand, a trajectory-based representation module (a denoising autoencoder with temporal self-attention) learns citywide mobility patterns and derives accessibility-related signals that remain available even in demand-sparse areas. Third, we formulate a constrained multi-objective siting problem that jointly considers demand-oriented service effectiveness, accessibility, and equity-oriented objectives, as well as infrastructure feasibility, which is proxied by network connection frictions. We solve it using NSGA-II to obtain Pareto-optimal portfolios. Finally, TOPSIS is used to rank Pareto solutions and recommend implementable deployment plans under different budget levels, enabling transparent comparison of efficiency–equity–cost trade-offs and supporting phased planning.

The remainder of the paper is organized as follows. Section 2 introduces the study area and datasets. Section 3 describes the hierarchical modeling and optimization framework. Section 4 reports forecasting performance, mobility-layer characteristics, and multi-objective siting results, including recommended plans. Section 5 and Section 6 discuss implications, limitations, and conclusions.

2. Study Area and Data

2.1. Overview of Experimental Area

This study was conducted in Wuhan, a major megacity in central China, located approximately. The city covers a total area of 8569.2 km² and has a resident population of approximately 11.21 million, providing a large and diverse urban context for examining public EV charging demand. Administratively, Wuhan administers 13 districts (including Jiang’an, Jianghan, Qiaokou, Hanyang, Wuchang, Qingshan, Hongshan, Dongxihu, Caidian, Jiangxia, Huangpi, Xinzhou, and Hannan). These are commonly described as consisting of seven central urban districts and six suburban districts, reflecting a distinct core–periphery structure in urban functions and mobility. Wuhan has experienced rapid urban development and maintains a high level of urbanization; for instance, official statistics reported an urbanization level of 80.29% in 2018. Against this backdrop, the city has witnessed fast growth in EV adoption. Public reporting indicates that by 2023, Wuhan’s EV ownership had risen to around 360,000 vehicles, implying increasing pressure on public charging infrastructure to serve both routine and intensive users. In terms of urban structure, Wuhan has historically been shaped by the “three towns” (Hankou, Hanyang, and Wuchang), separated by the Yangtze and Han rivers, and has evolved into a polycentric metropolis. Such geography and functional heterogeneity tend to produce spatially concentrated activity hotspots and corridor effects, while also creating frictions (e.g., river-crossing constraints and uneven land-use intensity) that can lead to localized service gaps. These characteristics make Wuhan a suitable empirical setting for studying the spatial concentration of public charging demand and for evaluating planning strategies under realistic metropolitan conditions.

2.2. Charging Dataset Description

This study utilizes EV charging demand data collected from the Charging Bar mobile application. Charging Bar is an online platform that helps EV users locate nearby public charging stations and provides real-time availability at the connector level. A distinct advantage of this data source is its cross-platform aggregation: the dataset covers public charging stations operated by 22 charging service providers, which mitigates single-operator platform bias and offers a more comprehensive view of citywide public charging activity.

Within Wuhan, the platform lists 1701 public charging stations and 24,763 charging connectors. To capture realistic short-term demand dynamics, we conducted high-frequency monitoring from 00:00 on 14 February 2025 to 00:00 on 20 February 2025 (see

Table 1. Charging Pile Dataset Field Structure.

Field Name	Data Type	Description	Value Range
stationLatGcj02	Float	Charging station latitude coordinate (GCJ02 coordinate system)	30.35–31.37° N
stationLngGcj02	Float	Charging station longitude coordinate (GCJ02 coordinate system)	113.68–115.05° E
standard_time	DateTime	Standard timestamp	14 February 2025 00:00 to 20 February 2025 00:00
power	Float	Real-time charging power (kW)	0–200
price	Float	Cumulative charging cost (Yuan)	0–500
stationId	String	Charging station unique identifier	-
portId	String	Charging pile unique identifier	-
connectorStatus	Integer	Connector occupancy status	0: Idle (Available) 1: Charging (Occupied)

). Data acquisition was performed using a time-series crawler that periodically queried the platform’s real-time status feed. At each snapshot, every connector is labeled as either “occupied” or “idle”. Because the platform API occasionally returns incomplete station lists and duplicated entries, we performed validity filtering and retained 5,859,191 connector-status records as the cleaned snapshot dataset.

Because a single snapshot does not represent a complete charging session, we optionally derive a session-like indicator from status transitions in each connector’s time series. Specifically, for a given connector, if its status is observed as occupied at time t and idle at the subsequent snapshot t′, we record an occupied-to-idle transition, indicating that a charging session likely ended within [t, t′]. Aggregating such transitions across all connectors during the observation window yields 1,823,781 transition-based events, which we use as an auxiliary behavioral statistic rather than the primary forecasting target.

Finally, all stations are mapped to a regular 1 km grid system, and the connector-level snapshots are aggregated into an hourly grid-level time series. For each grid cell i and hour t, the demand variable $D_i(t)$ is defined as the hourly count of active connectors (i.e., connectors in an occupied/charging state) within the cell. This connector-occupancy demand proxy serves as the primary input for both spatiotemporal forecasting and downstream location optimization. The transition-based events provide additional supporting evidence on usage intensity and charging dynamics, complementing the main connector-level demand representation.

2.3. Trajectory Dataset Description

GPS trajectory data enable the characterization of urban mobility patterns and the identification of potential public-charging hotspots. Unlike static built-environment variables, trajectory records capture dynamic activity intensity and spatial mobility flows, which serve as a strong behavioral precursor of where and when public charging demand is likely to occur. In this study, we use ride-hailing vehicle trajectories as a city-scale mobility proxy (see

Table 2. Traffic Trajectory Dataset Field Structure.

Field Name	Data Type	Description	Value Range
Vehicle_ID	String	Ride-hailing vehicle unique identifier
Longitude	Float	GPS longitude coordinate	113.68–115.05° E
Latitude	Float	GPS latitude coordinate	30.35–31.37° N
Data_Send_Time	DateTime	GPS positioning timestamp	17 October 2019 00:00 to 19 October 2019 23:59
Speed	Float	Instantaneous speed (km/h)	0–120
Direction_Angle	Float	Driving direction angle (degrees)	0–360
Passenger_Status	Integer	0-Empty, 1-Occupied	{0, 1}
Operation_Status	Integer	0-Off-duty, 1-Operating	{0, 1}

).

