Methods and Technologies for NextGeneration Public Transport Planning and Operations
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Ming Wei, Binbin Jing, Jian Yin, Yang Zang, "A Green DemandResponsive Airport Shuttle Service Problem with TimeVarying Speeds", Journal of Advanced Transportation, vol. 2020, Article ID 9853164, 13 pages, 2020. https://doi.org/10.1155/2020/9853164
A Green DemandResponsive Airport Shuttle Service Problem with TimeVarying Speeds
Abstract
This study proposes a multiobjective mixed integer linear programming (MOMILP) model for a demandresponsive airport shuttle service. The approach aims to assign a set of alternative fuel vehicles (AFVs) located at different depots to visit each demand point within the specified time and transport all of them to the airport. The proposed model effectively captures the interactions between path selection and environmental protection. Moreover, users with flexible pickup time windows, the timevarying speed of vehicles on the road network, and the limited fuel for the route duration are also fully considered in this model. The work aims at simultaneously minimizing the operating cost, vehicle fuel consumption, and CO_{2} emissions. Since this task is an NPhard problem, a heuristicbased nondominated sorting genetic algorithm (NSGAII) is also presented to find Pareto optimal solutions in a reasonable amount of time. Finally, a realworld example is provided to illustrate the proposed methodology. The results demonstrate that the model not only selects an optimal depot for each AFV but also determines its route and timetable plan. A sensitivity analysis is also given to assess the effect of early/late arrival penalty weights and the number of AFVs on the model performance, and the difference in quality between the proposed and traditional models is compared.
1. Introduction
Airports are generally located in the suburbs of a city; therefore, passengers living in urban areas need to be transported to the airport by shuttle buses. To increase the flexibility and accessibility of airport services, an increasing number of traffic authorities in different countries have realized airport shuttle services in a regular bus or subway system as one of the most effective strategies to meet passengers’ accessibility needs. Most of the existing shuttle services are fixedroute regular bus or subway systems, which are suitable for highdensity residential areas. However, this can often have high operating costs and low service levels in some remote areas with few people. Currently, with the rapid expansion of mobile internet, the demandresponsive airport shuttle services (DRASS) using appbased ride services is a future trend in designing a customized supplytodemand transit route. Some of the benefits of this may include reduced operational cost and carbon emission and improved mobility [1, 2].
A DRASS transit system, in which passengers place their travel orders through a mobile app to obtain a doortodoortype airport shuttle service and many vehicle routes located at different depots are assigned to visit these demand points and transport them to the airport, is an important component of a demandresponsive transit system (DRT) [3]. As with DRT, the increase in consciousness about environmental impact has made green DRASS a critical issue. In this case, DRASS route decisions determine operating cost, vehicle fuel consumption, and carbon emissions [4, 5]. Therefore, green DRASS is different from traditional systems, and a study considering the environmental impact on AFVs route design is timely.
The carbon emissions of airport shuttle buses are mainly related to their travel speed and load [6]. Recent research on minimizing emissions in DRASS models can be divided into two main categories. The first is the set of models where vehicle speed is assumed to be constant [1, 2, 7], and the second set includes models where the vehicle speed is timevarying based on different road conditions [5, 8]. Although the first models are not accurate, they are suitable where there is a lack of traffic data. Recently, remote vehicle tracking techniques have been used to collect detailed traffic data on transit times for different roads by time of day and day of the week, which provides the possibility for the second models to accurately estimate carbon emissions. Therefore, it is important to find the optimal relationship between timevarying networks, DRASS route design, and carbon emissions in order to reduce the negative impact on the environment.
The main contribution of this paper is to investigate a multiobjective green DRASS with a timevarying network in order to minimize operating cost, vehicle fuel consumption, and CO_{2} emissions. The main research tasks are summarized as follows: (1) coordination of a DRASS transit routing and departure time guidance process based on a timevarying network to balance path selection and environmental protection; (2) development of a heuristicbased NSGAII algorithm to efficiently obtain a set of Pareto optimal solutions. Finally, a numerical simulation example in the real world is provided to illustrate the optimization approach.
The remainder of this paper is organized as follows: Section 2 reviews the related literature concerning green DRASS; Section 3 details the framework of green DRASS with a timevarying network; Section 4 presents a heuristic method based on NSGAII for resolving MOMILP; a realworld case study is used to demonstrate the applicability of the proposed approach in Section 5; and some conclusions and possible future work are discussed in Section 6.
