Introduction

With the continuous development of motorization and urbanization, transportation emission has become a main source of air pollution. Compared to traditional fossil fuel vehicles, electric vehicles (EVs) offer advantages in reducing pollutant emissions and conserving fuel oil energy. Accordingly, the Chinese government has introduced many policy incentives to promote the adoption of EVs, such as financial benefits, substantial investments in EV charging infrastructure and R&D, and exemption from road toll fees and license plate rules [11]. China has also sustained rapid growth in its number of new energy vehicles, which exceeded a million for three consecutive years [9]. By 2025, the sales of new energy vehicles in China are expected to account for approximately 20% of the new vehicle sales in this country [18].

However, people still have some concerns about purchasing an EV, the most significant of which is the availability of charging infrastructure and technical support [22]. To alleviate this range anxiety, the public parking lots in most cities of China have installed charging piles in some parking spaces, i.e., EV parking spaces. In 2010, Shenzhen, one of China’s biggest city, started charging piles deployment in residential communities (5% of community parking spaces) and public parking lots (10% of public parking spaces) [16]. The Hangzhou Municipal Government requires each public parking lot to reserve 10% of its parking spaces for charging EVs [27]. This one-size-fits-all strategy is widely used in China, that is, regardless of size, allocate the same proportion of parking spaces for EV to charge. This proportion is recommended and required by the government. The original motivation for promoting this strategy lies in two aspects. On the one hand, it can increase the number of charging piles simply and directly. On the other hand, public parking lots are generally located near travel destinations, and charging stations can effectively meet the charging demand of EVs. However, with the growth of EVs, transforming ordinary parking spaces into EV parking spaces with charging piles based on one-size-fits-all strategy faces three problems. First, whether some charging stations close to hot destinations will overheat. Second, how many demands of EVs can be meet by charging stations set up in accordance with this one-size-fits-all strategy. Third, how much impact this one-size-fits-all strategy has on the entire parking lots system.

To address these problems, an accurate assessment of this one-size-fits-all strategy is key. The prediction of charging demand is affected by the individual behavior of the EV drivers and the dynamic state of the parking lot. How to predict and evaluate this process becomes a challenge. Agent-based model (ABM) is a simulation model, which can simulate real-world scenarios and provides a natural description of a complex system. It has the ability to take into account individual heterogeneity. Over the past decade, agent-based simulation (ABS) has been widely used in the field of transportation to achieve an accurate prediction of drivers’ responses under various road conditions [15]. In this study, an agent-based model is proposed to explore the feasibility and sustainability of this one-size-fits-all setting strategy in this study. Based on this ABM, a GA-based optimized setting strategy is proposed as well. In this model, each EV and fuel vehicle in the road network is treated as an independent agent. And the charging demand of EV is obtained by summarizing across all agents. This work provides a set of tools to support the decision makings relative to the future construction of charging stations in parking lots, so as to enhance the accessibility of charging facilities for EV drivers.

The rest of this paper is structured as follows. “Literature review” reviews the related work and highlights the research gaps that this work aims to fill. “Agent-based simulation model” describes the construction of ABM, which is applied in “Case study” for a real scenario to test the one-size-fits-all setting strategy and try to find a better strategy. “Conclusions and prospects” concludes the paper and discusses potential future works.

Literature review

Parking and charging behavior is affected by the characteristics of drivers, road conditions, and other factors. Establishing a mathematical model that describes all types of individual behavior is difficult. Bae and Kwasinski [3] proposed a spatial and temporal model, based on the fluid dynamic traffic model and M/M/s queuing theory, to forecast the EV charging demand for a rapid charging station along a highway. Arias and Bae [1] forecasted EV charging demand utilizing historical traffic and weather data in South Korea. Their model determines the charging starting time based on real-world traffic patterns and considers the initial state-of-charge of each battery in analyzing EV charging demand. However, several of the parameters of these models, such as departure and arrival rates, do not conform to practical application. Moreover, the analytic method usually only derives the result of the target element in the system. For instance, when studying the parking demand in the transportation system, a demand model needs to be established, but if you want to know the detour distance caused by parking in the same system, another travel distance model probably needs to build. Besides, a mathematical model is difficult to simulate every parking choice behavior. Instead, a simulation model allows simultaneous results for every element of the system.

