A Sustainable Dynamic Capacity Estimation Method Based on Bike-Sharing E-Fences

Abstract

Increasing urban traffic congestion and environmental pollution have led to the embrace of bike-sharing for its low-carbon convenience. This study enhances the operational efficiency and environmental benefits of bike-sharing systems by optimizing electronic fences (e-fences). Using bike-sharing order data from Shenzhen, China, a data-driven multi-objective optimization approach is proposed to design the sustainable dynamic capacity of e-fences. A dynamic planning model, solved with an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II), adjusts e-fence capacities to match fluctuating user demand, optimizing resource utilization. The results show that an initial placement of 20 bicycles per e-fence provided a balance between cost efficiency and user convenience, with the enterprise cost being approximately 76,000 CNY and an extra walking distance for users of 15.1 m. The optimal number of e-fence sites was determined to be 40 based on the solution algorithm constructed in the study. These sites are strategically located in high-demand areas, such as residential zones, commercial districts, educational institutions, subway stations, and parks. This strategic placement enhances urban mobility and reduces disorderly parking.

1. Introduction

As urban traffic congestion and environmental pollution escalate, bike sharing is increasingly embraced for its low-carbon and convenient attributes [1,2,3]. This popularity can be attributed to the various socioeconomic and environmental benefits associated with bike sharing, such as decreased CO₂ emissions, reduced disease rates, and diminished traffic congestion and noise pollution [4]. These benefits result from providing alternatives to automobile commuting and increasing public transit use. The rapid expansion of bike-sharing systems significantly enhances these benefits, contributing to the development of sustainable cities [1,5,6,7,8].

However, the operational efficiency of bike-sharing systems is intrinsically linked to optimizing the capacity and layout of electronic fences (e-fences) [9]. The examination of an environmentally friendly dynamic capacity estimation method for bike sharing seeks to accomplish two primary objectives: mitigating the environmental impact and enhancing service efficiency. First, judicious e-fence distribution can reduce the idle time of bicycles within urban areas, thereby diminishing energy consumption and exhaust emissions [10]. Second, strategically located e-fences can augment users’ propensity and frequency of use, which not only alleviates urban traffic congestion but also fosters low-carbon travel behaviors [11,12]. The research context for environmentally sustainable e-fence capacity estimation also encompasses considerations of urban spatial structure. The configuration of various functional zones, such as residential, commercial, and educational areas, directly influences the demand for shared bicycles [13]. For instance, deploying additional e-fences in densely populated locales or areas with suboptimal public transportation can effectively enhance travel efficiency and curtail private vehicle usage, consequently reducing environmental pollution.

The emergence of a new generation of bike-sharing systems, known as internet-based dockless bike sharing, is presently being observed [14]. Originating in China, it is swiftly expanding worldwide [15,16]. Unlike traditional bike-sharing systems that require docking at specific stations, dockless services allow users to unlock and pay for bikes using a smartphone and leave them at any convenient location [17,18]. This dockless bike-sharing model is developing at an unprecedented pace [19]. A pivotal component of this system is the implementation of e-fences, which are predetermined ‘virtual fences’ without physical barriers. These e-fence systems utilize Global Positioning Systems (GPS), Radio Frequency Identification Devices (RFID), or Bluetooth signals to ascertain the proximity of bikes to designated zones. Users who park bikes outside the authorized areas are unable to lock them and will continue to incur charges [20]. Furthermore, bike riders receive guidance from their app or navigation voices to direct them to appropriate parking locations [21]. However, this growth also brings new urban challenges, such as in Beijing and Singapore. One of the most pressing issues is inappropriate parking behavior. Due to the convenience of ‘dockless’ or ‘free to leave’ policies, a significant number of users park bikes in unsuitable locations, such as in pedestrian streets, in areas near metro entrances, or within gated communities. This behavior results in negative impacts, including the violation of vehicle right-of-way, obstruction of pedestrian movement, and reduced accessibility of bikes for subsequent users [22,23]. Shifting from free-floating parking to e-fencing parking inevitably decreases convenience, service levels, and user experiences, while also requiring operators to invest more in upgrading information systems for parking enforcement to meet governmental regulations. Hence, finding a practical design method for e-fencing capacity that balances user convenience, service levels, and operational costs is essential.