2. Literature
Both DRT and DRASS are extensions of the vehicle routing problem (VRP) and the pickup and delivery problem (PDP), which aim at assigning all customers in demand points to vehicles located at different bus depots and designing routes to transport them from their home or workplace to destinations [1, 2, 5, 8]. The only difference between them is that DRT strengthens the connectivity between residential areas and rail stations, while DRASS transports air passengers to airports [1, 7]. They have similar objective functions (i.e., operating cost, carbon emissions, and passenger satisfaction) and constraints (i.e., time windows, vehicle capacity, and mileage). Fortunately, these factors normally do not change the properties of the problem, and thus, their models and algorithms are universal [8–11]. Because rail transit is more popular than civil aviation, the amount of research on DRT is greater than that of DRASS.
In general, DRT and DRASS often involve customers being picked up within specific time windows, which is related to the customers’ satisfaction level in the airport shuttle service [9]. A variant of vehicle routing with time windows has been studied by researchers and can be divided into hard time windows [3, 4, 7, 9] and soft time windows [12–14]. In the former, time windows cannot be violated, where the vehicles must arrive at the earliest arrival time and leave the customers before the latest departure time. However, a little tardiness is acceptable to a person if they can still catch their trip. To deal with the latter issues pertaining to a small deviation from time windows, an early or late penalty cost is calculated once a predetermined time window is unmet. Obviously, DRT and DRASS with soft time windows can reduce fleet size and improve operating efficiency, compared to that of hard time windows. Most existing studies only allow the vehicle to visit customers in a single period of time. Sometimes, passengers may provide multiple time windows, and a vehicle can arrive at the pickup locations within one of the specified periods. DRT and DRASS with multiple time windows can reduce the operating cost compared to the singletime window problem [9, 15, 16].
Currently, there is an increasing amount of interest in a new variant of DRT and DRASS with timevarying speeds. Due to road traffic congestion depending on the time of day, the speed is not constant. This differs significantly by the hour of the day, by the day of the week, and by the season of the year [5, 17]. Generally speaking, historical data are used to obtain the hypothetical distribution of fuzzy, grey, and random variables [18–20]. However, a piecewise function can describe timevarying speeds more precisely, in the absence of statistics [21]. When vehicle speeds are replaced by traffic volumes, these models are further expanded to timedependent DRT and DRASS [22, 23]. Also, the vehicle speed may also be used as an additional decision variable in timedependent models, which is useful in reducing the waiting time for all customers [24, 25]. To avoid the situation where a vehicle with a later departure time arrives before a vehicle with an earlier departure time, these models are constructed based on the first in first out (FIFO) or queuing approach [26].
In recent years, another variant of DRT and DRASS has attracted widespread attention regarding the environment. Here, not only the operational cost is considered but also the energy consumption/CO_{2} emissions. Compared to the traditional problem, this would save energy consumption and CO_{2} emissions but increase some operating costs. Most research has only focused on energy minimizing [27] or CO_{2} emission minimizing vehicle routing [28]. Few have investigated an integrated routing, energy consumption, and CO_{2} emission model [21, 29]. These studies were also extended by taking driver wages into account [21, 29]. Furthermore, this research can be divided into timeindependent and timedependent models: in the former, the energy consumption and CO_{2} emissions are only related to routes, not schedules; in the latter, carbon emissions also depend on the departure time of the vehicles. Due to the fuel consumption and CO_{2} emissions of delivery vehicles being closely related to the driving speed, load and road conditions, and other factors, the result of timedependent models is more accurate and reliable than that of timeindependent models [5, 21].
As DRT and DRASS belongs to the class of NPhard problems, two solution methods, i.e., routebuilding heuristics and evolutionary algorithms, are often used to resolve largescale problem instances. For routebuilding heuristics, a set of feasible solution is quickly found, and better solutions can be obtained by further search based on the finetuned initial solutions [30–32]. There are two ways to get the initial solution: (1) all customers are grouped into several vehicles, and then, the order in which the vehicles will visit the customers is determined; (2) each route is gradually constructed to visit some customers until the travel demand is met. Some widely used evolutionary algorithms that are often used include the column generation metaheuristic [12], ant colony algorithms [3, 15, 19], Tabu search [12, 16, 17], particle swarm optimization [20], and genetic algorithms [7, 10, 33–35].
To the best of our knowledge, the following important issues deserve further investigation:(1)Most studies have neglected the integrated operation of depot selection, vehicle scheduling, and routing to transport passengers from home to the airport. Since different depots for each vehicle route influences the time the vehicle arrives and leaves the demand point, the ignorance of assigning optimal depots to the vehicle route often results in increasing the operational costs [36, 37].(2)Few studies have analyzed the impact of timevarying road conditions and soft time windows on AFV scheduling and routing, which leads to a lack of an integrated solution that balances fuel consumption, CO_{2} emissions, and operating costs [32].(3)DRASS is an NPhard problem. Although some methods have been explicitly used to solve the two relevant objectives between operating costs and fuel consumption/CO_{2} emissions, a heuristic algorithm should be used to efficiently find a set of Pareto solutions to balance all of the three objectives [34, 35].