Simulation-based models have been investigated to demonstrate the performance of individual decisions in a system. Yang et al. [26] used the Monte Carlo simulation method to establish the charging demand prediction model of the large-scale commuter EV under certain hypothetical conditions based on the analysis of the driving regularity of the traditional vehicle. Xi et al. [25] proposed a simulation–optimization model to determine the optimal location of EV chargers to maximize their use by privately owned EVs. Many recent studies have reported progress in the use of agent technology for building ITS (Intelligent Transportation System), including parking system and EV system. Karfopoulos and Hatziargyriou [14] proposed a distributed, multi-agent EV management system based on the Nash certainty equivalence principle. Their ABM takes the preferences of EV owners into account while ensuring the efficient operation of the network. Boudali and Ouada [4] proposed a smart parking system that provided a real-time decision guide for drivers by considering their preferences, based on multi-agent approach. Inturri et al. [13] used an ABM fed with GIS data (i.e., population and employment data) to explore different system configurations (i.e., flexible transit) of a demand response shared transport service. Oh et al. [19] systematically examined the impacts of automated mobility-on-demand on transportation in Singapore for the year 2030 through agent-based simulation, by explicitly modeling demand, supply, and their interactions. Agent-based simulation is suitable for presenting the individual behaviors of EV drivers and fuel vehicles drivers, and describing the process of cruising for available charging facilities, especially when the combination of parking and EV charging process is considered.

Simulation optimization method can be used as the objective function and/or constraint functions in optimizing stochastic complex systems. Comprehensive reviews of the literature on simulation optimization have been provided by [5, 10, 21], etc. Carson listed several commonly used simulation optimization methods, including gradient-based search methods, stochastic optimization, response surface methodology (RSM), heuristic methods, A-teams, statistical methods, etc. Among the heuristic methods, some direct search methods are discussed, including genetic algorithm (GA), evolutionary strategies (ES), tabu search (TS), etc. Azadivar [2] discussed issues that make simulation optimization distinct from generic optimization procedures. Fu et al. [8] also gave a descriptive review of the main approaches for carrying out simulation optimization. In summary, simulation optimization with the use of a genetic algorithm in this paper is suitable for optimizing the solution of combining different reserved parking space proportion configurations.

An agent-based simulation model was established in this study. The basic idea is to divide complex systems into agents by simulating the real world. The micro-behavior of individuals was investigated in a bottom–up manner, and the macro-behavior of the system was obtained. In this model, each vehicle on the road is considered an independent agent, the macroscopic information of the system is obtained by summing up the agents, and a GA-based optimized setting strategy is also proposed.

Agent-based simulation model

Purpose

The proposed agent-based simulation model simulates the traffic operation under the one-size-fits-all strategy and predicts the demand for charging and parking. Therefore, it can evaluate the feasibility of the one-size-fits-all strategy by evaluating the supply and demand of charging, charging satisfaction and the impact on the parking of fuel vehicles.

Entities and state parameters

The main entities in the simulation model include the vehicles (i.e., fuel vehicles and EVs), roads, and parking lots. Each of agent types are employed, respectively. The road agents simulate the traffic operation in the road network during various periods, which is of great importance to the vehicle agents’ path decision-making. The vehicle agents simulate the behaviors of drivers in a road network and make appropriate route and parking lot choices based on their current locations and destinations. At road intersections, each vehicle agent adjusts its driving path according to the target parking lot and the current network traffic condition. Each EV agent is aware of when and where to recharge his/her vehicle. The parking lot agents represent the real parking lot and manage the parking and queuing of vehicles inside.

The state parameters of each agent are updated in real time during the simulation iterations, from which we obtain the simulation results. Some of these parameters, such as time and location, are common to all agent types. Each road agent has static (i.e., length and capacity) and dynamic parameters (i.e., traffic volume, travel speed, and time). Each vehicle agent has parameters for its origin–destination, movement, and parking. Each EV agent has a state of charge (SOC) parameter to indicate whether the vehicle needs to be recharged. Similarly, each parking lot has parameters that indicate its capacity and its remaining number of parking spaces and charging facilities. Parameters that reflect the queuing of vehicles are also included.