Ride-hailing trajectories are adopted for three reasons. First, ride-hailing vehicles are commercial vehicles with substantially higher daily mileage and operating hours than private cars, and thus tend to rely more heavily on public charging facilities, making them an informative proxy for intensive public-charging demand. Second, ride-hailing trips are strongly associated with significant activity centers such as commercial districts, transport hubs, and office clusters, which helps identify latent charging demand hotspots. Third, ride-hailing vehicles serve as a transport carrier and do not alter passengers’ underlying travel purposes, allowing them to represent urban residents’ macro-level mobility intentions with relatively low behavioral bias.

The GPS data are obtained from the Gaode Open Platform. It is important to note that unlike experimental datasets with fixed-frequency continuous sampling, this commercial dataset utilizes an event-triggered and non-uniform sampling mechanism to optimize data transmission efficiency. Specifically, the recording frequency adapts to vehicle status: our statistical analysis reveals a median sampling interval of 10.0 s during active movements, ensuring high-resolution capture of mobility flows, whereas intervals extend significantly during idling or congestion to avoid redundant data:

(1)

Spatial filtering: removing records with coordinates outside the Wuhan administrative boundary;

(2)

Outlier removal: filtering implausible jump points caused by GPS drift (e.g., abnormal displacement within a short time interval that implies unrealistic speed);

(3)

Invalid record cleaning: removing duplicates, missing values, and logically inconsistent trips (e.g., end time earlier than start time).

(4)

Activity filtering: To focus on effective mobility demand, we specifically excluded records corresponding to long-duration idling, parking, and inactive periods (e.g., driver rest breaks or offline shifts).

After strictly applying these cleaning criteria, we constructed a high-quality ride-hailing trajectory database containing 29,143 vehicles operating within Wuhan from 17 to 19 October 2019. The final dataset consists of 16,791,722 valid GPS waypoints. It is important to clarify that the vehicles were not sampled on a continuous 24 h basis. Instead, the dataset captures the discontinuous nature of ride-hailing operations (typically 8–12 h shifts), recording only active service periods while naturally excluding offline non-service time. Consequently, the retained data effectively represent the spatiotemporal distribution of urban charging demand without redundancy.

To quantify mobility intensity at a macro level, we map trajectory records to the same grid system used in the charging-demand analysis and discretize time at an hourly resolution. Within each grid cell and each hour, we compute grid-level summaries that reflect urban activity intensity (e.g., trajectory-point counts and/or vehicle-passage intensity). We then apply smoothing to reduce the influence of extreme values and differences in reporting frequency and obtain a stable grid-based mobility intensity layer. This mobility layer captures the spatial concentration of activity hotspots and serves as an input to downstream accessibility/activity characterization, as well as location-planning modules.

2.4. Data Preprocessing and Gridding

We discretize Wuhan into a regular 1 km × 1 km grid to construct a unified spatial analysis framework. The grid resolution is selected empirically as a practical trade-off: coarser grids can obscure localized demand hotspots and residential exposure, whereas finer grids rapidly expand the decision space and increase the computational cost of repeated coverage and distance evaluations in NSGA-II. Consistent with prior city-scale studies adopting kilometer-level gridding to balance spatial representativeness and computational feasibility [24,25], we select a 1 km grid. This produces 9023 valid cells within the Wuhan administrative boundary, providing adequate granularity for planning without incurring prohibitive computational burden.

In addition to the charging-demand and trajectory-based mobility layers, the multi-objective station location model requires auxiliary spatial datasets to represent equity, connection frictions, and feasibility constraints. All auxiliary datasets are harmonized to the Wuhan municipal boundary and aggregated to the same 1 km grid to ensure spatial consistency across layers and objectives. To operationalize equity in service provision, we use gridded population data derived from China’s Seventh National Population Census. The population surface is clipped to the Wuhan boundary and aggregated to the analysis grid via zonal summation, yielding a grid-level population indicator. This layer captures the spatial distribution of residents and supports equity-aware assessment of alternative station deployment plans [26] (see Figure 1a).

To represent power-infrastructure availability, we extract substation locations from OpenStreetMap (OSM). Substation point features are filtered to the Wuhan boundary and treated as proxy supply nodes for grid connection. For each candidate grid cell, we quantify connection friction by its proximity to the nearest substation and incorporate this indicator as a cost proxy in the optimization, discouraging solutions that systematically place new facilities far from existing power nodes. Because Euclidean distance can underestimate real-world connection frictions, distances between candidate locations and substations are computed as shortest-path distances on the drivable road network. Specifically, we construct a routable road graph (drivable links only) and calculate the shortest path length from each candidate cell centroid to its nearest substation, yielding a more realistic approximation of connection difficulty (see Figure 1b).

3. Methodology

3.1. Spatio-Temporal Charging Demand Forecasting

Public charging demand is highly sparse and exhibits strong spatio-temporal clustering. We therefore formulate short-term public-charging demand forecasting on a regular 1 KM grid as a planning-oriented prediction task, where the goal is to provide a reliable demand surface for subsequent siting decisions.

We discretize the study area into a regular lattice of valid grid cells indexed by $i$. For each hour $t$, we aggregate platform status observations within each cell to obtain a grid-level demand proxy $y_{i,t}$, defined as the number of charging connectors that are actively charging during hour $t$ (utilization intensity). Separately, we derive a capacity proxy ${\mathrm{cap}}_i$ as the total number of connectors located in cell $i$ (supply scale).

For each time step $t$, we construct a 6-channel input tensor $X_t\in {ℝ}^{H\times W\times 6}$ consisting of:

Demand channel: $\log (1+y_{i,t})$ to stabilize the heavy-tailed distribution of observed utilization.

Capacity channel: ${\mathrm{cap}}_i$ (broadcast over time), representing grid-level supply intensity.