3. Methodology
3.1. Research Framework
In the DRASS model, passengers will be transported by several AFVs from their workplaces or home addresses to the airport. The location, maximum expected riding time, preferred pickup time windows, and number of persons on board for each demand point is easily obtained using the mobile app in advance. If an AFV arrives at the passenger’s location early or late, there will be a penalty charge. Each AFV, initially located at a depot, has its own limited fuel for the duration of the route. The fuel consumption of an AFV is only related to its speed, vehicle load weight, and mileage [6]. It is obvious that the change in traffic volume in different periods determines the timevarying speed of vehicles on the road, and its rules can be depicted by a piecewise function. The main aim of this study is to assign all demand points to several AFVs, route each AFV starting from a selected depot, visit the points and end at the airport, and determine the time this vehicle arrives and leaves each demand point. A MOMILP model for DRASS is presented to simultaneously minimize operational cost, vehicle fuel consumption, and CO_{2} emissions. The key inputs of the model are the travel information of each demand point, endurance and energy consumption of AFVs, and the real travel speed/distance matrix between these vehicle nodes.
To better understand the underlying principles of the DRASS model, a small example consisting of one airport (M), eight demand points (C1–C8), and two depots (D1D2) is shown in Figure 1. The change curves of the average speeds on different roads are shown in Figure 2. The numbers in brackets around each demand point denotes time windows and maximum expected riding time. The red numbers on top of each demand point denotes the number of passengers to be picked up. The number inline linking two adjacent demand points is the travel distance. All customers in each demand point spend one minute getting on the bus. There are three generated AFV routes in the optimization process, i.e., (D1 (7 : 20)–C5 (7 : 35, 7 : 36)–C4 (7 : 56, 7 : 57)–M (8 : 12)), (D2 (7 : 15)–C2 (7 : 35, 7 : 36)–C6 (8 : 01, 8 : 02)–M (8 : 17)), and (D2 (7 : 25)–C3 (7 : 40, 7 : 41)–C1 (8 : 01, 8 : 02)–M (8 : 12)). For example, vehicle 3 departs from D2 at 7 : 25. Due to the speed of the vehicle on road section D2–C3 during this period being 20 km/h, this vehicle arrives and leaves at C3 at 7 : 40 and 7 : 41 with a speed of 15 km/h and loads three persons. Obviously, the vehicle does not arrive at the location within the time window and is about five minutes late. Similarly, the arrival and departure time for the vehicle at C1 are (8 : 01, 8 : 02) (nine minutes early), and the vehicle picks up four passengers. Finally, it returns back to M at 8 : 12, and a total of seven passengers are unloaded. In this case, each objective function of all AFV routes can be calculated easily.
To deal with reallife situations, this DRASS model will be based on the following assumptions:(1)All demand points must be visited by AFVs, and each of them can only be covered once by one AFV.(2)The unit cost of fuel, the unit cost of carbon emissions, and the perunittime reward of vehicles arriving at the demand point normally, early, or late can be estimated.(3)Biggest continue voyage course of each AFV can be predicted using an intelligent carcarried terminal in advance.(4)The travel distance matrix between these vehicle nodes as well as timevarying speed on the road can be obtained from an Open GIS tool.
3.2. Model Formulation
3.2.1. Notation
To facilitate model presentation, all definitions and notations used hereafter are summarized in Table 1.

3.2.2. Formulation
The proposed problem can be formulated as the following mixed integer program (MIP), which requires minimization:which is subject towhere is a function used to calculate the fuel consumption of vehicles passing through a given arc when considering timevarying speeds. The speed is a piecewise function.
and its value depend on . denotes the total weight, including the vehicle weight and the load weight for the vehicle leaving the demand point . Using the formulation proposed by Demir et al. [6, 34, 35, 38], this can be expressed as follows:
In this formulation, the objective function (1) aims at minimizing the penalty cost of timewindow violation. The objective functions (2) and (3) simultaneously aim at minimizing the operating cost, including the fixed cost and cost of fuel consumption and cost of CO_{2} emissions. Constraint (4) guarantees that each AFV visits at least one demand point. Constraint (5) is used to assign one depot to each AFV. Constraint (6) guarantees that all demand points are visited by AFVs. Constraints (7) and (8) guarantee that each AFV starts at the selected bus depot. Constraints (9) and (10) guarantee that each AFV eventually ends at the airport. Constraint (11) sets all demand points (except the airport and bus depot) being served by each AFV to have the same incoming and outgoing arcs. Constraint (12) is used for the subtour elimination in the vehicle routing. Constraints (13) and (14) are used for calculating the time for each AFV passing through adjacent vehicular points i and j. Constraint (15) guarantees that the riding time of each demand point must be less than the expected value. Constraints (16) and (17) are used for calculating the load weight for each AFV passing through adjacent vehicular points i and j. Constraint (18) guarantees that the number of passengers in each AFV must be less than the vehicle capacity. Constraint (19) guarantees that the total mileage of each AFV should not exceed its maximum range. Constraint (20) guarantees that the travel time of each AFV must meet its lower limits.