Basic assumption

The proposed simulation model is based on the following assumptions:

  1. 1.

    Travel demand: The road network and OD (origin–destination) travel demand are fixed. All vehicle agents have access to timely traffic information to update their driving routes with the shortest travel time.

  2. 2.

    Charging supply: All charging facilities are built-in parking lots, and every parking lot has charging facilities. Parking lots are all off-road, and they have the same proportion of parking spaces with charging facilities and charge the same amount of charging fees.

  3. 3.

    Charging demand: The proportion of EVs in a road network is fixed and whether a vehicle agent is EV is decided randomly based on the proportion. The SOC of each EV is supposed to be normally distributed. The mean for the normal distribution is 0.5 and the standard deviation is 0.25 (Hu 2019). An EV with SOC of battery less than 30% is considered to be low battery. For each low-battery EV, an EV parking space to get itself recharged is necessary when they are parking.

  4. 4.

    Parking management: Only EVs can park in the EV parking spaces, while ordinary parking spaces are available to both EVs and fuel vehicles. Although a few parking lots now have been connected to some traveler information platform, such as Baidu map, Gaode map or some government apps, a larger number of parking lots have not been and the information is often not updated in a timely manner, especially the EV parking spaces information. Therefore, we assumed that the remaining number of parking spaces and charging facilities in real time are not known to all vehicle agents until they reach the gate of the parking lots. For every vehicle, when there is no parking space available in a parking lot, it will decide whether to wait for an available parking spaces or check other parking lots based on whether the numbers of queuing vehicles is accepted or not.

Vehicle trip description

Each vehicle agent plans the minimum-time route according to real-time traffic conditions and dynamically adjusts his/her route at each intersection. Each agent selects a parking lot based on the destination, travel time, walking distance, estimated cruising time, estimated waiting time, parking fee, and other factors.

Upon arriving at the target parking lot, a low-battery EV agent needs to find a parking space and recharge his/her vehicle. If a spare EV parking space is available, then this agent fulfills his/her parking and charging objectives. However, if no spare EV parking space is available yet the number of EVs in the queue is reasonable, then the EV agent enters the queue and waits for an available EV parking space. These two cases are both defined as first-attempt charging success (FCS). However, if the number of EVs in the queue is too large, then the EV agent re-enters the road network and searches for another parking lot. After a period of cruising, the agent eventually finds an EV parking space where he/she can park and charge his/her vehicle. We define the first-attempt charging success ratio (FCSR) as the probability for low-battery EVs to find an available EV parking space upon reaching a parking lot, without needing to search for other parking lots. FCSR can indicate the charging satisfactory of EV drivers. FCSR can then be computed as

$$\begin{array}{*{20}c} {{\text{FCSR}} = \frac{{n_{{{\text{FCS}}}} }}{{N_{{\text{low-battery}}} }}} \\ \end{array}$$
(1)

where \(n_{{{\text{FCS}}}}\) is the number of EVs that achieve FCS, and \(N_{{\text{low-battery}}}\) is the number of low-battery EVs. In this case, FCSR can well reflect the accessibility of charging facilities.

Those EVs that do not need to recharge and those fuel vehicles that only need to park follow the same parking process as low-battery EVs, that is, they initially arrive at certain parking lots and check for available parking spaces. If there is an available parking space, they will finish parking. If not, they consider the length of the queue to decide whether to leave the current parking lot. The decision-making process of these three kinds of vehicle agents in a parking lot is illustrated in Fig. 1.

Fig. 1
figure 1

Flow chart of decisions at a parking lot

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Simulation procedure

The basic procedure of the agent-based simulation model is illustrated in Fig. 2.

Fig. 2
figure 2

Flow chart of the simulation procedure

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Each step in the proposed simulation model is described as follows.

Step 1: Initialize parameters of the road network and parking lot.