Time encodings (four channels): deterministic cyclic features capturing hour-of-day and day-of-week seasonality:

$$\sin (2\pi \cdot h_t/24),\hspace{1em}\cos (2\pi \cdot h_t/24),\hspace{1em}\sin (2\pi \cdot d_t/7),\hspace{1em}\cos (2\pi \cdot d_t/7)$$

(1)

These time-encoding channels are broadcast to all grid cells for the corresponding time step. Given an input window length $L$ ($L=12$ h), the model predicts the next-hour demand map:

$${\widehat{y}}_{t+1}=f_{\theta }(X_{t-L+1},\dots ,X_t)$$

(2)

Training samples are generated by sliding the window across the full time series. We split sequences chronologically into $80\%$ training, $10\%$ validation, and $10\%$ test. Demand and capacity channels are standardized using training-set statistics and then denormalized for evaluation on the original scale (inverse transform of $\log (1+y)$).

We employ a multi-layer ConvLSTM backbone with attention to capture local spatio-temporal dynamics. Specifically, the network consists of three stacked ConvLSTM layers (16.8 and 4 filters, $3\times 3$ kernels) with batch normalization and dropout (0.2) after the first two layers, followed by a Convolutional Block Attention Module (CBAM) to refine features via channel and spatial attention. A $1\times 1$ convolution with ReLU activation produces the non-negative prediction in the $\log (1+y)$ space.

To address extreme sparsity, we optimize a composite loss that emphasizes active regions while maintaining global fit and spatial coherence:

$$\mathcal{L}={\mathcal{L}}_{\mathrm{sparse}}+{\lambda }_g\cdot {\mathcal{L}}_{\mathrm{grad}}$$

(3)

The sparse-aware regression term combines a masked MSE on active cells with an unmasked global MSE:

$${\mathcal{L}}_{\mathrm{sparse}}=\alpha \cdot {\mathrm{MSE}}_{\mathrm{masked}}(\widehat{y},y)+(1-\alpha )\cdot {\mathrm{MSE}}_{\mathrm{global}}(\widehat{y},y)$$

(4)

where the binary mask is defined as $m_{i,t}=1 \mathrm{if} y_{i,t}>0, \mathrm{and} 0 \mathrm{otherwise}$ (computed on the original-scale y, applied in the transformed space). The gradient term penalizes discrepancies in first-order spatial gradients to preserve hotspot structure and avoid spurious speckle:

$${\mathcal{L}}_{\mathrm{grad}}=\Vert {\nabla }_x\widehat{y}-{\nabla }_{x}y{\Vert }_1+\Vert {\nabla }_y\widehat{y}-{\nabla }_{y}y{\Vert }_1$$

(5)

The model is trained with Adam, early stopping (patience 12), and ReduceLROnPlateau scheduling (factor 0.5, patience 6), with mixed precision enabled for efficiency.

For benchmarking, we evaluate two standard baselines on the original scale: (i) Persistence, which predicts $y_{t+1}=y_t$; and (ii) Historical Average (HistAvg), which uses the mean demand for the same (day-of-week, hour) computed from the training period, with hierarchical backoff (same hour; same day-of-week; global mean) if a specific slot is missing. Given the sparsity of grid demand, we report two complementary evaluation sets computed after inverse transformation: (i) active-only metrics (MAE, RMSE, WMAPE) computed on cells with $y_{i,t}>0$, and (ii) a global WMAPE computed over all grid cells and time steps (including zeros), reflecting system-level aggregate error.

3.2. Trajectory-Driven Denoising Autoencoder with Temporal Self-Attention

Public charging demand is shaped not only by realized utilization (which is supply-constrained) but also by the broader mobility structure of the city. We therefore learn a mobility-informed representation from ride-hailing trajectories and derive a unitless, rank-based accessibility index (${\mathrm{access}}_{\mathrm{rel}}$) that captures relative structural connectivity rather than an absolute travel-time measure.

Let $g_{i,t}$ denote the hourly ride-hailing trajectory intensity aggregated to grid cell $i$ at hour $t$ (e.g., the number of GPS waypoints or trajectory counts falling within the cell). We apply a log transform and min-max scaling to obtain $x_{i,t}=\mathrm{MinMax}(\log (1+g_{i,t}))$, where the scaling parameters are estimated from the training period and then applied consistently to all splits to avoid leakage.

Because mobility signals are dominated by persistent level differences (core vs. periphery), we construct a de-seasonalized residual series to emphasize local temporal deviations:

$$r_{i,t}=x_{i,t}-{\mu }_{h(t),d(t)},$$

(6)

where ${\mu }_{h,d}$ is the mean of $x_{i,t}$ over the training period at the same hour-of-day $h$ and day-of-week $d$. This revisualization suppresses stationary intensity levels and highlights temporal signatures linked to commuting and activity rhythms.

We then extract fixed-length windows $r_i^{(k)}\in {ℝ}^{L_m}$ for each grid cell $i$ with window length $L_m=48$ h and stride $3$ h (Table S1). To improve robustness against missing records and measurement noise, we train a denoising sequence autoencoder. Each input window is corrupted by (i) random element masking (mask ratio $\rho =0.20$) and (ii) additive Gaussian noise $\epsilon ~\mathcal{N}(0,{\sigma }^2)$ with $\sigma =0.05$ on the scaled residual series:

$$\tilde{r}=b\odot r+\epsilon$$

(7)

where b is a Bernoulli mask. The model reconstructs the clean residual sequence by minimizing mean squared reconstruction error.

The encoder uses stacked LSTMs (64 and 32 units) to obtain a latent sequence representation, followed by temporal self-attention to focus on critical time steps. Given hidden states $H=[h_1,\dots ,h_{L_m}]$, we compute:

$$Q=H{W}^Q,\hspace{1em}K=H{W}^K,\hspace{1em}V=H{W}^V;$$

$$A=\mathrm{softmax}(Q{K}^T/\sqrt{d});\hspace{1em}{H}^{\prime }=AV.$$

(8)

The attended sequence H′ is then pooled (global average pooling) to yield a fixed-length embedding $z_i^{(k)}\in {ℝ}^{d_z}$ with $d_z=16$ (Table S1). The decoder (32 and 64 units) reconstructs the residual sequence from $z_i^{(k)}$, enforcing information preservation through the bottleneck.