4. HeuristicBased NSGAII to Resolve Green DRASS
In this study, three possibly conflicting objectives require optimization. To avoid the disadvantages of the weighted sum approach to set weights to characterize the decisionmakers preferences, NSGAII is used to find a set of Pareto optimal solutions. As mentioned above, our model involves three core variables, including , and ，where decides . Obviously, once several demand points and one depot can be assigned to an AFV (i.e., ), its route (i.e., ) is also easily obtained according to the shortest distance principle. Hence, a twostage NSGAIIbased heuristic approach is developed to solve this problem [39–41]. In the first stage, NSGAII is used to determine the assignment of demand points and depots to different AFVs as well as departure time of each AFV. In the second stage, the algorithm is embedded in NSGAII to construct the route of each AFV: leaving the depot, visiting the selected demand points, and returning to the airport. Through these two operations, the speed, weight, and time for an AFV arriving and leaving the location of demand points in the objective function are also determined.
4.1. NSGAII in the First Stage
A threedimensional vector represents the chromosome of a feasible solution in green DRASS, where each element in , being a natural number in 1, 2, ... ,, denotes an AFV visiting demand point . Each element in , being a real number, denotes the departure time of the AFV . Each element in , being a natural number in 1, 2, ..., , denotes the departure depot of the AFV . For example, a chromosome vector = {1 1 2 2 1 2 6 : 00 6 : 10 3 4 } of two AFVs, four depots, and six demand points can be understood as follows: vehicle 1 leaves depot 3 at 6 : 00 and visits demand points 1, 2, and 5; vehicle 2 leaves depot 4 at 6 : 10 and visits demand points 3, 4, and 6.
Figure 3 describes the optimization procedure of NSGAII. An initial population consisting of individuals is randomly generated. At each iteration, each individual is firstly decoded as an assignment of demand points and depots to vehicles as well as the determination of departure time for the vehicle, and the algorithm is used to search for the shortest distance route of each vehicle. After this, all objective functions are calculated for fitness evaluation. The selected individuals in the parent population exchange genes to generate new individuals by using crossover and mutation operators. The current population with older and new individuals is sorted and selected again based on nondomination to obtain offspring. The selection depends on rank and crowding distance for an individual. The crowding distance, related to averaging the distances between individuals in a front, is used to find a consistent spread of solutions along the Pareto front. If the solutions are in the same nondominated front, those with a higher crowding distance are chosen first; otherwise, those with the lowest rank are chosen first. The algorithm continues until the maximum number of iterations is reached.
4.2. Algorithm in the Second Stage
In the first stage, all demand points, the depots, and the airport are assigned to different AFVs. Based on the output of the first stage algorithm, a route for each AFV would be found based on the shortest distance principle. The algorithm is one of the most efficient algorithms for finding the shortest path [42]. The detailed process for this algorithm in solving the problem is given as follows:(i)Step 1: define three sets, , , and , where and are used to record visited and unvisited demand points and is used to record the route.(ii)Step 2: put the depot into and set and .(iii)Step 3: in , select a demand point with the minimum travel distance as the current node. Remove the current node from, and put it into .(iv)Step 4: if the current node is the airport, the search ends; otherwise, search the adjacent nodes of the current node. Put these adjacent nodes into , and the current node is set as a node in .(v)Step 5: if the current node is in , its total travel distance is recalculated and updated when the result is less than the previous one; is also updated. If the current node is in , go to step 3.
