Self-driving travel is a kind of independent travel that is an organized and planned form of tourism based on the primary transportation means of driving oneself [1
]; at present, self-driving travel has become the most popular travel form in the world, as well as a family gathering pattern [2
]. This prevalence of self-driving travel has not only brought vitality and prosperity to the global tourism market but has also placed higher demands on the infrastructure and management services that support self-driving travel; in particular, the challenge of refueling a vast number of self-driving vehicles is one of the issues gas station owners and drivers focus on. Stories of vehicles breaking down on the road due to fuel exhaustion have been reported [3
]. Some such vehicles have caused traffic accidents [4
], and Saarinen’s study also revealed an increase in drivers who ran out of fuel on the roadside in Great Britain in 2014 [5
]. Although it is feasible to solve the embarrassing situation of fuel exhaustion during travel by road rescue and other means, no self-driving traveler wishes to experience such an accident. This indicates that timely refueling on the road is one of the most fundamental guarantees for the safety of self-driving travel [2
]. Currently, the vehicle refueling strategy is judged and executed mainly by relying on the driver’s experiences during self-driving travel [6
]; although this kind of “experience refueling” method is feasible, it still has the following obvious defects.
First, the “experience refueling” method requires the driver to be familiar with the conditions of the road and the self-driving vehicle, so that the driver can determine where and when to refuel. However, in most cases, the drivers in self-driving travel are not always familiar with the road conditions or even the vehicle condition (for example, when renting a car), which often causes excessive or insufficient refueling [8
]. Second, the “experience refueling” method requires the driver to put considerable effort into the calculation and judgment of refueling, which may increase the risk of fatigue driving and is not conducive to driving safety [9
]. Finally, self-driving travel has been characterized by freedom, individuality, and mavericks since its appearance. In order to pursue this travel experience, some self-driving tourists tend to avoid the traditional tourist route and visit more obscure tourist destinations, which generally feature fewer tourists, less modern tourism services and infrastructure, fewer gas stations, and inconsistent oil quality; consequently, the timely replenishment of standard fuel can be difficult after entering such scenic areas [10
In conclusion, “experience refueling” is a common method for self-driving vehicles to refuel on the road, but this method also has some disadvantages: the timing of refueling cannot easily be accurately controlled, tourists’ energy is wasted, driving costs are increased, driving safety is adversely affected, and the pleasure of self-driving travel is reduced. Therefore, how to judiciously plan vehicle refueling according to the travel schedule to improve the safety of self-driving travel is an important scientific problem worthy of further study. Being motivated by the refueling problem in self-driving travel, we proposed this study in order to solve that very problem. Considering parameters including the number of refueling gas stations, the maximum driving distance of the vehicle, the distances between gas stations, the route length, and other distance variables, and based on the spatial clustering characteristics of gas stations along the route and the urgency of refueling, the algorithm constructed recommendation rules and a refueling service warning mechanism, which could provide humanized intelligent refueling strategies for the driver so that he would not be distracted by the refueling problem. The results of this study could fundamentally remedy the deficiencies of “experience refueling” and finally achieve the objective of improving the safety and quality of self-driving travel.
1.2. Literature Review
At present, the vehicle refueling problem has led to several research areas, including the following fields: (1) the green vehicle route problem from a low carbon perspective (GVRP), (2) the location problem of gas stations, (3) scheduling of mobile refueling and recharging facilities, and (4) the refueling optimization problem, among others. Field (1) mainly studies the vehicle routing optimization problem as determined according to the minimum driving distance, the shortest driving time, and the fewest dispatched vehicles, and as an extension of traditional VRP research, GVRP focuses on the vehicle routing optimization problem as determined according to the lowest overall oil consumption while driving [11
]. The core issue in this field is how to establish the objective function of energy consumption and optimally solve it: for example, Jabbarpour [12
] and Kwon [13
] studied a multiple-variable GVRP computational model, as well as model solution methods based on the ant colony optimization algorithm and tabu search algorithm. In addition, some researchers took vehicle fuel supply demand as a constraint to solve the vehicle routing problem, forming the Fuel-Constrained Vehicle Routing Problem (FCVRP). For instance, Montoya [14
] studied the influence of nonlinear charging time on the route planning of electric vehicles; Sundar [15
] studied path planning algorithms for small Unmanned Aerial Vehicles (UAVs) with resource constraints; and Bruglieri [16
] examined how to optimally route Electric Vehicles (EVs) to handle a set of customers in a given time considering recharging needs during trips. The research content in reference [17
] was similar to that in reference [15
], but the objective function and decision variables in reference [17
] were more complex, addressing a multiple depot, multiple unmanned vehicle routing problem with fuel constraints. Field (2) mainly studies the reasonable location problem of gas stations, the core of which is the construction and evaluation of gas station location models, which are typically analyzed and evaluated based on Geography Information System (GIS) spatial analysis and the actual demand for vehicle refueling [18
]. For example, based on different route choices and traveling conditions, Hosseini [19
] and Miralinaghi [20
] studied the construction methods of a gas station location model, as well as its heuristic algorithm, and finally showed that GIS spatial analysis can be used to scientifically optimize the location of gas stations. In Field (3), the major research is concerned with scientific scheduling and routing optimization for mobile refueling facilities, such as airport tankers, space refueling aircraft, etc. For example, Heng [21
] and Feng [22
] studied a scheduling optimization model and found solutions for an airport tanker based on planning time windows and genetic algorithms.
