This paper analyzes the impact factors and principles of siting urban refueling stations and proposes a three-stage method. The main objective of the method is to minimize refueling vehicles’ detour time. The first stage aims at identifying the most frequently traveled road segments for siting refueling stations. The second stage focuses on adding additional refueling stations to serve vehicles whose demands are not directly satisfied by the refueling stations identified in the first stage. The last stage further adjusts and optimizes the refueling station plan generated by the first two stages. A genetic simulated annealing algorithm is proposed to solve the optimization problem in the second stage and the results are compared to those from the genetic algorithm. A case study is also conducted to demonstrate the effectiveness of the proposed method and algorithm. The results indicate the proposed method can provide practical and effective solutions that help planners and government agencies make informed refueling station location decisions.
With the rapid economic development in China, automobile ownership has increased drastically in the past decade. Due to this, there is an urgent need for upgrading transportation infrastructure to accommodate the newly generated traffic. Refueling stations, either gasoline stations or electric vehicle charging stations, are a very important type of service facility and are essential for the appropriate operations of urban transportation systems. The locations of refueling stations can directly affect the efficacy of urban road traffic system. Inappropriate location designs can substantially increase vehicle travel distances for finding refueling stations and cause unnecessary congestion and emissions. Therefore, investigating the optimal refueling station locations has important practical significance for developing countries such as China. This research is also important for some developed countries that are investing heavily in alternative-fueled vehicles (e.g., electric vehicles), where needs for optimally locating electric vehicle charging stations exist.
Some existing refueling station location models are based on qualitative analysis. These methods can generally be categorized into two groups: maximum coverage and maximum profit methods [
Several related quantitative researches have also been conducted. Current et al. [
Goodchild and Noronha [
In the following subsection, a comprehensive analysis of factors affecting refueling station location planning is presented. Based upon this analysis, a three-stage method is proposed to optimally locate refueling stations. Instead of focusing on the regional level and considering each city as a single demand point [
Siting urban refueling stations should consider a comprehensive set of factors. Government agencies are mostly concerned about congestion, safety, environment, and land use factors, while refueling station operators are more concerned about demand and profit. Besides, fuel price difference at various refueling stations is also an important factor to consider. However, in China gasoline prices are decided by the government and there is almost no difference in terms of price among different gas stations. Therefore, the price competition among different refueling stations/companies is not considered in this study. In general, siting refueling stations should (a) minimize their impacts on urban traffic, (b) be on main roads to ensure profitability, (c) keep an appropriate distance between refueling stations, (d) be far from residential and other sensitive areas, and (e) be based on urban land use planning.
Principle (a) is from the perspective of minimizing the influence of refueling stations on urban road traffic. For example, a vehicle with refueling need should not have to detour too far for refueling. Intuitively, this requires refueling stations to be located on or near the paths of most vehicles, so that they do not need to make a detour or just need to make a very short detour.
Principle (b) considers the economic benefit of refueling stations. The number of refueling vehicles that may potentially be served by a refueling station should be taken into consideration during the location design. Ideally, this number should be within a reasonable range to ensure that a refueling station’s profit is above certain level and the refueling demand does not exceed its capacity.
Principle (c) takes the service ranges of refueling stations into consideration. It is to make sure that refueling stations are not too concentrated in certain areas. Keeping an appropriate distance between refueling stations sometimes is necessary due to reasons such as safety.
Principle (d) is mainly about the safety and environmental concerns. Based on this principle, siting refueling stations should consider the safety of refueling station facilities and equipment, refueling vehicles, travelers, and nearby residents. Also, refueling stations should be far away from some environmentally and socially sensitive areas.
Last but certainly not least, principle (e) optimizes refueling station locations from the urban planning point of view. Specifically, urban refueling station locations should take into account land use development and future land use planning. Land use directly affects trip productions and attractions. Consequently, it has major impacts on the distribution of future refueling demand and refueling station locations.
From the standpoint of model development for optimally siting refueling stations, principle (a) can be considered in the objective function, and principles (b) through (e) can be either included as constraints or used to determine candidate locations for future refueling stations.
Based on the analysis in the previous section, if principle (a) is adopted as the objective, there will be two cases in the refueling station location planning. The first case is that refueling stations are located on the paths of some refueling vehicles. Hence, these vehicles do not need to detour for refueling. The other case is that refueling stations are not the paths of the remaining refueling vehicles and these vehicles have to detour for refueling. In light of these two cases, siting refueling stations can be implemented in three stages. In the first stage, candidate refueling stations on road segments traveled by most refueling vehicles are selected. In the second stage, the focus is on refueling vehicles that are not covered in the first stage. The objective is to minimize the total detour distance of these vehicles by properly selecting additional refueling stations. The third stage is based on the results of the first and second stages. It considers the redistribution of the paths for refueling vehicles due to traffic congestion and refueling station capacities. The redistribution result is used to fine-tune the location plan generated in the first and second stages.