(1) Initialize the road network

The origin node set O, destination node set D, parking lot node set P, intersection node set C, and road set S are first initialized. The connectivity and distances amongst these nodes, the road grade (arterial or sub-arterial), road capacity \({C}_{s}\), and free flow speed \({v}_{s}^{0}\) are then initialized. The background traffic volume \({q}_{s}\left(0\right)\) of each road is preloaded. The BPR (Bureau of Public Roads) function is used to calculate the initial travel speed \({v}_{s}\left(0\right)\) and travel time \({t}_{s}\left(0\right)\) of each road, as follows:

$$\begin{array}{*{20}c} {v_{s} \left( 0 \right) = \frac{{v_{s}^{0} }}{{\left( {1 + \alpha_{s} \left( {\frac{{q_{s} \left( 0 \right)}}{{C_{s} }}} \right)^{{\beta_{s} }} } \right)}}} \\ \end{array}$$
(2)
$$\begin{array}{*{20}c} {t_{s} \left( 0 \right) = \frac{{L_{s} }}{{v_{s} \left( 0 \right)}}} \\ \end{array}$$
(3)

where \({\alpha }_{s}\) and \({\beta }_{s}\) are the parameters of the BPR function, and \({L}_{s}\) is the length of road s.

(2) Initialize the parking lot

The capacity of each parking lot \({C}_{p}^{\mathrm{all}}\) and parking rate \({f}_{p}\) are first initialized. Other parking space parameters are then categorized into EV and ordinary parking spaces. The parameters of ordinary parking spaces, including the capacity of the ordinary parking lot \({C}_{p}\), initial number of parked vehicles \({x}_{p}\left(0\right)\), the maximum tolerable queuing length \({m}_{p}\), queuing sequence \({\text{queue}}_{p}\), and queuing length \({l}_{p}\), and those of EV parking spaces, including \({C}_{p}^{\mathrm{ev}}\), \({x}_{p}^{\mathrm{ev}}\left(0\right)\), \({m}_{p}^{\mathrm{ev}}\), \({\text{queue}}_{p}^{\mathrm{ev}}\), and \({l}_{p}^{\mathrm{ev}}\), are then initialized.

The amount of available EV parking spaces is formulated as \({C}_{p}^{\mathrm{ev}}=[{C}_{p}^{\mathrm{all}}\bullet {\eta }_{p}^{\mathrm{ev}}]\), where \({\eta }_{p}^{\mathrm{ev}}\) is the EV parking space proportion, [] is a rounding symbol. Then, \({C}_{p}\), the amount of ordinary parking spaces, can be formulated as \({C}_{p}={C}_{p}^{\mathrm{all}}-{C}_{p}^{\mathrm{ev}}\).

(3) Initialize the simulation environment

The simulation interval \(\Delta t\), current number of iterations m, and the maximum number of iterations M need to be initialized first. Afterward, the OD trip table, and the proportion of EVs in the road network \({\eta }_{\mathrm{ev}}\) are initialized.

Step 2: Vehicles leave, update the parking quantity and sequence.

(1) Vehicle departure update

According to a field survey in [20], the parking and charging duration in this area obeys a normal distribution with a mean of 1.63 h and a standard deviation of 0.82 h. A certain parking or charging time is set for each vehicle based on this normal distribution. These vehicles will drive off after the parking or charging time has elapsed, and then the actual quantities of the EV parking space and ordinary parking spaces are updated.

(2) Queuing sequence update

If the actual queue length \({l}_{p}^{\mathrm{ev}}\) > 0, then EVs are waiting for available parking spaces at the parking lots. As some EVs finish charging and drive away, some EV parking spaces become available. The waiting EVs receive the EV parking spaces in sequence \({\mathrm{queue}}_{p}^{\mathrm{ev}}\), so do fuel vehicles.

The queuing sequence, queue lengths, number of parked vehicles, and other attributes of parked vehicles (e.g., parking and walking time) are also updated.

Step 3: Generate the vehicle agent into network.