5. Numerical Example
5.1. Example Description
In this section, a case study of designing green DRASS for Nantong City in China is given to demonstrate the applicability of the proposed model. There is one airport (M), five depot centers (D1–D5), and 33 demand points (–). Figure 4 is used to map the spatial distribution of these vehicular nodes, in which timevarying speeds on the road are obtained from a Baidu Open GIS tool using http://api.map.baidu.com. Moreover, the number of passengers and their preferred time windows and expected ride time in demand points are shown in Table 2. The parameters of NSGAII are given in [34]. The proposed algorithm is run on Matlab 2017 B using a Dell Inspiron N5040 laptop with Core i3 processor and 4 GB memory. The key parameters used in the case study are as follows:(i)Number of AFVs: .(ii)Maximum capacity of each AFV: = 12 per.(iii)Biggest continue voyage course of each AFV: = 100 km.(iv)Weight of each AFV: = 2300 kg.(v)Fixed use cost of each AFV: = 120 CNY.(vi)Minimum travel time of vehicle route: = 3 min.(vii)Boarding time of per passenger: = 0.5 min.(viii)Average weight of each person: = 60 kg.(ix)Penalty fee for early arrival: = 1 CNY/min.(x)Penalty fee for late arrival: = 3 CNY/min.(xi)Unit cost of the fuel: = 7.59 CNY/liter.(xii)Unit CO_{2} emission cost: = 80 CNY/ton.(xiii)CO_{2} emission factor: = 0.785 kg/liter.

5.2. Results
The CPU time for finding a set of Pareto optimal solutions is usually less than 1 minute. As explained previously, the proposed model could yield 10 feasible metaoptimal solutions in three dimensions, including the assignment of each demand point to an AFV, its route, and timetable. The upper and lower bounds of objective function 1 are 1305.8 RMB and 693.7 RMB, that of objective function 2 are 1187.2 RMB and 1156.7 RMB, and that of objective function 3 are 3.9 RMB and 3.7 RMB, respectively. Figures 5 and 6 reveal the changing relationship between any two goals. As the value of objective function 1 becomes larger, that of objective function 2 becomes smaller. This is because the reduction in the total penalty charges for violating the passenger’s time window leads to the need for more mileage for vehicles covering all demand points, thus increasing energy consumption costs. Objective 2 and objective 3 are positively linearly correlated, which determines that the change in trend of objective 1 and objective 2 is consistent with the change in trend of objective 1 and objective 3. This is because energy consumption determines carbon emissions.
Tables 3 and 4 are used to provide the routing and scheduling results related to the metaoptimal solution (693.7, 1187.2, 3.9). The pickup time, riding time, and early/late arrival time of the AFV at each pickup location are detailed in Table 3, in which zero, positive, and negative numbers in the fourth column of the table represent normal, early, and late arrival, respectively. The arrival and departure time for all AFVs visiting their demand points as well as fuel consumption and CO_{2} emissions of each AFV are detailed in Table 4. Taking the AFV of V1 as an example, the vehicle leaves the depot D5 at 06 : 28 and arrives at the demand point 29 at 7 : 36. Since the client’s time window is (7 : 50, 8 : 00), the early arrival time is 13.9 minutes. After 1 minute to pick up 2 persons, it leaves this location at 7 : 37. Similarly, the arrival and departure time of 30 and 33 are (7 : 53, 7 : 54) and (8 : 07, 8 : 08), and their early or late arrival times are 0 minutes and 0 minutes. Finally, this vehicle reaches its airport of M at 8 : 37 to unload 6 persons. As above mentioned, the riding times of 29, 30, and 33 for V4 are calculated as 61.1 minutes, 44.2 minutes, and 29.6 minutes. The vehicle travels a total of 52.6 km, consuming 9 liters of petrol and emitting 7.1 kg of CO_{2}. The costs in terms of energy consumption and carbon emissions are 68.3 CNY and 0.5 CNY, and the penalty for violating the time window is 27.8 CNY.


Furthermore, the proposed model has unique features compared to traditional DRASS with fixed speed. As shown in Figure 7, mileage of the proposed model is 0.36% more than for the traditional one, but the carbon emissions and fuel consumption of the proposed model are 0.87% and 0.66% less than those of the traditional one. In traditional DRASS with fixed speed, the more the mileage, the more the carbon emissions and fuel consumption. However, the flexible departure time of each AFV in timevarying traffic conditions can avoid vehicles driving on congested roads, thus increasing energy consumption costs.
5.3. Comparative Analysis and Parameter Sensitivity
In this section, sensitivity analyses are also given to investigate the impact of the number of AFVs and the changes in weight coefficient on the model performance. Comparison of the results is shown in Tables 5 and 6, from which the following holds:(1)As the weight coefficient gradually increases, early arrival time will be increased while late arrival time will be reduced. Besides, total mileage, fuel consumption, and CO_{2} emissions remain the same, except for the boundary conditions being met. When it happens, DRASS plan with an increase in mileage would lead to more fuel consumption and CO_{2} emissions. This is because increased weight coefficient may cause an increase in early arrival time and a reduction in late arrival time, which leads to more mileage.