For each grid cell $i$, we aggregate embeddings across all windows by temporal averaging, $z_i={\mathrm{mean}}_k{z}_i^{(k)}$. To obtain a comparable scalar accessibility score, we project the embeddings onto a one-dimensional structural axis via principal-component projection (first PC), yielding $s_i$. Finally, we convert $s_i$ into a unitless, rank-based index:

$${\mathrm{access}}_{\mathrm{rel}}(i)={\displaystyle \frac{\mathrm{rank}(s_i)}{N-1}}$$

(9)

where $N$ is the number of valid cells (ties broken by average rank). By construction, ${\mathrm{access}}_{\mathrm{rel}}$ reflects the relative ordering of structural connectivity (higher values indicate more centrally connected mobility signatures) and is therefore suitable for equity stratification without claiming absolute accessibility levels.

Model training uses Adam with a batch size of 1024 for up to 60 epochs with an x $80/20$ window split into training/validation (Table S1). The learned ${\mathrm{access}}_{\mathrm{rel}}$ surface is exported as a planning layer for downstream optimization.

3.3. Multi-Objective Optimization and Spatial Economics-Based EV Charging Station Location Planning

We formulate EV charging station expansion as a discrete, grid-based location planning problem that integrates (i) demand potential, (ii) mobility-derived relative accessibility, (iii) population exposure, and (iv) implementation feasibility.

For each feasible buildable grid cell $i$, we construct four planning attributes: (1) a demand score $D_i$ from the ConvLSTM demand surface (mean predicted daily peak intensity); (2) the mobility-derived relative accessibility index ${\mathrm{access}}_{\mathrm{rel}}(i)$; (3) population $P_i$ aggregated to the grid from a population raster; and (4) an implementation feasibility proxy $C_i$ defined as the road-network shortest-path distance (km) from cell $i$ to its nearest power substation (connection friction).

We screen feasible cells to form a tractable candidate pool $\mathcal{I}$ (maximum size 600 in the main configuration). Let $x_i\in \{0,1\}$ indicate whether a candidate cell $i$ is selected, with the deployment scale fixed to ${\displaystyle \sum _{i\in \mathcal{I}}{x}_i}=K$ ($K\in \{15,30\}$).

Neighborhood service rule (served indicator). Because service is evaluated on a discrete grid and planners often interpret coverage in neighborhood terms, we define a binary served indicator for each demand cell j based on the 3\times 3 Moore neighborhood $N(j)$ centered at $j$:

$$\mathrm{served}(j)=1 \mathrm{if} \exists i\in N(j) \mathrm{such} \mathrm{that} x_i=1; \mathrm{otherwise} 0$$

(10)

Under a $1 \mathrm{km}$ grid, the farthest neighbor in $N(j)$ is at distance $\sqrt{2} \mathrm{km}$ ($\approx 1.41 \mathrm{km}$), which is consistent with the neighborhood-scale service radius used in mapped interpretation.

Smooth distance-decayed coverage (kernel). To provide a smooth optimization signal and reflect diminishing marginal returns with distance, we define the effective service received by cell j from the selected set $S=\{i\in I\mid x_i=1\}$ as the best (closest) exponential influence:

$$\mathrm{cov}(j)={\max }_{i\in S}\exp (-d_{ij}/\lambda )$$

(11)

where $d_{ij}$ is the centroid-to-centroid Euclidean distance (km) between grid cells $i$ and $j$, and $\lambda$ is the decay scale ($\lambda =2.5 \mathrm{km}$ in the main configuration; Table S2).

Objective 1: Maximize demand-weighted service effectiveness (kernel-based coverage). We maximize:

$$F_1(x)={\displaystyle \sum _j{D}_j}\cdot \mathrm{cov}(j)$$

(12)

This objective prioritizes locating new sites near high-demand areas while allowing benefits to attenuate smoothly with distance and preventing double counting via the max operator.

Objective 2: Minimize equity gap (Group Parity Gap, GPG) under the served indicator. We define low-accessibility zones as the bottom quantile of ${\mathrm{access}}_{\mathrm{rel}}$ (q = 0.25 in the main configuration), and compute population-weighted served shares:

$$S(G)={\displaystyle \frac{{\displaystyle \sum _{j\in G}{P}_j}\cdot \mathrm{served}(j)}{{\displaystyle \sum _{j\in G}{P}_j}}}.$$

(13)

The equity objective is then the absolute parity gap between the low-access group $G_L$ and the overall population $G_{\mathrm{all}}$:

$$F_2(x)=|S(G_L)-S(G_{\mathrm{all}})|.$$

(14)

To ensure a minimum level of investment in structurally disadvantaged areas, we impose a hard quota constraint on selected sites:

$${\displaystyle \sum _{i\in \mathcal{I}\cap G_L}{x}_i}\ge m_{\mathrm{low}},$$

(15)

where $m_{\mathrm{low}}$ is set in the main configuration as reported in Table S2 (e.g., $m_{\mathrm{low}}=3$).

Objective 3: Minimize implementation feasibility friction. We minimize the mean substation-distance proxy of selected sites:

$$F_3(x)={\displaystyle \frac{1}{K}}{\displaystyle \sum _{i\in \mathcal{I}}{x}_i}\cdot C_i.$$

(16)

Spatial dispersion constraint. To avoid redundant clustering and reflect practical spacing, we enforce a minimum separation distance $d_{\min }$ between any two selected sites ($d_{\min }=1.0 \mathrm{km}$ in the main configuration; Table S2), computed on centroid Euclidean distance:

$$d(i,k)\ge d_{\min } \mathrm{for} \mathrm{all} i\ne k \mathrm{with} x_i=x_k=1.$$

(17)

We solve the constrained three-objective problem using NSGA-II and run three independent trials per deployment scale to address algorithmic stochasticity.

Because the Pareto set contains multiple efficient trade-offs, we select an implementable compromise plan using TOPSIS in the normalized objective space with explicit weights ($w_{\mathrm{cov}}/w_{\mathrm{eq}}/w_{\mathrm{cost}}=0.45/0.35/0.20$; Table S2).

4. Results

4.1. ConvLSTM Demand Forecasting Results

As public charging activity is highly uneven across space and time, the hourly grid tensor is dominated by zero-demand cells, with only 7.75% of grid–time observations being active. Under such sparsity, overall error metrics can be misleading because a model may appear accurate simply by predicting near-zero values, while still failing in operationally relevant hotspots. We therefore report two complementary sets of metrics (see

Table 3. Forecasting performance of demand prediction models.