Vehicle agents are randomly generated in the road network based on the simulation OD demand. The unique identifier \({\mathrm{ID}}_{c}\), trip origin \({O}_{c}\), destination \({D}_{c}\), parking time \({q}_{c}\), and vehicle generating time \({t}_{c}^{\mathrm{birth}}\) are all recorded for each vehicle agent. Furthermore, whether the generated vehicle agent is an EV or not is stochastically determined in accordance with the proportion of EVs in the road network \({\eta }_{\mathrm{ev}}\), and whether an EV needs to be recharged is determined in accordance with the SOC level of the battery. Here an EV with SOC less than 30% must be charged. In fact, to avoid low power on driving, EV owners will not wait until the battery level is very low to charge. Quite a few EV drivers choose to charge when the electric power is still high (more than 50%) [12].

Step 4: Vehicle agents run in the road network (select the route and parking lot).

Each vehicle agent has three location states, namely, on a general road section, at an intersection, and in front of a parking lot. Vehicles need to update travel routes or parking behaviors when they are at intersections or in front of parking lots.

(1) Route decision at an intersection

Each vehicle agent drives along the minimum-time route according to the current traffic condition and the selected parking lot.

(2) Parking decision in front of a parking lot

As discussed in “Vehicle trip description” and shown in Fig. 1, when both EVs and fuel vehicles arrive at a parking lot, they initially check for available parking spaces that meet their parking or charging needs. If no such spaces are available or too many vehicles are waiting in the queue, then these vehicles leave the parking lot and search for another. When ordinary parking spaces are all occupied, the EVs that do not require charging will park at an empty EV parking space, which is permitted.

The corresponding parameters will be updated regardless of whether a vehicle finishes parking and charging or enters the queue.

Step 5: Update vehicle location and network traffic condition.

The locations of vehicle agents are updated as they move. After the locations of all vehicles are determined, the traffic condition of the network can be updated. Then, travel speed \({v}_{s} \left(\text{m}\right)\) and travel time \({t}_{s} \left(\text{m}\right)\) can be calculated using the BPR function.

Step 6: Record the simulation state and decide whether to terminate.

(1) Save the simulation state

The traffic condition of the road network in each iteration and the actual parking state of each parking lot are saved.

(2) Decide whether to terminate

If the current number of iterations does not exceed the maximum number of iterations (i.e., m ≤ M), then repeat the simulation from step 2.

If the termination condition is satisfied, then the relevant time attributes of all vehicles, including travel time, searching time, waiting time, and total travel time, are updated and recorded for further analysis.

Case study

The proposed agent-based simulation model was built in MATLAB and implemented for a real scenario. To deal with the stochasticity in simulation, each case was simulated five times and take the average as the final result. First, we simulate a real network to see whether the present charging demand can be satisfied. Second, given that the quantity of EVs will continue increasing in future, we discuss the FCSR of EV parking spaces under different penetration rates of EVs. Finally, a GA-based optimized setting strategy is proposed as well.

Simulation road network and key parameters

The road network employed in this study is a sub-network of the city center of Hangzhou, China, as shown in Fig. 3. This road network has 4 origin points, 4 destination points, 18 intersections, 9 off-street parking lots, and 27 two-way road sections.

Fig. 3
figure 3

Simulation network: a sub-network of Hangzhou, China

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The simulation time step is set to \(\Delta t=1\,\text{s}\), whereas the simulation time horizon is set to 9000 s. According to our survey of travel conditions in this area and considering the increasing number of motor vehicles, OD in our simulation is approximately determined and the total number of trips is 3300 [17]. OD matrix is shown in Table 1.

Table 1 Origin–destination trip matrix
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The parking space capacities are 180, 300, 160, 310, 190, 210, 230, 240, and 280. The total number of parking spaces is 2100, and the cooling time is set to 3600 s (i.e., no vehicle agents are generated after 5400 s).

Simulation results of state-of-the-practice in Hangzhou

The current EV parking operation in Hangzhou is simulated firstly. The simulation parameters are set according to the current proportion of EVs in the road network of Hangzhou (approximately 10%) and the actual one-size-fits-all construction standard of EV parking spaces in public parking lots (15%).

The supply and demand of EV parking spaces at nine parking lots are counted separately, which are shown in Fig. 4, where the blue dash line represents supply across different periods, and the orange curve represents demand. The demand for each period includes the occupied EV parking spaces, the queued EVs, and those EVs that choose to leave because of a long queue. The gradual increase of the orange curve may be ascribed to the continuous generation of EV agents in the simulation, whereas the decrease may be ascribed to the cooling effect (i.e., after 5400 s) when no additional EVs are generated and those existing EVs in parking lots finish charging and leave.