Specifically, the first stage starts with assigning all vehicles (including refueling vehicles) to the road network. Based on the traffic assignment results, the paths of refueling vehicles are identified. From these paths, road segments that cover the highest refueling vehicle OD demand are selected for constructing refueling stations. The refueling ODs covered/served by these road segments are then removed from the original refueling vehicle OD. The regular vehicle OD and the unsatisfied refueling vehicle OD are assigned again to the road network to find additional candidate locations.
At the end of the first stage, the demands of some refueling ODs may still be unmet. Therefore, additional refueling stations need to be constructed and some refueling vehicles have to detour. When selecting locations for these additional refueling stations, it is natural to consider the objective of minimizing the total detour distance.
In the first and second stages, refueling vehicles are assigned to the road network in an incremental manner and refueling station locations are added gradually. In the third stage, all vehicles (including refueling vehicles) are assigned to the network simultaneously given the locations selected in the first and second stages. This most likely will result in a traffic flow pattern (e.g., choice of stations for refueling vehicles) that is different from those in the previous two stages. For instance, some previously overloaded refueling stations (based on the result of the second stage) may end up with not having enough demand. For those without enough demand in the second stage, they may not have adequate capacity to satisfy the refueling demand. For the lack of demand scenario, the corresponding refueling stations can be simply removed/unselected. For the lack of capacity scenario, additional refueling stations need to be added. To add new refueling stations, the first step is to find refueling vehicle ODs being assigned to the overloaded refueling stations. Next, road segments on these OD pairs’ paths and the refueling traffic volume on each of these segments are identified. Based on the principles discussed in the previous section, these segments’ refueling volumes are then sorted in a descending order and used to select new refueling stations. During this adjustment process, at least one new station that helps with diverting refueling demand should be selected. The new location plan may need to be fed into the second stage to be further improved. This three-stage model is summarized in Figure
Flowchart for the three stages.
Given a road network
Except for the vehicle refueling demand
For different OD pairs, even the same vehicle’s average refueling frequencies can be different. This is mainly due to two factors. First, different OD pairs have different average travel distances, which naturally result in different fuel consumptions. Second, vehicles from different OD pairs may experience different levels of congestion, which will also affect their fuel consumptions. On a particular day, travel demand of an OD pair is separated into demand with refueling needs and demand without refueling needs. The demand between origin
In (
The first-stage model is shown in (
First-stage location model based on FCLM.
After completing the first stage, the refueling demands of some vehicles are still unmet. When adding additional refueling stations (also called public refueling stations in this study) to address this issue, our objective is to minimize the total detour distance for those ODs with unmet refueling demands. Specifically, a bilevel location model is proposed that reflects the concerns of both government agencies and travelers. In the upper-level model, the total detour time is used as the objective function. Constraints considered include travel time between refueling stations, average construction cost, and refueling station density. The lower-level model assigns the unmet refueling ODs to the network using Stochastic User Equilibrium (SUE). This assignment is based on the resultant road network of the first stage. This bilevel second-stage model is also shown in Figure
Location models of the second stage.
Consider
Consider
In constraint (
This study relies on two core models: the first-stage model based on the FCLM and the second-stage model for adding and fine-tuning refueling stations. The first-stage model is relatively simple. Thus, this paper will briefly discuss the algorithm for the first-stage model and will focus on developing the algorithm for solving the second-stage model.
The traffic assignment in the first-stage model is based on SUE assignment. From the result of each assignment, a road segment with the highest refueling traffic volume is selected. This segment is selected for constructing a refueling station if its refueling volume is greater than a prespecified value. The corresponding OD will be excluded from further considerations. This process repeats until no qualified segments can be found for constructing refueling stations.
The upper-level of the second-stage model is a nonlinear program and the lower-level is a SUE problem. Heuristic algorithms are very popular for solving nonlinear programming problems. For instance, genetic algorithm (GA) is often used for finding global optimal solutions, and simulated annealing (SA) has good local search capability. This paper proposes an integrated genetic simulated annealing (GSA) algorithm to solve the upper-level model, generating feasible solutions for the lower-level model. The lower-level model basically performs SUE traffic assignments and provides the upper-level model with
GA was motivated by Darwin’s theory of natural selection, while SA was inspired by the process of heating and cooling of materials in a controlled setting. By integrating these two algorithms, we hope to further improve GA by enhancing its local search with SA.