Model	MAE_Active	RMSE_Active	WMAPE_Active%	WMAPE_Total_%
ConvLSTM	2.586	3.941	19.89	21.03
Persistence	4.422	8.449	34.02	34.64
HistAvg	3.315	6.058	25.03	34.67

): (i) active-only errors computed on non-zero grid–time cells to assess hotspot dynamics, and (ii) citywide aggregate error (WMAPE_total) computed on the sum over grids to evaluate whether the model preserves the overall demand trajectory. This dual reporting provides a balanced assessment of both local fidelity and system-level consistency, which is particularly important when forecasts are later used to parameterize planning objectives and spatial prioritization. Table 3 shows that ConvLSTM achieves the strongest performance across all metrics. On active cells, it reduces MAE_active to 2.586 and RMSE_active to 3.941, compared with 4.422/8.449 for Persistence and 3.315/6.058 for Historical Average. In relative terms, this corresponds to a 41.5% reduction in MAE_active compared to Persistence and 22.0% compared to HistAvg; for RMSE_active, the reductions are 53.4% and 34.9%, respectively. The same advantage is reflected in WMAPE_active, where ConvLSTM achieves 19.90%, substantially lower than Persistence (34.02%) and HistAvg (25.50%). Crucially, the improvement is not achieved by merely fitting sparse zeros: at the citywide level, ConvLSTM also attains the lowest WMAPE_total (21.04%), representing an approximately 39.3% reduction relative to both Persistence (34.64%) and HistAvg (34.67%). This indicates that the proposed model better captures not only the magnitude of demand in active locations but also the aggregate evolution of urban charging load, thereby reducing systematic underestimation or overestimation in total demand.

To interpret these improvements, Figure 2 shows the citywide total demand time series (sum over all grids) for observed versus predicted values across the test horizon. Persistence typically reproduces short-term inertia but struggles with turning points, leading to lagged responses around demand ramps and peak hours. HistAvg provides a smoother baseline but tends to regress toward an “average day profile,” dampening peak amplitude under non-stationary conditions. By contrast, ConvLSTM tracks both timing and amplitude more closely, showing reduced peak underestimation and fewer phase shifts at high-demand hours. This behavior is consistent with the lower WMAPE_total, suggesting that the model learns transferable spatio-temporal dependencies beyond simple carry-forward or average seasonal patterns. Importantly for planning, improved peak tracking means hotspot prioritization is driven by meaningful temporal variation rather than being biased toward the “average” condition. Beyond temporal alignment, the model’s value for spatial planning depends on whether it preserves the geography of demand hotspots.

Figure 3 compares the observed and predicted peak demand surfaces, visualizing the absolute error. ConvLSTM reproduces the dominant hotspot structure (core clusters and corridor-like patterns) while controlling spurious diffusion into low-demand areas. The error map further shows that residuals are concentrated in a limited subset of high-intensity cells rather than being spatially widespread, indicating that the model’s remaining mistakes are primarily associated with the most volatile hotspots (where short-term fluctuations and local constraints are most substantial). This spatial behavior supports using the predicted demand layer as a planning-relevant surface: it maintains the relative ranking of high-priority grids while avoiding systematic false positives in peripheral cells. A common pitfall in short observation windows is that a weekday–hour historical average can degenerate into near-constant predictions when the training period does not cover the same day-of-week patterns as the test period. In our aligned implementation, the HistAvg baseline is corrected using a backoff strategy, ensuring it remains informative and preventing the creation of an artificially weak comparator. Under this fair setting, ConvLSTM still yields substantial gains, particularly on active grids and aggregate demand, demonstrating that the improvement is not a result of “win by baseline collapse” but reflects genuinely stronger predictive skill. From a planning perspective, the improved accuracy at both active-grid and total-demand levels reduces the risk of misallocating resources due to distorted hotspot intensity or biased citywide load estimates, thereby providing a more reliable demand layer for subsequent multi-objective siting.

4.2. Mobility-Derived Spatial Layers from Ride-Hailing Trajectories

This section reports the mobility-derived grid surfaces constructed from the ride-hailing GPS dataset using the trajectory encoder (TDAE). The purpose is not to forecast mobility itself, but to extract planning-relevant spatial representations of (i) mobility exposure and (ii) relative accessibility at the grid level. These layers are subsequently used to parameterize the accessibility-related objective and spatial constraints in the multi-objective siting model. Accordingly, our evaluation focuses on whether the learned surfaces are spatially interpretable, stable under rank-based comparison, and consistent with the observed charging-demand pattern (Figure 4).

Figure 4a visualizes the grid-level mobility intensity surface, which reflects the concentration of vehicle activity captured by the cleaned ride-hailing trajectories. The resulting field exhibits a pronounced core–corridor structure, with high-intensity clusters centered around the central urban area and elongated corridors aligned with principal transportation axes, while the peripheral grids are markedly weaker. This spatial organization is consistent with the expected activity pattern of a polycentric metropolis, indicating that the mobility signal is not dominated by random sampling noise. This concentration implies that mobility exposure is highly clustered and that siting decisions based on uniform spatial allocation would be inefficient in terms of serving high-activity locations.

Figure 4b reports the derived relative accessibility surface. Importantly, we interpret relative accessibility as a relative ranking/index of grid accessibility or attractiveness within the citywide mobility system, rather than an absolute travel-time measure. This framing is essential because the mobility trajectories (October 2019) and charging observations (February 2025) are not temporally aligned. By focusing on a unitless, rank-based accessibility index, we avoid over-claiming year-specific traffic conditions while still capturing the more persistent spatial structure of activity centers and corridor connectivity. The access_rel surface displays a coherent pattern in which central hubs and well-connected corridors consistently achieve higher relative accessibility, providing a complementary planning layer that reflects structural connectivity rather than demand realization alone.

To verify the stability of the accessibility pattern over time, we conducted a perturbation-based sensitivity analysis (see Figure 5). We compared the 48 h baseline against 24 h and 72 h windows and also tested a scenario random noise to simulate potential future changes (20% masking + Gaussian noise std 0.05). The results show that the core hotspots remain highly stable. The top 10% hotspots achieved an overlap of 94.6–95.7% across time windows and maintained 89.6% even under random noise. Furthermore, the global rank correlation remained near-perfect ($\rho >0.99$). These findings confirm that permanent urban infrastructure (e.g., road networks and commercial centers) drives these hotspots rather than short-term fluctuations. This justifies using the 2019 data as a robust proxy for the long-term relative spatial structure.