Fig. 4
figure 4

Supply of and demand for EV parking spaces at parking lots

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The uneven spatial distribution of charging demand is shown in Fig. 4. Some parking lots face shortages in EV parking spaces during the simulation (i.e., parking lots 3, 5 and 7). However, oversupplies of EV parking spaces are observed in other parking lots. For instance, the peak demand in parking lot 9 accounts for only about 25% of the total supply throughout the simulation.

The total regional supply and demand of EV parking spaces are shown in Fig. 5. It can be observed that the total charging demand of the entire study area is below the total supply. About 40% of EV parking spaces are still available during peak period. However, Fig. 4 shows both shortage and surplus across different parking lots. Therefore, the one-size-fits-all construction strategy may cause an unequal distribution of charging resources, and some coordination mechanism is required to ensure better utilization of EV parking spaces.

Fig. 5
figure 5

Supply and demand of charging stations at parking lots

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The FCSR in this scenario reaches about 88.6%, which suggests that 88.6% of low-battery EV drivers can find EV parking spaces to recharge their vehicles upon entering a parking lot. The range anxieties of these drivers may be significantly reduced. In summary, most of the current charging demand can be satisfied under the current charging facility construction standard, while some facilities may be underutilized.

Simulation results with EVs growth

With strong policy support and growing awareness of environmental protection, the amount of EVs is expected to increase in the future. This section further evaluates the one-size-fits-all strategy under different EV penetration rates. The charging demand, charging satisfaction, and the travel distance of EVs and fuel vehicles are discussed here.

Charging demand

By keeping the current EV parking space quota unchanged (i.e., 15% or 0.15), we performed simulations for multiple scenarios with increasing EV penetration rate. The results are shown in Fig. 6, where supply (0.15) indicates that the proportion of EV parking spaces is 0.15, whereas Demand () indicates the penetration rate of EVs.

Fig. 6
figure 6

Effect of different charging demand levels

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The demand for charging parking spaces continues increasing along with the EV ratio, and the demand will not exceed the total supply until the penetration rate of EVs reaches 0.2. In other words, under the current construction standard, the charging facilities can be fully utilized until the EV ratio reaches 0.2, which is not a very distant goal. At the same time, the FCSR decreases from 0.89 to 0.60 as the EV ratio increases from 0.1 to 0.3, as indicated in the red box in Fig. 6. When the demand exactly slightly exceeds the supply, the FCSR is 0.70, which suggests accomplishing balance between supply and demand may be accompanied by not very good charging satisfaction under the one-size-fits-all strategy.

FCSR

Figure 7 shows the contour of FCSR in the 2D space of EV and EV parking space ratios. Under the same FCSR, the EV and EV parking space ratios show an approximately linear relationship. As the number of EVs in the road network increases, more low-battery EVs need to be charged during their trips. To achieve a certain FCSR level, the number of charging facilities should be increased to meet the demand.

Fig. 7
figure 7

FCSR under different EV parking space and EV ratios

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We perform a linear regression under the FCSR of 0.9, which indicates a very high charging service satisfaction. The coefficient is 1.938, whereas the intercept is − 0.02994 (\({R}^{2}\) = 0.9934). The coefficient exceeds 1, suggesting that the proportion of EV parking spaces should exceed that of EVs in the road network to ensure high accessibility of charging facilities. Although the proportion of EV parking spaces is the same across all parking lots, the popularity of parking lots varies across locations and is often related to the popularity of a trip destination. So that the FCSR is greatly affected by the charging demand in popular parking lots. The current one-size-fits-all strategy may be revised to allocate higher proportions of EV parking spaces in these parking lots so as to satisfy the charging demand.