The proposed algorithm consists of an inner loop and an outer loop, which are based on GA and SA, respectively. The inner loop generates binary vectors (e.g., chromosomes) representing various refueling station location solutions and evaluates their fitness. The algorithm then switches to the outer loop and applies SA to further improve the fitness of these chromosomes locally. Upon finishing the local search, the algorithm returns to the inner loop and applies crossover and mutation operators to avoid being stuck at local minimum solutions. The crossover and mutation operators, initial temperature of annealing, and the annealing rate are all important factors that may affect the algorithm’s performance and should be carefully considered. The following steps describe the proposed algorithm in more detail.
Since this is essentially a facility location problem, a binary vector of length
This step calculates the fitness values for individual solutions/chromosomes. Based on the results, the fittest chromosome
The entire algorithm will stop upon reaching the final temperature
This step calculates the fitness values
Crossover and mutation are applied to
Calculate the probabilities for genes to be selected from Generate a sequence
The mutation operator is applied to chromosomes with the highest and lowest fitness values. Applying it to the fittest chromosome is for accelerating the speed for local search, while applying it to the least-fit chromosome is to increase the diversity of the population and to avoid premature convergences.
Set
To validate the proposed model and algorithm, a case study was conducted using the urban road network in Figures
Road network with node and segment numbers.
Segment capacity and travel time.
Additionally, the following assumptions were made: the maximum average construction cost for a refueling station is 3 million Chinese yuan; the density of refueling stations is between 0.1 and 0.3 stations/km2; the minimum distance between two refueling stations is 4 km; and each station should serve at least 300 vehicles in order to be profitable and no more than 500 vehicles due to capacity constraint.
It was assumed that each node is the centroid of a Traffic Analysis Zone (TAZ). The travel demand between two TAZs was estimated by
Considering peak-hour factor and mode split, the peak-hour travel demand between two TAZs was estimated to be 38,537 pcu/h. By applying (
TransCAD 5.0 was used to solve the first-stage model. As shown in Table
Result of the first-stage model.
Number of iterations | Segment number | Segment direction | Segment flow (pcu/h) | Refueling demand (pcu/h) |
---|---|---|---|---|
1 | 125 | 112 → 121 | 4637 | 788 |
2 | 162 | 133 → 132 | 2902 | 610 |
3 | 111 | 105 → 106 | 3966 | 552 |
4 | 103 | 101 → 102 | 2341 | 421 |
5 | 56 | 75 → 74 | 2612 | 418 |
6 | 154 | 128 → 129 | 1983 | 333 |
7 | 98 | 98 → 107 | 1853 | 308 |
8 | 194 | 154 → 202 | 2141 | 278 |
Table
Locations selected for refueling station during the first stage.
The stations selected during the first stage can directly satisfy a refueling demand of 3,430 pcu/h, which is about half of the total demand, meaning that approximately 50% of the refueling vehicles do not need to detour. In the following section, the unmet refueling demand will be discussed.
The constraints in the second-stage model were considered by introducing a penalty. All solutions not meeting constraints (
Table
Result of the second-stage model.
Number of iterations | Shortest total detour time (min) | Detour times of other solutions (min) | ||||||
---|---|---|---|---|---|---|---|---|
1 | 26752 | 27078 | 28244 | 27927 | 28470 | ⋯ | 28154 | 28637 |
2 | 26066 | 27129 | 28141 | 28923 | 28228 | ⋯ | 27130 | 26639 |
3 | 25045 | 28991 | 26479 | 27130 | 27910 | ⋯ | 28192 | 28087 |
4 | 25384 | 28136 | 28467 | 26486 | 27130 | ⋯ | 25631 | 26177 |
5 | 25218 | 25596 | 25922 | 26140 | 26551 | ⋯ | 26841 | 25676 |
6 | 23806 | 24469 | 25921 | 26685 | 24534 | ⋯ | 25170 | 25191 |
7 | 22362 | 22796 | 22344 | 22867 | 22845 | ⋯ | 25917 | 22948 |
8 | 22269 | 23082 | 23505 | 23600 | 22796 | ⋯ | 22796 | 25692 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
872 | 6991 | 8729 | 9455 | 7086 | 7138 | ⋯ | 7283 | 7136 |
873 | 6782 | 8007 | 8795 | 6926 | 6792 | ⋯ | 8869 | 6936 |
874 | 6688 | 6688 | 6688 | 8360 | 8024 | ⋯ | 6688 | 6688 |
875 | 6688 | 6688 | 6688 | 8125 | 7727 | ⋯ | 6688 | 6688 |
876 | 6688 | 6688 | 6688 | 6688 | 6688 | ⋯ | 6688 | 6688 |
Iterative process of the second-stage model.