To resolve this problem, bike-sharing order data from Shenzhen, China, is utilized to design an environmentally friendly dynamic capacity estimation method for e-fence systems. These data encompass comprehensive details about bicycle trips, including start time, end time, start location, and end location. Such high-resolution information on bike-sharing demand is typically unavailable when planning a conventional fixed dock site. For designing an e-fence with dynamic capacity, this fluctuating demand can be accessed from the transaction records of the bike-sharing order data. Thus, a data-driven multi-objective optimization approach is proposed, which considers enterprise cost and user satisfaction maximization to plan environmentally sustainable e-fence systems utilizing bike-sharing order data. Moreover, an improved strategy of the NSGA-II algorithm is put forward in this paper to solve for the approach results with the large size while ensuring good solution quality.

The remainder of this study is organized as follows: Section 2 reviews existing studies and highlights research gaps. Section 3 establishes the methodology, including problem descriptions, assumptions, the optimization model, and problem statements. Section 4 proposes solution algorithms for our model. Section 5 presents a numerical experiment to demonstrate the feasibility of the proposed methodology, along with a case study in Shenzhen, China. Finally, Section 6 offers conclusions for this study.

2. Literature Review

The essence of planning and siting e-fences for bike sharing lies in the strategic placement of facilities to maximize efficiency, enhance user satisfaction, and promote urban transportation development [3,15,24]. Unlike traditional public bicycles that rely on fixed docking stations, the siting of e-fences for bike sharing is relatively novel [17,20]. Factors such as the location, number, and area of the e-fences must be considered due to the random parking behavior of users and the pronounced tidal phenomenon complicating the siting process [20,23,25].

Academics have increasingly concentrated on optimizing bike-sharing site planning in practical contexts, addressing both site selection and relocation challenges [2,20,25,26]. For example, Ho and Szeto examined the static bicycle relocation problem and proposed an efficient hybrid neighborhood search method for optimization [27]. Wang et al. introduced a static green bicycle relocation problem, formulating it with a mixed-integer linear programming model aimed at minimizing total carbon dioxide emissions during vehicle relocation [28]. Legros addressed the routing problem using a Markov decision process, developing a decision support tool to minimize the occurrence of unsatisfied users at empty or full stations [29]. Ren et al. developed a nonlinear model to minimize the sum of travel costs and inventory costs for static bike-sharing rebalancing [30]. Duran et al. tackled site equity in low-income areas, employing a hybrid method combining heuristics and data mining to plan parking locations for bike sharing [13]. Nair et al. constructed a two-layer mathematical model to optimize the bike-sharing system in Washington, focusing on maximizing user travel demand and bicycle utilization rates [12]. Kabak et al. evaluated the current status of the bike-sharing system in Izmir, Turkey, utilizing 12 criteria to propose new station locations [10]. Mix et al. proposed an integrated approach incorporating built environment and accessibility variables to model demand for bike-sharing trips and determine optimal station locations, establishing a maximum demand coverage model for station allocation [31]. Recent academic efforts have also sought to optimize bike-sharing system operations, including minimizing time, carbon dioxide emissions, and walking costs as well as maximizing social welfare through balanced dispatch operations. Fu et al. introduced an integrated siting model for bike-sharing stations, aiming to maximize daily revenue based on station location and total investment in bike acquisition [24]. Shi et al. developed an accelerated maximum coverage model with complementary coverage, targeting the maximum coverage location problem to identify ideal locations for electric fences [32]. Cai et al. established a multi-objective integer non-linear programming model to transform an existing free-floating BSS into a geo-fence-based system by identifying the geo-fencing stations to be opened, their respective parking capacities, and the deployment of bikes [22].

Existing research provides a foundation for the planning and layout of e-fences for bike-sharing. However, most studies focus on peak periods and fixed-capacity, one-time e-fence siting layouts, while user demand for bike sharing fluctuates over time. Bike-sharing travel exhibits spatial and temporal heterogeneity and a pronounced tidal phenomenon. Although fixed and static e-fences are simple to manage, they can lead to issues such as insufficient space, preventing users from returning bicycles, or excess space, resulting in wasted resources. This mismatch in resource utilization and lack of data interaction underscores the need for a different approach. Therefore, this paper focuses on the dynamic planning of environmentally sustainable e-fence capacity, taking into account the travel characteristics of bike sharing.