Figure 8 shows the detailed relationship between FCSR and EV parking space ratio under different EV penetration rates. The figure shows an obvious diminishing marginal utility, that is, more EV parking spaces correspond to lower improvements in FCSR. Meanwhile, increase in the EV ratio will increase the significance of such a diminishing marginal effect. Specifically, when the FCSR increases from 0.6 to 0.9, the EV parking spaces ratio only needs to increase from 0.04 to 0.18 at an EV ratio of 0.1, but it needs to increase from 0.24 to 0.97 at an EV ratio of 0.5. That is to say, as the EV ratio increases, to maintain a good charging environment, for example to keep FCSR at 0.9, a large proportion of EV parking spaces is required to build, which will lead to a rapid increase in costs. Therefore, this one-size-fits-all setting results in an obvious strategy failure.

Fig. 8
figure 8

FCSR under different EV parking space ratios

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AVKT

With the FCSR kept at 0.9, we further explore how addressing the charging anxieties of EV drivers influence fuel car drivers under different EV penetration rates. To this end, we calculate the average vehicle kilometer of travel (AVKT) of both EVs and fuel vehicles to examine the efficiency of searching for parking spaces.

The AVKTs of EVs and fuel vehicles are shown in Fig. 9. Given that the FCSR is stabilized at 0.9, the AVKT of EVs does not fluctuate much and stays around 1.5 km. This observation shows that FCSR is an appropriate indicator of EV charging convenience. Meanwhile, the AVKT of fuel vehicles grows exponentially as the number of EVs increases. This is because the parking spaces for fuel vehicles are squeezed largely when more EV parking spaces are built. Having more EV parking spaces will cause larger negative impacts on fuel vehicles, that is, fuel vehicles need to travel long distances to find parking spaces.

Fig. 9
figure 9

AVKTs of EVs and fuel vehicles under different EV ratios

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Back to now, we can imagine whether EV drivers confront the same dilemma where low-battery EV drivers are having trouble in finding charging facilities despite having visited multiple parking lots. This dilemma further reduces the intention of consumers to purchase EVs, thereby curtailing the widespread adoption of these vehicles. The present one-size-fits-all strategy may not lead to a very huge contradiction between the charging of EVs and the parking of fuel vehicles. However, such contradiction may escalate in the long run unless this trade-off problem is solved properly.

GA-based optimization

Discussion above demonstrates that the one-size-fits-all construction strategy can not deal with the uneven spatial distribution of charging demand or balance the benefit of EVs and fuel vehicles well. So it’s of great importance to put forward a more reasonable construction strategy. Since the popularity of different parking lots is quite different, it’s natural to think of installing more charging facility in the parking lot with greater demand. The scenario we study is still the EVs penetration rate of 10%, so as to make a comparison with “Simulation results of state-of-the-practice in Hangzhou”.

Here, we try to determine the EV parking spaces ratio of each parking lot, i.e., by the demand instead of one-size-fits-all, to achieve the most overall benefit. To solve this problem, an optimization model based on a genetic algorithm (GA) is constructed. Genetic algorithms are widely used in transportation research such as traffic forecasting, traffic signals, and urban daily travel, which have proven to be effective and easy to understand [6, 7, 23]. In this case, each parking lots’ EV parking spaces ratio can be from 0 to 100%, so enumerating all possibilities is infeasible. Especially in our problem, we don’t try to find the best global optimal solution. The heuristic GA is often used to generate useful solutions for nonlinear optimization problems. GA is sufficient to find a better solution than the one-size-fits-all strategy. In this model, to a minimum the Total Vehicle Kilometer of Travel (TVKT) is treated as the objective function for our GA-based optimization model. At the same time, for the purpose to encourage the use of EV, we put a weight, \(\omega =10\), for EV in the objective function, which is shown as:

$$\begin{array}{*{20}c} {W = \omega \cdot {\text{TVKT}}_{{{\text{ev}}}} + {\text{TVKT}}_{{\text{fuel vehicle}}} } \\ \end{array}$$
(5)

where \({\mathrm{TVKT}}_{\mathrm{ev}}\) is the TVKT of EVs and \({\mathrm{TVKT}}_{\text{fuel vehicle}}\) is the TVKT of fuel vehicles.