To examine whether mobility-derived signals are descriptively aligned with charging behaviors, Figure 6 compares hotspots from the mobility exposure layer against hotspots from the charging-demand surface. We define the analytical universe as the complete grid set (N = 9023). A key finding is the extreme sparsity of realized charging demand: non-zero charging observations occur in only 679 grids (accounting for just 7.53% of the map). In contrast, mobility signals derived from the TDAE layer provide a ubiquitous measure of potential exposure across the city. Comparing the spatial peaks, the hotspot sets (defined as the top 10% of grids in the valid intersection universe) show a moderate spatial overlap, with a Jaccard index of 0.39. This suggests that while high-mobility corridors often exhibit high charging demand, the two are distinct: mobility represents potential, while demand represents actual usage. Within the subset of locations that actually capture charging demand (active grids, N = 679), the distribution is moderately concentrated, with the top 10% of busiest grids accounting for 35.05% of the total realized load. This suggests a hierarchical service structure where a minority of core stations serve a significant portion of demand, but not to the extent of total monopolization. These results fundamentally justify the multi-objective integration of ConvLSTM and TDAE. Optimization driven solely by predicted demand would be blinded by the 7.53% sparsity, likely reinforcing existing cores while ignoring the vast majority of the city where latent demand exists but historical data is zero. By incorporating TDAE, which provides a continuous accessibility surface even in demand-blind zones, the framework can identify and serve structurally well-connected locations that are currently underserved, balancing the exploitation of known demand hotspots with the exploration of high-mobility potentials.

4.3. Multi-Objective Optimization Results and Trade-Offs

We solve the charging-station siting problem as a constrained multi-objective optimization problem. To address the stochastic nature of the NSGA-II algorithm and ensure the statistical reliability of the results, we executed three independent runs for each deployment scale (K = 15 and K = 30). The detailed hyperparameter settings for the optimization (e.g., population size, crossover/mutation rates) are provided in Table S2.

Across all independent runs, the distributions of objective values remained highly stable, confirming robust search behavior and reproducible trade-off patterns. Notably, the “allow existing” and “new-only” settings yielded identical objective summaries in our experiments, indicating that the existing-site option is not binding under the current candidate pool and constraints; thus, we report the aggregated results below.

Trade-offs for K = 15 (Figure 7a): The solution set exhibits an apparent tension among efficiency, equity, and cost. The coverage-oriented extreme achieves a coverage of 1504.5–1528.9, but with higher equity gaps (0.0853–0.0995) and moderate costs (1.866–2.491 km). In contrast, the equity-oriented extreme reduces the equity gap to a near-zero level (≈0),) at the expense of lower coverage (739.7–1027.2) and higher cost (1.529–2.938 km). Cost minimization alone yields very low-cost solutions (0.655–0.831 km), but these come with inferior service effectiveness (coverage 457.1–866.2) and non-negligible equity gaps (0.0152–0.0409). To obtain a balanced plan, we select a best-compromise solution from the Pareto set using TOPSIS. The compromise solutions are highly stable across the three independent runs: Coverage = 1009.0 ± 54.6, Equity Gap = 0.0078 ± 0.0045, and Cost = 1.550 ± 0.114 km (Mean ± SD). For the representative replicate shown in Figure 7a (rep_03; red star), the selected plan achieves Coverage = 1070.2, Equity Gap = 0.0129, and Cost = 1.462 km.

Trade-offs for K = 30 (Figure 7b): Increasing the deployment scale shifts the feasible trade-off surface upward in coverage while preserving the equity–cost tension. The coverage-oriented extreme ranges from 2530.5 to 2574.6, but with substantially larger equity gaps (0.1885–0.2264) and costs of 1.795–2.106 km. The equity-oriented extreme again achieves a near-zero equity gap (≈0) but requires higher cost (1.973–5.967 km) and sacrifices coverage (556.0–1176.9). The cost-oriented extreme attains relatively low costs (1.042–1.176 km) while maintaining moderate coverage (859.5–1561.1), albeit with higher equity gaps (0.0181–0.0825).The TOPSIS compromise solutions for K = 30 are likewise stable across runs: Coverage = 1728.9 ± 124.8, Equity Gap = 0.0179 ± 0.0113, and Cost = 2.535 ± 0.362 km (Mean ± SD). For the representative replicate shown in Figure 7b (rep_03; red star), the selected plan achieves Coverage = 1872.7, Equity Gap = 0.0229, and Cost = 2.704 km. Overall, the results highlight (i) diminishing coverage returns relative to cost, and (ii) a persistent equity–cost tension, where near-zero equity gaps are achievable only by accepting higher infrastructure costs and moderate coverage reductions.

4.4. Recommended Siting Plan and Spatial Characteristics of Selected Sites

Figure 8 maps the selected new-build stations under the Strictly New + Neighborhood setting, overlaid on the feasible buildable grid (dark gray) and existing stations (light gray). The K = 15 solution (Figure 8a) exhibits a clearly core-oriented but non-redundant spatial pattern. Most selected cells cluster in the central urban corridor, where existing stations are already dense. However, the new sites are placed in adjacent buildable cells rather than on existing-station cells, indicating a gap-filling strategy around saturated hubs. Beyond this central cluster, only a small number of sites are allocated to outer gaps—including a few cells in the north and south—which act as early “anchors” to reduce uncovered pockets under a 1.5 km neighborhood service radius.

When the budget increases to K = 30 (Figure 8b), the solution retains the K = 15 core (red) and adds an expansion set (yellow) that follows two dominant spatial logics. First, it densifies the central corridor by filling remaining adjacent buildable cells around the main activity cluster, strengthening local redundancy resistance while improving neighborhood coverage continuity. Second, the expansion sites extend along a north–northeast belt, forming a more elongated chain of new-build cells that pushes service toward peripheral and secondary-demand areas. This produces a more citywide footprint without uniformly dispersing sites, suggesting that the optimizer prioritizes connecting and extending existing service basins rather than scattering stations across low-demand areas. n addition to the layer-level stability test, we conducted a decision-level robustness check by perturbing the learned accessibility index access_rel with a ±20% noise scenario and re-running the full NSGA-II siting procedure under the same configuration (three independent runs). The TOPSIS-selected compromise plans remain broadly consistent with the baseline recommendations: for K = 15, the overlap is 11/15, 12/15, and 11/15 across runs (overlap ratio 0.733–0.800), and for K = 30, the overlap is 23/30, 25/30, and 22/30 (overlap ratio 0.733–0.833). Differences are limited to a small number of marginal substitutions near selection thresholds, while the overall spatial targeting and the two dominant logics identified above (central infill around hubs without co-location, and targeted peripheral extensions) remain consistent.