The vehicle refueling problem we are examining here and the areas of study of the above three fields intersect in part, but there are also some obvious differences in research objective, content, and methods, which are mainly reflected in the following aspects: (1) First, the GVRP or FCVRP problem is aimed at optimizing total oil consumption and does not consider how to refuel along the way; however, refueling en route is the core research content of this study, i.e., where and when the vehicle “can”, “needs to”, and “must” refuel during travel. (2) Second, the location of gas stations is considered when planning gas station construction. In this case, more consideration is given to optimizing the spatial layout of gas stations, and the main object of the research is gas stations themselves rather than vehicles that need refueling. However, the research subjects of the present study are self-driving vehicles and their refueling environment (the driving route, the number of gas stations, and the layout of gas stations along the route), focusing on the scientific planning problem of refueling during travel based on GIS spatial calculations and spatial analysis. (3) Third, the research subjects of the scientific scheduling problem for mobile refueling facilities are mobile; however, the refueling facilities in the present study are gas stations, which are immobile.
Field (4) mainly studies the decision-making model and intelligent management of vehicle refueling, and the correlation between Field (4) and this study may be the closest among the above four fields. Studies have shown that rational planning of the refueling process can help reduce fuel costs; for example, U.S. truckload (TL) carriers developed a software program called “Fuel optimizers” for fuel cost management, which reduces the fuel cost of motor carriers at the “point of purchase” by way of an optimization algorithm [23
]. However, Suzuki has argued that these products upset many truck drivers by “confiscating” their freedom to choose truck stops. Then, a decision support system was developed, which reduced the fuel cost of motor carriers at the point of purchase without confiscating the drivers’ freedom to choose truck stops, so that higher driver compliance rates were expected [23
]. Also, Lin [28
] considered the fixed-route vehicle refueling problem, similar to that addressed by commercial fuel optimizers, and developed a linear-time greedy algorithm for finding optimal fueling policies. Nicholas et al. [29
] studied whether the refueling of AFVs (Alternative Fuel Vehicles) could be informed by refueling experiences from the traditional petrochemical refueling network. Kuby [30
] and Kelly [31
] systematically studied the differences in refueling behavior between liquid fossil fuel vehicles and alternative fuel vehicles and proposed a decision model of AFV refueling according to actual refueling data for Alternative Fuel Vehicles in Southern California. As seen from the above references, the existing refueling decision models have mainly studied the problem of how to plan the refueling route to save fuel costs, optimizing the economy of refueling by using mathematical modeling and other methods, which has been very useful for guiding people to save more in fuel costs. However, these decision and optimization models might also deprive drivers of the choice freedom of “where to refuel”: not only are the mathematical formulas used in these models often comparatively complex, but the refueling recommendations are difficult to understand during the actual refueling process, and therefore the models’ decision-making effectiveness is far from satisfactory.
To sum up, the refueling decision-making model for moving vehicles is still a scientific problem worthy of current study in the field of intelligent transportation. Thus, taking vehicle refueling with traditional liquid fossil fuels as an example, a distance-adaptive refueling recommendation algorithm for self-driving travel was put forward in this study in order to assist in refueling decision-making for moving vehicles. Utilizing the strong geo-computation ability of GIS, this refueling recommendation algorithm calculated various distance variables affecting the refueling behavior of moving vehicles, and an optimized spatial clustering algorithm was used to calculate the refueling priority at gas stations along the route; finally, the refueling recommendation results were visualized based on the rich mapping function of GIS to verify the practicability and effectiveness of the algorithm. Although the work we did may be relatively simple, we propose that our study may be quite helpful for self-driving drivers to make reasonable choices about the timing and location of refueling. The expectation of this study is that our work and results can promote the intersection and integration of intelligent transportation and GIS, as well as other geospatial sciences, and can also provide a theoretical foundation and feasible technical means for rational refueling of and automatic warnings in self-driving vehicles.