3. Methodology

The sustainable dynamic capacity of e-fence problem involves planning the open capacity of each e-fence for each time unit based on the temporal and spatial usage characteristics of bike sharing. The problem schematic is illustrated in Figure 1. During the dynamic time period, the locations of bike-sharing e-fences can be designed and planned using our methodology to adjust the area of the e-fence according to user demand for borrowing and returning bicycles. Users borrow and return bicycles at designated locations through a mobile app. For instance, there are three e-fences within the same parcel of land. During period t + n, when user demand is high, the area of the e-fence is increased accordingly. Conversely, during period t, when user demand is lower, the area of the e-fence is decreased. This dynamic adjustment not only saves land resources but also improves the utilization rate of bike-sharing e-fences. During peak times, the capacity of the e-fence is expanded to better meet user demand by increasing the site area. During off-peak times, the open capacity is reduced to release excess space, thereby lowering maintenance and management costs. This approach makes the sustainable e-fence system more flexible and better able to adapt to changes in user demand.

3.1. Notation and Assumptions

Due to the numerous parameters involved in the dynamic planning of bike-sharing e-fences, the process is quite complex. To effectively transform the dynamic capacity optimization problem of bike-sharing e-fences into a mathematical model, the following assumptions were made:

• Bike-sharing e-fence locations are determined based on distribution planning optimization.
• Users can locate nearby e-fences via a mobile app and choose the nearest location to borrow or return a shared bicycle.
• There are multiple user travel demand points and e-fence locations. Each e-fence can serve multiple user demand points, but only one e-fence can be selected for a given demand point.
• Users can only borrow and return bicycles within the planned bike-sharing e-fences.
• Euclidean distances are used in the model instead of street distances. The study area is an urban region with a high density of roads and intersections, allowing users to travel in any direction. Thus, travel distances are unlikely to be significantly greater than straight-line distances. Bicyclists are less likely to take long detours compared to other transportation users (e.g., subways, buses). Therefore, O’Brien et al. suggest that using Euclidean distances in a bicycle system is effective [33].
• The area of e-fences will not be adjusted frequently and will change in integral multiples of peak hourly periods.

The following notations are used in the model formulation:

Sets

J	E-fence collection, $J=\left\{\mathrm{1,2},\dots ,j\right\}$;
B	User borrowing points of requirement collection, $B=\left\{\mathrm{1,2},\dots ,b\right\}$;
R	User return points of requirement collection, $R=\left\{\mathrm{1,2},\dots ,r\right\}$;
T	Time period slot assemblies, $T=\left\{\mathrm{1,2},\dots ,t\right\}$.

Parameters

$p_l^t$	The probability that a user travels to the e-fence at time period t, conditional on walking l meter;
$S_j^t$	Capacity of the e-fence j at time period t;
$S_{min}^t$	Minimum capacity of the e-fence;
$S_{max}^t$	Maximum capacity of the e-fence;
$D_r^t$	In time period t, the demand of users to return the bicycle at I;
$D_b^t$	In time period t, the demand of users to borrow the bicycle at k;
$\alpha$	E-fence capacity change time period unit;
$\beta$	E-fence capacity weight factor;
$\theta$	Initial number of bicycles placed on the e-fence;
$d_{rj}^t$	Distance generated by the user’s return process;
$d_{bj}^t$	Distance generated by the user’s borrowing process;
$d_{max}$	Maximum distance for borrowing and returning bicycles.

Variables

$X_{bj}^t$	Whether the borrowing demand point k is serviced by the e-fence j at time period t (1 if it is serviced and 0 if it is not serviced);
$X_{rj}^t$	Whether the return demand point is serviced by the e-fence j at time period t (1 if it is serviced and 0 if it is not serviced).

3.2. Multi-Objective Integer Programming Models

The proposed dynamic capacity of e-fence problem elaborated in Section 3.1 can be formulated into the multi-objective integer non-linear programming model:

$$Min {\mathrm{Z}}_1=C_1\sum _{t=1}^T\sum _{j\in J}{S}_{jt}+C_2\sum _{t=1}^T\sum _{j\in J}\sum _{b\in B}(1-p_{bj}^t)D_b^t{x}_{bj}^t+C_3\sum _{t=1}^T\sum _{j\in J}\mathit{sgn}(\left|S_{j(t+1)}-S_{jt}\right|)$$

(1)

$$Min {\mathrm{Z}}_2=C_4\left(\sum _{t=1}^T\sum _{j\in J}\sum _{r\in R}{d}_{rj}^t{D}_r^t{p}_{rj}^t{x}_{rj}^t+\sum _{t=1}^T\sum _{j\in J}\sum _{b\in B}{d}_{bj}^t{D}_b^t{p}_{bj}^t{x}_{bj}^t\right)$$