Overall, the mapped results confirm that the “Strictly New” requirement does not force unrealistic relocation away from demand. Instead, it yields a structured pattern of (i) central infill around existing hubs (without co-location) and (ii) targeted peripheral extensions that exploit neighborhood spillovers while directing part of the additional capacity to underserved edges.

To improve interpretability of the TOPSIS-recommended plan beyond Pareto summaries, we provide a compact descriptive table of representative selected cells and their key grid-level attributes (see

Table 4. Representative selected cells from the TOPSIS compromise plan and their neighborhood-level attributes (K = 30).

Location (gx, gy)	Neighborhood Demand (Sum)	Neighborhood Demand (Max)	Density Proxy	Access Rel	Substation Dist (km)	Population
(57, 57)	161.133	81.067	1.736	0.391	2.985	10.7k
(68, 55)	140.400	62.267	3.333	0.420	1.423	10.3k
(72, 51)	122.600	54.667	1.097	0.335	1.531	10.3k
(61, 57)	113.333	34.733	2.278	0.408	1.251	19.8k
(71, 53)	143.733	54.667	2.083	0.404	1.711	11.5k
(65, 73)	131.733	34.200	2.014	0.402	2.111	27.0k
(62, 68)	120.667	42.200	3.500	0.421	2.978	27.4k

). The table reports neighborhood-level served-demand indicators—computed over the 3 × 3 neighborhood centered at each selected cell, consistent with the neighborhood service rule—together with density proxy, baseline accessibility (trajectory-derived), substation-distance feasibility proxy, and population. These examples illustrate the typical placement logic under the joint coverage–equity–feasibility objectives: several selected cells are located adjacent to strong demand neighbors and therefore exhibit high neighborhood demand (e.g., neighborhood-demand sums of 161.133 at (57,57) and 143.733 at (71,53)), while still spanning heterogeneous urban contexts (density proxy 1.097–3.500; access_rel 0.335–0.421) and moderate substation distances (1.251–2.985 km). Importantly, because service is evaluated at the neighborhood level, a station does not need to coincide with the demand peak cell to deliver substantial coverage, and the neighborhood-demand columns provide a decision-relevant summary of the effective demand served around each selected location. For completeness, the full list of selected cells for the TOPSIS plan is provided in the exported results.

Finally, Figure 9 reports a like-for-like comparison of siting strategies under the same candidate pool (the exported 600-cell pool), the same constraints (fixed $K$, the $3\times 3$ neighborhood service rule, $d_{\min }$, and $K_{\mathrm{low}}$), and the same metric definitions for coverage, GPG, and cost. All values are normalized to the selected MOO compromise solution (MOO = 1.0; values $>1$ indicate better performance after orienting cost-type criteria).Across both $K=15$ and $K=30$, the greedy MaxCov baseline achieves higher coverage than MOO (=1.36 and =1.30), but its equity performance drops sharply (GPG ratios 0.10 in both scenarios) and its cost performance is also weaker (0.61–0.71), indicating that coverage maximization alone can severely compromise parity and feasibility. Conversely, MaxEq improves parity relative to MOO (1.25–1.11) but delivers substantially lower coverage (0.36–0.40) and poorer cost performance (0.40–0.39), reflecting efficiency losses when equity is pursued in isolation. Overall, the MOO framework avoids these one-sided extremes and provides a stable compromise solution that jointly manages the coverage–equity–cost tension under realistic constraints.

5. Discussion

This research developed a comprehensive hierarchical framework for optimizing EV charging station locations, with results demonstrating significant improvements in efficiency, cost-effectiveness, and equity. The findings have direct implications for sustainable urban development.

5.1. Principal Findings and Interpretation

This study yields three substantive insights that are relevant to charging-infrastructure planning. First, forecasting must be formulated and evaluated as a planning signal under sparsity, not as a purely predictive exercise. At the 1 km grid–hour resolution, the demand tensor is dominated by zero values (only 7.75% of grid–time observations are active), so “overall” metrics can reward models that fit zeros while remaining uninformative for operational hotspots. The dual evaluation protocol—hotspot-oriented errors on active cells plus system-level WMAPE on the citywide aggregate—therefore reflects a planning logic: siting decisions are driven by where peak stress emerges and whether the total demand trajectory is preserved.

Second, the analysis clarifies that mobility exposure and realized charging demand capture different constructs. The trajectory-derived layers provide ubiquitous citywide signals and exhibit a stable core–corridor structure, while realized charging demand is highly spatially sparse and constrained by the existing network. The moderate hotspot overlap (Jaccard = 0.39) indicates complementarity rather than redundancy: mobility represents potential exposure/structural connectivity, whereas demand reflects realized utilization shaped by supply and behavioral adaptation. This distinction explains why integrating both layers can mitigate “demand-blind” zones and supports an exploration–exploitation balance in siting.

Third, the optimization results show that equity gains are not a by-product of coverage expansion. Across deployment scales, the Pareto structure reveals a persistent tension between equity and cost: approaching near-zero equity gaps typically requires accepting higher connection frictions and/or moderate coverage reductions. Importantly, the TOPSIS-selected compromise solutions remain stable across independent NSGA-II runs, providing an implementable recommendation while keeping the underlying trade-offs transparent.