5.4. Validation of Algorithm
In order to verify the validity of proposed algorithm, the multiobjective DRASS could be transformed into a single objective function with minimization of the weighted sum of two objective functions (1), (2), and (3). Several instances with different problem scales are randomly generated. Globally optimal solutions are gained by using CPLEX 12.6 to solve small size instances. We also implement the ACObased heuristic algorithm to solve largescale instances. Table 7 shows their difference in terms of computation efficiency and solution quality. As more demand points are covered by all routes, more solved time is required to obtain the solutions, where the computation time of CPLEX increases geometrically, while that of heuristic algorithm increases gently. We can observe that CPLEX takes more than 1 h to solve optimal solutions in case of more than 30 demand points, while the heuristic spends 5.1 seconds to obtain locally optimal solutions. The difference of best solutions is controlled under 10%, but that of solved time will grow at a geometric rate as well.

6. Conclusions
In this paper, a novel MOMILP model was proposed for green DRASS with timevarying speeds to balance the operating cost, vehicle fuel consumption, and CO_{2} emissions. Furthermore, customer’s soft time windows and limited fuel capacity for an AFV are incorporated into the proposed model in order to represent realworld conditions. The metaoptimal solutions are obtained using NSGAII. The main findings can be summarized as follows:(1)Carbon emissions cost and fuel consumption cost of the proposed model are positively linearly correlated, and both these and the total penalty charges for violating the passenger’s time window are negatively nonlinearly correlated.(2)When mileage of two DRASS plans varies widely, DRASS plan with a greater mileage means more energy consumption and emissions. However, DRASS plan with small mileage in congested road conditions may consume more energy and emit more emissions than DRASS plan with big mileage in good road conditions, as the mileage difference in them is small.(3)The carbon emissions and fuel consumption of the proposed model are less than those of DRASS with fixed speeds. This is because the flexible departure time of each AFV in timevarying traffic conditions can avoid vehicles driving on congested roads, thus increasing energy consumption costs.
Note that the vehicle in this DRASS model is an AFV, not an electric bus (EC). An EC emits almost no carbon, but it can be recharged at any of the available stations during the workday. In this sense, the collaborative design of DRASS routes and recharging station locations should consider the interactions between construction and operating expenses of charging piles and operation costs of these ECs. As a result, extending the DRASS model to simultaneously select the optimal locations of charging piles, design ECs routes, and assign ECs to recharging stations is worth further studying.
Data Availability
Some or all data, models, or code generated or used during the study are available from the corresponding author on request.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
This study was financially supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China (20YJCZH176) and the central college basic scientific research operating expenses fund in Civil Aviation University of China (3122020079).
References
 T. Liu and A. Ceder, “Analysis of a new publictransportservice concept: customized bus in China,” Transport Policy, vol. 39, pp. 63–76, 2015. View at: Publisher Site  Google Scholar
 J. Wang, T. Yamamoto, and K. Liu, “Key determinants and heterogeneous frailties in passenger loyalty toward customized buses: an empirical investigation of the subscription termination hazard of users,” Transportation Research Part C: Emerging Technologies, vol. 115, Article ID 102636, 2020. View at: Publisher Site  Google Scholar
 J. Wang, T. Yamamoto, and K. Liu, “Role of customized bus services in the transportation system: insight from actual performance,” Journal of Advanced Transportation, vol. 2019, Article ID 6171532, 14 pages, 2019. View at: Publisher Site  Google Scholar
 P.Y. Yang, J.F. Tang, Y. Yu, and J.X. Pei, “Minimizing carbon emissions through vehicle routing and scheduling in the shuttle service of picking up and delivering customers to the airport,” Acta Automatica Sinica, vol. 39, no. 4, pp. 424–432, 2013. View at: Publisher Site  Google Scholar
 Y. Xiao and A. Konak, “The heterogeneous green vehicle routing and scheduling problem with timevarying traffic congestion,” Transportation Research Part E: Logistics and Transportation Review, vol. 88, pp. 146–166, 2016. View at: Publisher Site  Google Scholar
 E. Demir, T. Bektaş, and G. Laporte, “A review of recent research on green road freight transportation,” European Journal of Operational Research, vol. 237, no. 3, pp. 775–793, 2014. View at: Publisher Site  Google Scholar