(2)

subject to

$$p_{ij}^t=\left\{\begin{array}{c}(1-0.00194{)}^{d_{rj}^t},0\le d_{rj}^t\le 300\\ (1-0.00194{)}^{300}\times (1-0.01307{)}^{d_{rj}^t-300},300\le d_{rj}^t\le 500\end{array}\right.\forall t\in T,r\in R,j\in J$$

(3)

$$S_{jt}={\displaystyle \frac{\left(S_{j(t-1)}+{\sum }_{r\in R}{D}_r^t{p}_{rj}^t{x}_{rj}^t-{\sum }_{b\in B}{D}_b^t{p}_{bj}^t{x}_{bj}^t\right)}{\beta }}\forall t\in T,j\in J$$

(4)

$$S_{j0}=\theta$$

(5)

$$\sum _{j\in J}{x}_{bj}^t=1\forall t\in T,k\in K$$

(6)

$$\sum _{j\in J}{x}_{rj}^t=1\forall t\in T,r\in R$$

(7)

$$\left\{\begin{array}{c}{d}_{bj}^t\le d_{max}\forall b\in B,t\in T\\ d_{rj}^t\le d_{max}\forall r\in R,t\in T\end{array}\right.$$

(8)

$$T_n=\left\{[\left(t_0+\alpha \left(t-1\right),t_0+\alpha t\right]\left|n\in Z^{+},\alpha \in Z^{+}\right.\right\}$$

(9)

$${S_{min}^t<S}_{rj}^t<S_{max}^t\forall j\in J,t\in T$$

(10)

$$x_{bj}^t=\left\{\mathrm{0,1}\right\} x_{rj}^t=\left\{\mathrm{0,1}\right\}$$

(11)

The objectives (1) and (2) represent multiple objective functions expressing cost, including business costs Z₁ and users’ first-/last-mile travel distance cost Z₂. Objective (1) is the business costs, and the cost consists of the footprint cost of the e-fence $C_1{\sum }_{t=1}^T{\sum }_{j\in J}{S}_{jt}$, the cost of lost user orders $C_2{\sum }_{t=1}^T{\sum }_{j\in J}{\sum }_{b\in B}\left(1-p_{bj}^t\right)D_b^t{x}_{bj}^t$, and the cost of technical support for capacity adjustment $C_3{\sum }_{t=1}^T{\sum }_{j\in J}\mathit{sgn}(|S_{j(t+1)}-S_{jt}|)$. Objective (2) represents the users’ first-/last-mile travel distance cost. It aims to maximize user satisfaction by minimizing user return distance cost $C_4{\sum }_{t=1}^T{\sum }_{j\in J}{\sum }_{r\in B}{d}_{rj}^t{D}_r^t{p}_{rj}^t{x}_{rj}^t$ and borrowing distance cost $C_4{\sum }_{t=1}^T{\sum }_{j\in J}{\sum }_{b\in B}{d}_{bj}^t{D}_b^t{p}_{bj}^t{x}_{bj}^t$, and C₁, C₂, C₃, C₄ are cost factors, respectively.

Constraint (3) represents the probability that a user continues to use a shared bicycle for every additional 1 m of walking in the distance from 0 to 500 m.

Constraint (4) represents the change in the capacity of the e-fence and consists of the number of bicycles in the e-fence in the previous time period and the number of borrowed and returned bicycles in the current time period.

Constraint (5) indicates the number of bicycles initially placed at each e-fence in the region.

Constraint (6) indicates that a user’s need to borrow a bicycle can be satisfied by an e-fence.

Constraint (7) indicates that a user’s need to return a bicycle can be satisfied by an e-fence.

Constraint (8) indicates that users will not walk more than the maximum walking distance to borrow or return bicycles.

Constraint (9) denotes the collection of time periods of e-fence capacity change in integer multiples of the peak hour length.

Constraint (10) indicates the upper and lower limits of the capacity of the e-fence at each location.

Constraint (11) indicates that the two decision variables are binary variables (0 or 1).

4. Solution Algorithms

Given the complexity of the dynamic capacity of the e-fence model, especially for large-scale problems, a straightforward enumeration of all Pareto efficient solutions is impractical. Therefore, an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II) is proposed to solve large-scale problems while ensuring good solution quality [34]. The NSGA-II is a widely recognized and extensively utilized multi-objective optimization algorithm within the domain of evolutionary computation. It was proposed by Deb et al. in 2002 as an enhancement over its predecessor NSGA, addressing several limitations, such as high computational complexity, a lack of elitism, and the need for specifying a sharing parameter [35].