In this GA-based model, the EV parking spaces ratio of these 9 parking lot is taken as the population, i.e., the number of design variable is 9. The ratio has no range limit, which could be from 0 to 1. To speed up the convergence, the initial population consists of all nine parking lots with a ratio of 0.1, 0.15, 0.2. The TVKT as shown in Eq. 5, is taken as the fitness evaluation so we could seek the smallest travel distance. A simplified flow chart of the model is shown in Fig. 10.

Fig. 10
figure 10

Flow chart of the GA-based optimization procedure

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The optimal ratio of each parking lot obtained from GA is [0.1, 0.1, 0.1, 0.006, 0.15, 0.1, 0.1, 0.1, 0.1]. The total amount of EV parking space drop from 317 to 191, which could reduce construction and operating costs. The FCSR is 0.832, just a little lower than 0.886 (one-size-fits-all of 0.15), which is also a quite good level of charging satisfactory.

The supply and demand in each parking lot before and after optimization is shown in Fig. 11. The supply-GA and demand-GA, respectively, represent the supply and demand of EV parking spaces after optimized by GA. Basically, the oversupply has been improved, such as in parking lot 1, 2, 6, 8, where the demand hasn’t changed too much and the supply is more close to the peak demand. Meanwhile, charging demand for the hot parking lot, like parking lot 3, 7 is shifted to parking lot 1, 2, 9, which can reduce some traffic around node 8. As shown in Fig. 12, the bright area expands in the heatmap, which means the parking concentrations index of EV parking spaces in every parking lots after optimization is more close to 1. The supply and demand for charging are more balanced and more evenly distributed in space.

Fig. 11
figure 11

Demand and supply of EV parking spaces before and after optimization

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Fig. 12
figure 12

Parking concentration index of EV parking spaces in each parking lot

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However, it can be seen in Fig. 11 that peak demand in parking lot 3, 5, 7 is still greater than supply. That’s because if the queue length is acceptable, it will take more time and distance to find another parking lot and EVs will accumulate in front of the parking lot. How to coordinate this part of the demand is worth future study, so that some market measures such as parking and charging pricing can be adopted to regulate demand to further optimize the matching of charging supply and demand.

Conclusions and prospects

This research mainly explores setting up charging facilities in public parking lots. We evaluate the existing one-size-fits-all strategy and propose a GA-based optimized setting method to improve charging accessibility and alleviate the contradiction between supply and demand. This study uses agent simulation to analyze the impact of the existing one-size-fits-all setting. Scenarios under different charging facilities proportion and EVs penetration rates are discussed. Genetic algorithm is used to optimize charging facility proportion settings. The main contributions of this research are as follows:

  1. 1.

    An agent-based simulation model is established to simulate the driver’s individual behavior and the process of finding available charging facilities or available parking spaces. ABM shows its good reliability to simulate the coexistence of EVs charging and fuel vehicles parking.

  2. 2.

    Based on the simulation model, the current one-size-fits-all strategy is evaluated. 15% of all parking spaces are allocated to EV charging, which can meet the current overall charging demand. However, with the increase of EVs, this strategy can not meet the uneven demand. The FCSR drops sharply. When the penetration rate of EVs reaches 50%, to ensure the FCRS of 0.9, the installation proportion of EV parking spaces needs to reach 0.97.

  3. 3.

    From a system perspective, since this one-size-fits-all strategy takes up the parking spaces for fuel vehicle, the supply–demand contradiction of fuel vehicle parking in some parking lots has become more prominent, resulting in an overall benefit decline of the parking system consisting of EVs and fuel vehicles.

  4. 4.

    Considering the uneven spatial distribution of charging demand, it is necessary to design a customized EV parking space allocation ratio for each parking lot. We build an optimized model based on GA to get a better strategy. The results show that a more personalized strategy rather than a one-size-fits-all approach can reduce the waste of parking and charging resources and make supply and demand more balanced.

This article attempts to explore new charging facilities in public parking lots. Future research may consider improving the model and solution process discussed here. For example, although this research is mainly to meet the needs of EV drivers, the construction of EV parking spaces involves many factors such as coordination with fuel vehicles, economic costs, and power supply, and these are worth further studying. Balancing and guiding the unbalanced charging needs in space are other issues worthy of attention.