 B. Sun, M. Wei, and W. Wu, “An optimization model for demandresponsive feeder transit services based on ridesharing car,” Information, vol. 10, no. 12, pp. 370–386, 2019. View at: Publisher Site  Google Scholar
 L. Q. Wang, Z. Jun, and W. Wei, “Hyperpathbased vehicle routing and scheduling method in timevarying networks for airport shuttle service,” Natural Computing, vol. 18, no. 4, pp. 769–784, 2017. View at: Google Scholar
 B. Sun, M. Wei, and S. Zhu, “Optimal design of demandresponsive feeder transit services with passengers’ multiple time windows and satisfaction,” Future Internet, vol. 10, no. 3, pp. 30–46, 2018. View at: Publisher Site  Google Scholar
 X. Li, M. Wei, J. Hu, Y. Yuan, and H. Jiang, “An agentbased model for dispatching realtime demandresponsive feeder bus,” Mathematical Problems in Engineering, vol. 2018, no. 1, Article ID 6925764, 11 pages, 2018. View at: Publisher Site  Google Scholar
 M. Wei, B. Sun, and S. L. Zhu, “A hybridtype indicator set pairs analysis model for evaluating transit operational efficiency,” Journal of Nonlinear and Convex Analysis, vol. 30, no. 5, pp. 895–904, 2019. View at: Google Scholar
 Y. Xia and Z. Fu, “Improved tabu search algorithm for the open vehicle routing problem with soft time windows and satisfaction rate,” Cluster Computing, vol. 22, no. S4, pp. 8725–8733, 2019. View at: Publisher Site  Google Scholar
 A. K. Beheshti and S. R. Hejazi, “A novel hybrid column generationmetaheuristic approach for the vehicle routing problem with general soft time window,” Information Sciences, vol. 316, no. 6, pp. 598–615, 2015. View at: Publisher Site  Google Scholar
 J. Xu, F. Yan, and S. Li, “Vehicle routing optimization with soft time windows in a fuzzy random environment,” Transportation Research Part E Logistics & Transportation Review, vol. 47, no. 6, pp. 1071–1091, 2011. View at: Publisher Site  Google Scholar
 F. Daniela, M. Elena, and P. Paola, “Ant colony system for a VRP with multiple time windows and multiple visits,” Journal of Interdisciplinary Mathematics, vol. 10, no. 2, pp. 263–284, 2007. View at: Publisher Site  Google Scholar
 S. Belhaiza, P. Hansen, and G. Laporte, “A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows,” Computers & Operations Research, vol. 52, pp. 269–281, 2014. View at: Publisher Site  Google Scholar
 W. Jun and L. I. Bo, “Multiobjective tabu search algorithm for vehicle routing problem with fuzzy duetime,” Computer Integrated Manufacturing Systems, vol. 17, no. 4, pp. 858–866, 2011. View at: Google Scholar
 M. Adelzadeh, V. Mahdavi Asl, and M. Koosha, “A mathematical model and a solving procedure for multidepot vehicle routing problem with fuzzy time window and heterogeneous vehicle,” The International Journal of Advanced Manufacturing Technology, vol. 75, no. 5–8, pp. 793–802, 2014. View at: Publisher Site  Google Scholar
 J. Brito, F. J. Martínez, J. A. Moreno, and J. L. Verdegay, “An ACO hybrid metaheuristic for closeopen vehicle routing problems with time windows and fuzzy constraints,” Applied Soft Computing, vol. 32, pp. 154–163, 2015. View at: Publisher Site  Google Scholar
 N. Norouz, M. SadeghAmalnick, and R. TavakkoliMoghaddam, “Modified particle swarm optimization in a timedependent vehicle routing problem: minimizing fuel consumption,” Optimization Letters, vol. 11, no. 1, pp. 1–14, 2016. View at: Publisher Site  Google Scholar
 D. Z. Zhang, X. Wang, S. Y. Li, N. Li, and Z. Zhang, “An Joint optimization of green vehicle scheduling and routing problem with timevarying speeds,” PLoS One, vol. 13, no. 2, pp. 1–20, 2018. View at: Publisher Site  Google Scholar
 Y. Deng, W. Zhu, H. Li, and Y. Zheng, “Multitype ant system algorithm for the time dependent vehicle routing problem with time windows,” Journal of Systems Engineering and Electronics, vol. 29, no. 3, pp. 625–638, 2018. View at: Publisher Site  Google Scholar
 F. Hooshmand and S. A. MirHassani, “Time dependent green VRP with alternative fuel powered vehicles,” Energy Systems, vol. 10, no. 3, pp. 721–756, 2019. View at: Publisher Site  Google Scholar
 M. A. Figliozzi, “The impacts of congestion on timedefinitive urban freight distribution networks CO_{2} emission levels: results from a case study in Portland, Oregon,” Transportation Research Part C: Emerging Technologies, vol. 19, no. 5, pp. 766–778, 2011. View at: Publisher Site  Google Scholar
 O. Jabali, T. Van Woensel, and A. G. De Kok, “Analysis of travel times and CO_{2} emissions in timedependent vehicle routing,” Production and Operations Management, vol. 21, no. 6, pp. 1060–1074, 2012. View at: Publisher Site  Google Scholar
 K. Harwood, C. Mumford, and R. Eglese, “Investigating the use of metaheuristics for solving single vehicle routing problems with timevarying traversal costs,” Journal of the Operational Research Society, vol. 64, no. 1, pp. 34–47, 2013. View at: Publisher Site  Google Scholar
 İ. Kara, B. Y. Kara, and M. K. Yetis, Energy Minimizing Vehicle Routing Problem, Springer Berlin Heidelberg, Heidelberg, Germany, 2007.