However, NSGA-II has some limitations. For instance, in the gradient-based stochastic search method, the difference between a point and its adjacent local point is used to estimate the gradient information, which can increase computation time and make the problem prone to falling into local optima. Thus, this paper proposes an improved strategy for the NSGA-II algorithm, incorporating two main enhancements:

• Hybrid Operator Incorporation: Introducing a gradient operator that combines with the crossover and mutation operators to form a hybrid operator. This hybrid operator aids in generating a new population, thereby enhancing the algorithm’s search capability.
• Selection Strategy Enhancement: When selecting the new population generation, consideration is given to higher Pareto ranks in NSGA-II and smaller crowding distances of individuals. Additionally, poor individuals in the population may be replaced by candidates from a balanced space–time population according to specified probabilities aimed at guiding the algorithm away from local optima.

The process of the improved NSGA-II can be delineated through the following eight stages:

Step1: Initialization

A population P of candidate solutions is initialized randomly with a predefined population size N. Each candidate solution is evaluated based on multi-objective functions to establish their fitness values.

Step 2: Offspring generation

Combined with crossover and mutation operator to make up the hybrid operator, the hybrid operator is used to produce a new generation of population. An offspring population Q of size N is generated from the parent population P. These operators are instrumental in exploring the search space by combining and modifying existing solutions.

Step 3: Fitness evaluation and population combination

The fitness of each individual in the offspring population Q is evaluated based on the same set of multi-objective functions used for the parent population. The parent population P and the offspring population Q are combined to form an intermediate population R, whereas R = P ∪ Q. This combined population has a size of 2N.

Step 4: Non-dominated sorting

Non-dominated sorting is performed on the combined population R to categorize individuals into several non-dominated fronts F₁, F₂, …, F_k. Each front F_k represents a level of dominance, where F_k being the Pareto front containing the best non-dominated solutions.

Step 5: Crowding distance calculation

A crowding distance metric is calculated for each individual in each front to measure their proximity to other solutions within the same front. This metric helps maintain diversity in the population by ensuring solutions are well distributed along the Pareto front.

Step 6: New population selection

An empty population P′ is initialized. Starting with the first front F₁, individuals are iteratively added to P′ until the addition of the next front would cause P′ to exceed the population size N. When the population size limit is approached, the individuals in the current front are sorted in descending order based on their crowding distance. The most diverse individuals are selected to fill the remaining slots in P′ up to size N. When choosing a new generation of population, the space–time balance population candidate is applied to implement substitution operation according to certain conditions for keeping the diversity and the uniformity of the new generation of population.

Step 7: Population update

The newly formed population P′ becomes the parent population P for the next generation. The process of offspring generation, evaluation, combination, sorting, and selection is repeated for a predefined number of generations or until a convergence criterion is met.

Step 8: Termination and result

The algorithm is terminated upon satisfying the specified termination condition, such as reaching a maximum number of generations or achieving convergence to a stable Pareto front. The final population P represents the set of Pareto-optimal solutions that provide a diverse set of trade-offs among the multiple objectives.

The flow of the proposed improved NSGA-II algorithm is shown in Figure 2.

5. Numerical Experiment and Case Study

5.1. Data Description and Model Parameters

The data for this study on bike sharing originate from the Shenzhen Municipal Government’s Open Data Platform (https://opendata.sz.gov.cn/ accessed on 16 July 2024). The dataset spans from January to August 2021 and includes approximately 240 million bike-sharing orders. It comprises eight data items: user ID, start time, start longitude, start latitude, end time, end longitude, end latitude, and enterprise ID.

To ensure data quality, travel chains where users quickly return a bike after borrowing—possibly due to bike issues, discomfort, short usage, or distance—will be screened out as anomalies and excluded from the analysis. For incomplete data chains (e.g., only return orders or only borrowing orders), which may occur due to equipment failure or users forgetting to return the bike, these instances are rare and will also be excluded from the analysis.

From the bike-sharing data in Shenzhen, a single day’s order data were utilized to create a travel demand distribution map, depicted in Figure 3. The figure illustrates that the demand for bike sharing in Shenzhen is primarily concentrated in several core areas, such as Nanshan District, Futian District, and Bao’an District. To validate the proposed algorithm’s effectiveness, a rectangular area within Nanshan District of Shenzhen was selected for case validation. This area spans from latitude 22.5149 to 22.5221 and longitude 113.9296 to 113.9421, as illustrated in Figure 3. This area has a high population density of bike-sharing users and frequent travel demand. Additionally, it contains many residences, schools, commercial centers, attractions, and large event venues, which are hotspots for bike-sharing usage. The central area was chosen due to its well-developed transportation network and the relative congestion of public transportation and private vehicles, making bike sharing a convenient option. Furthermore, the roads in this area are spacious, and there are ample parking spaces, making it suitable for the location and deployment of e-fences.