Refueling stations selected during the second stage.
Algorithm performance comparison.
Algorithm | Average number of iterations | Average CPU time |
---|---|---|
Genetic simulated annealing algorithm | 876 | 24 min 46 s |
Genetic algorithm | 1226 | 34 min 39 s |
Algorithm parameter sensitivity analysis results.
Parameter | Population size | Crossover rate | Mutation rate | Iterations | Calculating time | Bypass time |
---|---|---|---|---|---|---|
Optimization scheme | 100 | 0.9 | 0.04 | 876 | 24′46′′ | 6688′ |
Test scheme 1 | 90 | 0.9 | 0.04 | 704 | 20′15′′ | 6847′ |
Test scheme 2 | 110 | 0.9 | 0.04 | 991 | 32′51′′ | 6688′ |
Test scheme 3 | 100 | 0.85 | 0.04 | 657 | 18′34′′ | 7351′ |
Test scheme 4 | 100 | 0.95 | 0.04 | 1324 | 40′42′′ | 6688′ |
Test scheme 5 | 100 | 0.9 | 0.03 | 754 | 21′23′′ | 7023′ |
Test scheme 6 | 100 | 0.9 | 0.05 | 1521 | 51′34′′ | 6688′ |
The stations selected in the previous two stages are shown in Figure
Refueling traffic volumes of each refueling station based on the location plan generated by the second-stage model.
Station number | Refueling demand |
---|---|
|
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Number 1 | 476 |
Number 3 | 468 |
Number 4 | 417 |
Number 7 | 378 |
Number 8 | 347 |
Number 14 | 332 |
Number 9 | 329 |
Number 10 | 327 |
Number 17 | 321 |
Number 11 | 318 |
Number 16 | 313 |
Number 12 | 316 |
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|
|
Preliminary location plan for refueling stations.
The purpose of the third stage was to adjust the solutions generated in the previous two stages according to the method described in Figure
Result of the third stage.
Number of adjustments | Adjusting station | Adjusting method | STDEV | Total detour time/min |
---|---|---|---|---|
0 | — | — | 114.7 | 6688 |
1 | Number 15 | link157 → link185 | 94.8 | 7058 |
2 | Number 18 | link165 → link168 | 71.3 | 7367 |
3 | Number 13 | Link34 → link13 | 62.1 | 7520 |
Final refueling traffic volumes at each station.
Station number | Refueling volume |
---|---|
Number 1 | 481 |
Number 2 | 473 |
Number 3 | 473 |
Number 5 | 450 |
Number 6 | 443 |
Number 4 | 421 |
Number 7 | 382 |
Number 8 | 364 |
Number 9 | 352 |
Number 14 | 342 |
Number 15 | 334 |
Number 10 | 333 |
Number 17 | 326 |
Number 13 | 324 |
Number 11 | 321 |
Number 18 | 320 |
Number 12 | 319 |
Number 16 | 317 |
Final solution to the case study.
The refueling stations selected during the first stage were directly on the paths of refueling vehicles, and the average detour time of these refueling vehicles was 0 minutes; the average detour time of detouring refueling vehicles served by stations selected during the second stage was approximately 2 minutes; the average detour time of new detouring refueling vehicles due to the adjustments in the third stage was 2.5 minutes; the average detour time of all detouring refueling vehicles was 2.1 minutes; and the average detouring time of all refueling vehicles was 1.1 minutes.
Urban refueling stations are an important component of urban transportation systems. Based on the potential impacts of urban refueling stations, several principles of siting urban refueling stations have been proposed. Built upon these principles and impact factors, this paper proposed a three-stage method to optimally site urban refueling stations, developed a genetic simulated annealing algorithm for solving the three-stage model, and conducted a case study to verify the effectiveness of the model and algorithm. The case study results suggest that (i) an optimal urban refueling station plan developed using the three-stage method can significantly shorten the detour time of refueling vehicles. Consequently, this can help reduce the negative impacts of detouring refueling vehicles on urban traffic, which in many cities is already highly congested; and (ii) the three-stage model takes the user equilibrium principle into consideration and can generate reasonable and practical facility location solutions.
The authors declare that there is no conflict of interests regarding the publication of this paper.