 Y.J. Kwon, Y.J. Choi, and D.H. Lee, “Heterogeneous fixed fleet vehicle routing considering carbon emission,” Transportation Research Part D: Transport and Environment, vol. 23, pp. 81–89, 2013. View at: Publisher Site  Google Scholar
 T. Bektaş and G. Laporte, “The pollutionrouting problem,” Transportation Research Part B: Methodological, vol. 45, no. 8, pp. 1232–1250, 2011. View at: Publisher Site  Google Scholar
 A. Lee and M. Savelsbergh, “An extended demand responsive connector,” EURO Journal on Transportation and Logistics, vol. 6, no. 1, pp. 25–50, 2017. View at: Publisher Site  Google Scholar
 J. X. Shen, S. Q. Yang, X. M. Gao, and F. Qiu, “Vehicle routing and scheduling of demandresponsive connector with ondemand stations,” Advances in Mechanical Engineering, vol. 9, no. 6, pp. 1–10, 2017. View at: Publisher Site  Google Scholar
 X. Lu, J. Yu, X. Yang, S. Pan, and N. Zou, “Flexible feeder transit route design to enhance service accessibility in urban area,” Journal of Advanced Transportation, vol. 50, no. 4, pp. 507–521, 2016. View at: Publisher Site  Google Scholar
 P. Carotenuto, C. Cis, S. Rismondo, and G. Storchi, “Hybrid genetic algorithm to approach the DaRP in a demand responsive passenger service,” IFAC Proceedings Volumes, vol. 39, no. 3, pp. 315–320, 2006. View at: Publisher Site  Google Scholar
 K. Liu, T. Yamamoto, and T. Morikawa, “Impact of road gradient on energy consumption of electric vehicles,” Transportation Research Part D: Transport and Environment, vol. 54, pp. 74–81, 2017. View at: Publisher Site  Google Scholar
 T. Q. Tang, J. Zhang, and K. Liu, “A speed guidance model accounting for the driver’s bounded rationality at a signalized intersection,” Physica A: Statistical Mechanics and its Applications, vol. 473, pp. 45–52, 2017. View at: Publisher Site  Google Scholar
 A. Ceder, “Stepwise multicriteria and multistrategy design of public transit shuttles,” Journal of MultiCriteria Decision Analysis, vol. 16, no. 12, pp. 21–38, 2009. View at: Publisher Site  Google Scholar
 B. Sun and M. Wei, “Optimal integrated location and dispatching decisions for feeder bus route design problem,” Transport, 2020, preprinting. View at: Google Scholar
 X. Luo, L. Dong, Y. Dou et al., “Factor decomposition analysis and causal mechanism investigation on urban transport CO_{2} emissions: comparative study on Shanghai and Tokyo,” Energy Policy, vol. 107, pp. 658–668, 2017. View at: Publisher Site  Google Scholar
 J. Jemai, M. Zekri, and K. Mellouli, “An NSGAII algorithm for the green vehicle routing problem,” Evolutionary Computation in Combinatorial Optimization, pp. 37–48, 2012. View at: Publisher Site  Google Scholar
 E. Demir, T. Bektaş, and G. Laporte, “The biobjective pollutionrouting problem,” European Journal of Operational Research, vol. 232, no. 3, pp. 464–478, 2014. View at: Publisher Site  Google Scholar
 A. Baniamerian, M. Bashiri, and F. Zabihi, “Two phase genetic algorithm for vehicle routing and scheduling problem with crossdocking and time windows considering customer satisfaction,” Journal of Industrial Engineering International, vol. 14, no. 1, pp. 15–30, 2018. View at: Publisher Site  Google Scholar
 S. Baldi, N. Maric, R. Dornberger, and T. Hanne, “Pathfinding optimization when solving the paparazzi problem comparing A and Dijkstra’s algorithm,” in Proceedings of the 2018 6th International Symposium on Computational and Business Intelligence (ISCBI), pp. 12–16, Basel, Switzerland, August 2018. View at: Publisher Site  Google Scholar
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Copyright © 2020 Ming Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.