The occupation cost of each shared bicycle is 10 Chinese Yuan (CNY) per bicycle. If a user abandons the use of a shared bicycle, the cost of order loss is 1 CNY per bicycle. The technical support cost for e-fence capacity adjustment is 2 CNY per place. The walking distance cost for users to borrow and return bicycles is 0.03 CNY per meter. The capacity of the e-fence ranges between 5 and 30 bicycles. In this paper, α represents the dynamic update time period of the electronic fence, which is set to 2 h. β is the e-fence capacity weight factor, with a range of 0 to 1. It indicates the ratio between the capacity of the e-fence and the number of user orders for borrowing a bicycle. In practical applications, the capacity of the e-fence should be slightly larger than the number of user orders. For this paper, we have set β to 0.8, as shown in

Table 1. Model parameter specification.

Parameters	Notation	Retrieve Value	Unit
Bicycle land-use costs	$C_1$	10	CNY/bicycle
Lost order costs	$C_2$	1	CNY/bicycle
Technical support costs for capacity adjustment	$C_3$	2	CNY/position
Walking distance cost	$C_4$	0.03	CNY/m
Bicycle capacity limits	$S_{min},S_{max}$	5, 30	Per bicycle
E-fence capacity change time period unit	$\alpha$	2	h
E-fence capacity weight factor	$\beta$	0.8	-

.

5.2. Sensitivity Analysis

Parameter θ represents the initial number of bike-sharing instances for each e-fence capacity. This parameter significantly influences the recommended design plans for the e-fence, including the cost to the business and the extra walking distance for the user. Therefore, it is crucial to investigate how these solutions vary with changes in θ. Given the low user demand for borrowing and returning shared bikes between 1:00 a.m. and 5:00 a.m., the study period for this model is from 6:00 a.m. to midnight. Since peak hours last two hours, the capacity change cycle is also set to two hours, excluding dynamic changes in parking spot capacity within this period, resulting in nine time periods. The initial number of bike-sharing instances was calculated using the methodology established in this paper, and the corresponding final calculations are depicted in Figure 4.

When the initial number of bike-sharing instances placed in the region is five, the algorithm iteration convergence curve is shown in Figure 4a. Convergence begins at the 34th iteration and stabilizes until reaching the maximum of 200 iterations; at this point, the enterprise cost is approximately 95,000 CNY, and users are required to walk an extra 17.5 m. Similarly, when the initial number of bike-sharing instances is 10, as shown in Figure 4b, convergence starts at the 96th iteration and stabilizes until the maximum of 200 iterations. At this point, the enterprise cost is about 113,000 CNY, and users are required to walk an extra 17.3 m. For an initial placement of 15 bikes, the convergence curve in Figure 4c shows that convergence begins at the 3rd iteration and stabilizes at the maximum of 200 iterations, with an enterprise cost of around 106,000 CNY and an extra walking distance of 17 m. When the initial placement is 20 bikes, as depicted in Figure 4d, the optimal value begins to converge at the 79th iteration and levels off at 200 iterations, with a cost of about 76,000 CNY and an extra walking distance of 15.1 m for users. Finally, with 25 bikes initially placed, shown in Figure 4e, convergence starts at the 34th iteration and stabilizes at 200 iterations, resulting in an enterprise cost of approximately 96,000 CNY and an extra walking distance of 17.3 m for users.

Following these five finalized results with varying θ values, simulation-based heuristics were performed to determine the optimal initial number of bike-sharing instances. The results are illustrated in Figure 5. It is worth noting that for θ = 20, in the planned deployment of the e-fence in the study area, the business cost is approximately 76,000 CNY (blue line in Figure 5), and the extra walking distance for the user is 15.1 m (orange line in Figure 5).