5.2. Planning Implications for Phased Deployment and Spatial Strategy

The framework provides several practical implications for planners. First, phased deployment is not merely an operational convenience but a rational response to structural trade-offs. Increasing the deployment budget (e.g., K = 15 to K = 30) expands the achievable service frontier and improves citywide coverage, yet it does not eliminate the equity–cost tension; rather, it reveals what additional coverage requires in terms of feasibility frictions (proxied here by substation-access distance) and distributional balance. This has two planning implications. On the one hand, early-stage investments should prioritize high-leverage “gap-filling” sites—locations that produce large neighborhood-level coverage gains while avoiding redundancy with already-served cores—because marginal returns are typically higher when service basins are fragmented. On the other hand, later-stage expansion can shift toward network consolidation and corridor extension, where the objective is not only to add coverage but to improve continuity of neighborhood service and to reduce persistent underserved pockets. From a management standpoint, this staged interpretation suggests a practical workflow: use smaller-K compromise solutions as “Phase-I candidates” for rapid deployment and pilot evaluation, then update the weight scenario (or the feasible candidate set) to generate Phase-II plans once utilization feedback and implementation constraints become clearer.

Second, the recommended layouts suggest a spatial logic that is more realistic than “uniform dispersion” interpretations of equity. Under the strictly new-build requirement and the minimum-separation constraint, the optimizer is discouraged from selecting already saturated cells and from co-locating with existing stations. Instead, it tends to place new sites in adjacent buildable cells around demand hubs—core-oriented but non-redundant infill—combined with a limited number of peripheral or secondary-center anchors that reduce uncovered pockets under the neighborhood service rule. This pattern carries a concrete equity message: equity-oriented planning does not necessarily mean reallocating investment away from the core; rather, it can be operationalized as (i) reducing local access gaps by targeting cells adjacent to saturated hubs, where marginal additions still improve neighborhood-level availability and reduce queuing pressure, while (ii) strategically extending service to edges and secondary belts where residents are otherwise persistently outside the service radius. In other words, the framework supports an interpretable “gap-filling + anchor” strategy that aligns with how networks are actually expanded: strengthening coverage in high-use basins without redundant co-location, while preventing peripheral exclusion via targeted expansions instead of diffuse scatter.

Finally, because TOPSIS is applied with an explicit weighting scheme (baseline weights: 0.45/0.35/0.20 for coverage/equity gap/cost; Supplementary Materials, Table S2), the framework naturally supports transparent scenario analysis. Rather than presenting a single “optimal” plan, the Pareto set provides the menu of feasible trade-offs, and TOPSIS offers a reproducible rule to select an implementable compromise under a stated policy preference. This enables planners to translate policy priorities into operational choices: for example, a reliability- or congestion-relief scenario may emphasize coverage (higher weight on coverage), a social-inclusion scenario may prioritize reducing disparity (higher weight on equity), and a grid-coordination scenario may emphasize feasibility (higher weight on cost proxy). Importantly, reweighting does not change the underlying optimization engine or the constraint environment; it changes only the decision rule for selecting a plan from the same trade-off surface, which keeps the planning process auditable and easy to communicate to stakeholders. We therefore view the weighting scheme not as a fixed “expert truth” but as a policy lever that can be stress-tested, documented, and updated as implementation feedback accumulates.

5.3. Limitations and Directions for Future Research

Several limitations define the boundary of interpretation and point to extensions:

(1)

Temporal representativeness: the demand layer is derived from a limited observation window; more extended temporal coverage would better capture seasonal and event-driven variability, thereby improving the stability of hotspot definitions.

(2)

Temporal mismatch between mobility and charging datasets: mobility trajectories and charging observations are not temporally aligned. We therefore interpret relative accessibility as a unitless, rank-based index that captures persistent structural connectivity, rather than an absolute measure of travel time. Future work should incorporate temporally matched trajectory data to strengthen contemporaneous access inference.

We also note that both city-scale ride-hailing GPS trajectories and real-world public-charging usage records are valuable yet inherently scarce datasets and fully synchronized multi-source data at this scale are rarely available in practice. We therefore aim to make a transparent and defensible use of the best-available data, while quantifying the associated uncertainty via sensitivity/robustness diagnostics wherever possible.

(3)

Engineering realism of the cost proxy: the cost term is modeled as road-network shortest-path distance to the nearest substation, capturing connection friction but not feeder capacity, transformer constraints, or permitting feasibility. Incorporating grid-capacity constraints and station-type heterogeneity would improve implementation realism and may reshape the equity–cost frontier.

6. Conclusions

This study develops a hierarchical spatio-temporal decision framework for public EV charging station expansion that integrates demand forecasting, mobility representation learning, and constrained multi-objective siting into a unified grid-based planning pipeline. The framework is designed to support sustainability-oriented planning decisions in the face of two persistent realities of urban charging systems: extreme demand sparsity and multi-objective trade-offs among service effectiveness, equity, and infrastructure feasibility.

Three conclusions can be drawn. First, planning-relevant demand forecasting must be hotspot-aware in the presence of sparse demand tensors. Because only a small share of grid–time observations are active, overall metrics alone can overstate performance for siting purposes. Using a dual evaluation protocol, the ConvLSTM with attention yields the most reliable planning signal, resulting in improved hotspot-oriented accuracy.

Second, mobility exposure and realized charging demand should be treated as complementary rather than interchangeable. Trajectory-derived layers supply ubiquitous citywide information about structural activity and accessibility patterns that remain visible even in demand-sparse zones. The moderate hotspot overlap between mobility and demand suggests that optimizing solely on demand risks reinforcing existing utilization patterns. In contrast, mobility-informed objectives can better identify structurally connected yet underserved locations.

Third, equity improvements are not a by-product of coverage expansion, and transparent trade-off management is therefore essential. The NSGA-II Pareto portfolios show persistent equity–cost tension under realistic constraints. TOPSIS provides an interpretable mechanism to select implementable compromise solutions from the Pareto set under an explicit weighting scheme, enabling scenario-based decision support and phased deployment comparisons.

Several limitations motivate future research. Demand is reconstructed from a limited temporal window, and longer observation horizons would strengthen generalizability. Mobility trajectories and charging observations are not temporally aligned; future work should incorporate temporally matched mobility data to support stronger contemporaneous accessibility inference. Finally, the infrastructure feasibility term is represented by a proxy based on road-network distance to substations; incorporating grid-capacity constraints, land feasibility, and station-type heterogeneity would improve implementation realism and may reshape the equity–cost frontier.

Overall, the proposed framework provides a reproducible pathway to integrate spatio-temporal prediction, mobility opportunity structures, and multi-objective optimization for equitable and operationally effective charging network expansion.