5.3. Optimal Dynamic Capacity of E-Fences

Based on the optimal initial number of bike-sharing instances identified in Section 5.2, we have calculated the distribution planning and dynamic capacity of e-fences over a 24 h period. Utilizing the solution algorithm outlined in Section 4, we determined that 40 e-fence sites are optimal. The distribution of these sites is depicted in Figure 6. This distribution is closely aligned with bike-sharing usage patterns, ensuring efficient bike-sharing operations and urban mobility. In contrast, the absence of e-fences results in the disorderly parking of bicycles, often obstructing sidewalks, subway entrances/exits, and shopping malls. Such disorderly parking infringes upon vehicular traffic rights, obstructs pedestrian pathways, and diminishes the availability of bicycles for subsequent users. Our rationally planned e-fence sites are strategically located in high-demand areas, including residential zones (stations 1, 2, 4, 9, 19, 20, etc.), commercial districts (stations 16, 17, 18, etc.), educational institutions (stations 6, 25, 35), subway stations (stations 3, 7, 8, 22, 33), and parks (stations 26, 27). This strategic placement ensures efficient bike-sharing operations and enhances urban mobility.

With an initial placement of 20 bicycles per e-fence,

Table 2. The capacity of the e-fence under various time periods.

E-Fence Number	Time Period (6.00~24.00)
	1	2	3	4	5	6	7	8	9
1	25	30	30	9	10	10	5	5	5
2	10	10	5	10	30	5	25	30	25
3	5	10	5	30	30	5	5	30	30
4	25	30	21	5	5	5	5	5	5
5	30	30	30	5	16	5	5	5	5
6	5	5	10	5	8	30	30	5	5
7	5	30	30	30	30	5	25	24	15
8	25	30	30	30	10	10	30	30	11
9	25	30	25	5	8	15	5	5	5
10	15	25	25	19	12	10	8	5	5
11	8	20	30	25	25	15	5	10	5
12	5	5	8	13	15	16	30	30	30
13	5	5	5	8	10	25	25	30	30
14	5	5	15	10	5	15	20	15	15
15	5	8	5	20	20	20	15	15	15
16	5	5	5	10	12	15	20	25	10
17	5	5	8	10	15	15	20	15	15
18	5	5	5	10	6	25	30	30	5
19	30	30	30	24	18	17	5	5	5
20	30	30	30	23	15	15	5	5	5
21	30	30	30	21	30	9	5	5	5
22	30	30	30	10	5	5	30	30	15
23	30	30	29	25	7	15	15	10	5
24	30	30	30	30	30	5	18	30	5
25	5	5	10	15	15	30	30	30	30
26	5	5	5	5	15	30	30	30	23
27	17	30	30	30	30	21	8	5	5
28	30	30	30	22	30	5	5	5	5
29	5	5	10	30	9	5	30	30	5
30	5	5	5	20	30	30	30	30	30
31	5	5	5	5	5	30	30	30	30
32	5	5	12	5	5	15	30	15	5
33	5	5	5	30	15	30	20	25	10
34	5	5	5	16	20	25	30	30	30
35	5	5	5	10	25	30	30	30	5
36	30	30	25	25	15	15	15	5	5
37	30	30	21	5	5	15	5	5	5
38	30	30	25	15	5	30	5	5	5
39	30	30	30	30	30	30	30	30	30
40	30	30	30	30	5	5	5	5	5

presents dynamically optimized capacities for each time period based on the planned locations of the bike-sharing e-fences. The optimization process considers various factors, such as user demand patterns, peak and off-peak hours, and the specific needs of different areas within the city. By doing so, the system can effectively balance the distribution of bicycles, ensuring availability where and when it is most needed while avoiding over-concentration in less critical areas. For instance, during peak commuting hours in the morning and evening, e-fences near residential areas and transit hubs, such as subway stations, are allocated higher capacities. This ensures that users have ample bicycles available for their journey to work or school. In contrast, during the daytime, when commercial activities peak, the capacity in business districts and shopping malls is increased to accommodate shoppers and employees.

Figure 7 illustrates the planned locations and capacity changes of the e-fences during each study period. The legend, ranging from blue to red, indicates an increasing capacity trend. This figure allows us to observe the changes in e-fence capacity across the region throughout the day.

For example, the demand for bike sharing varies across different areas and times, affecting the supply capacity of the e-fences. For instance, during the morning peak period (Figure 7a,b), the capacity of e-fences around residential areas (stations 1, 2, 4, 9, 19, 20, etc.) is higher to accommodate commuters. Similarly, the capacity near schools’ peaks between 6:00 and 8:00, coinciding with students’ commute times. Additionally, the morning train at Houhai Station at 5:55 requires that the capacity of the e-fences around subway stations meets the last-mile travel needs of subway commuters.

After the morning peak, the capacity of e-fences (Figure 7c–e) in residential areas (e.g., stations 2, 3, 13, 34, etc.) decreases, and when parked bicycles exceed the capacity limit, users need to walk an average of 20 m to park in nearby redundant e-fence locations, which are closer to commercial areas (stations 19, 21, 22, etc.). This arrangement benefits users in commercial areas.

During evening peak hours (Figure 7f,g), the capacity of e-fences near residential areas (stations 2, 5, 26, 30, etc.) and schools (stations 6, 25, 35) increases again. This not only facilitates the use of bike sharing but also ensures adequate parking capacity for users, reducing the need for bicycle redistribution the following morning.

At night (Figure 7h,i), to meet the commercial needs of shopping malls and subway stations, the capacity of shared bicycles in certain commercial areas (stations 12, 13, 35, etc.) and subway (stations 3, 7, 22) will be increased accordingly. During this time, the capacity in residential areas and other regions will be reduced. This adjustment is not intended to move already parked shared bicycles to other fences but to prevent additional users from parking their shared bicycles in these electronic fences. This dynamic management ensures bike resources are allocated effectively based on demand throughout the day. By increasing capacity in commercial areas and subway stations at night, the system accommodates the influx of users who frequent these locations for evening shopping or late-night commutes. Conversely, reducing capacity in residential areas during these hours reflects the decreased demand for bicycles, as most residents are likely to be home.

In conclusion, the dynamic planning model for e-fences developed in this study enables the precise parking and scheduling of bike sharing, reducing disorderly parking and enhancing the urban environment’s cleanliness and aesthetics. Dynamic planning optimizes bicycle distribution based on real-time data, improving resource utilization efficiency and reducing vacancy rates and scheduling costs. For example, if the dynamic changes in e-fence capacity are not considered and the maximum capacity required for each e-fence is selected for planning and deployment, an area of 10,800 square meters would need to be occupied. However, by considering the dynamic changes in e-fence capacity, only 6015 square meters of e-fence would need to be planned and deployed, resulting in a saving of 4785 square meters compared to the same period last year. This approach allows for the expansion of e-fence capacity during peak hours and the reduction of open capacity during low peak hours, thereby releasing excess space and reducing maintenance and management costs. User demand is met while the utilization rate and effectiveness of the e-fences are improved. Moreover, e-fence technology enhances the user experience and travel efficiency through data analysis and prediction.

6. Conclusions and Discussion

This paper investigates the optimization of bike-sharing e-fences (e-fences) to address urban traffic congestion and environmental pollution. Utilizing bike-sharing order data from Shenzhen, China, a data-driven multi-objective optimization approach is proposed to plan environmentally sustainable dockless e-fence systems (DES). The study aims to maximize enterprise cost efficiency and user satisfaction by dynamically adjusting e-fence capacities based on real-time demand. The dynamic capacity of e-fences is optimized using a multi-objective integer non-linear programming model. This model considers business costs and user satisfaction, and it is solved using an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II). The improved algorithm enhances search ability and avoids local optima through a hybrid operator combining crossover and mutation operators and space–time balance population candidate replacement. The methodology is validated through a case study in Shenzhen, using high-resolution data from the city’s open data platform. These results show that sensitivity analysis reveals the optimal initial number of bike-sharing instances per e-fence to balance business costs and user walking distance. The optimal initial number was found to be 20 bicycles, resulting in a business cost of approximately 76,000 CNY and an extra walking distance of 15.1 m. The dynamic capacity of e-fences was calculated for 40 sites over a 24 h period. The strategic placement of e-fences in residential, commercial, educational, and transit areas aligns with shared bicycle usage patterns. The dynamic model adjusts e-fence capacity based on real-time demand, enhancing urban mobility and reducing disorderly parking. This approach reduces the required e-fence area from 10,800 square meters to 6015 square meters, saving 4785 square meters.

The dynamic planning model for e-fences significantly improves resource utilization efficiency, reduces maintenance and management costs, and enhances user satisfaction. The study’s results demonstrate the effectiveness of dynamic e-fence planning in optimizing bike-sharing systems. However, there are still some shortcomings and areas for improvement in this paper. The applicability of the model to other modes of shared transport, such as electric bikes and scooters, will be explored. The requirement of docks or charging stations for these vehicles will be considered in future iterations of the model. It will be investigated whether the dynamic system, which has been validated in this specific case, can be generalized and adapted for other contexts and transport modes. Future work will also include refining the algorithms for dynamically adjusting e-fence capacities and locations based on real-time data and user feedback.