An online scheduling method for bus vehicles

Abstract

The present invention discloses an online scheduling method for bus vehicles, belonging to the technical field of intelligent transportation, and is particularly applicable to the online scheduling of bus vehicles under the conditions of uncertain road conditions and unfixed vehicle driving durations. The method of the present invention includes an online scheduling controller for bus vehicles and a parameter optimizer. A vehicle type dynamic converter and a departure vehicle selector are set in the controller; the controller merges the departure timetables of two control points of each bus line, reorders all departure time points, and makes a decision on departure for each time point in sequence; at each time point, the vehicle type dynamic converter makes a real-time decision on the vehicle type and status, and the departure vehicle selector selects the departure vehicle; the parameter optimizer uses an intelligent optimization algorithm to optimize the parameters of the online scheduling controller offline. The present invention realizes real-time online departure scheduling according to the real-time operation information of the vehicle, is not affected by random factors such as traffic congestion, and can reduce the bus operation cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent transportation, and particularly relates to bus vehicle scheduling and an online bus vehicle scheduling method under the conditions of uncertain road conditions and unfixed vehicle driving duration. Background Art

[0002] As a major means of transportation in cities, buses play an extremely important role in alleviating urban traffic pressure. Therefore, the problem of bus vehicle scheduling is a key issue that needs to be solved. Reasonable bus scheduling can reduce the waste of traffic resources and relieve traffic pressure.

[0003] The problem of bus vehicle scheduling can be described as follows:

[0004] Each bus line usually includes two control points (CPs), denoted as CP1 and CP2 respectively, and the bus vehicles travel back and forth between the two control points. Each control point has a departure schedule formulated according to the actual passenger flow situation, which includes departure time points. Let the sets of departure time points of CP1 and CP2 be T1 and T2 respectively, then all the departure time points in the schedule of a bus line are expressed as T = T1 ∪ T2. The driving of a vehicle from CP1 (CP2) to CP2 (CP1) is called a trip. The vehicle scheduling problem is to arrange the trips of all vehicles to cover all the departure time points in the departure schedule without overlapping any time point repeatedly, so as to achieve optimization goals such as minimizing the number of vehicles. Suppose a bus v has a total of N trips, as Figure 1 shown. Each slant line with an arrow represents a trip of v. Each trip of v must depart from a certain time point in T, that is, N trips cover N time points. For the j-th trip of v, its departure time and arrival time are denoted as l j and a j , then its driving duration h j = a j - l j . The time between the arrival time of the j-th trip and the departure time of the j + 1-th trip is the rest time r j = l j+1 - a j , (1 ≤ j < N). Then the total driving duration of the N trips of v is The total rest duration is The total working duration is W = H + R.

[0005] In the actual process of bus vehicle scheduling, the dispatcher may have to abide by some constraints. Some common constraints are listed below:

[0006] (1) Vehicle v must start the next trip after one trip ends, and the rest time cannot be less than the minimum rest time r min , that is, lj+1 -a j ≥r min 。

[0007] (2) The H and W of vehicle v are respectively not greater than the maximum driving time T H and the maximum working time T W to prevent v from driving for a long time, that is, H ≤ T H , W ≤ T W 。

[0008] (3) Generally, the driver's place of residence is relatively close to the origin control point. To ensure that the driver can get off work at the CP where he goes to work, the number of trips of v must be even, that is, N mod 2 = 0.

[0009] The bus vehicle scheduling problem (BVSP) is to arrange vehicles to complete the trips corresponding to all time points in the departure schedule while minimizing the bus operation cost under the condition of meeting the scheduling constraints.

[0010] Currently, the existing bus vehicle scheduling methods regard the vehicle scheduling problem as an optimization problem, and generally use exact algorithms or heuristic algorithms to pre-generate a vehicle scheduling plan, and then schedule vehicles according to this plan in practice. However, in the actual bus operation process, uncertain factors such as traffic congestion, bad weather, and emergencies are often faced, which will cause fluctuations in the vehicle travel time. If a certain vehicle is specified to depart at a certain moment in the vehicle scheduling plan, but in reality, the vehicle fails to return to the control point due to traffic congestion, making the vehicle unable to depart on time at that moment point, so the pre-generated vehicle scheduling plan cannot be executed as planned.

[0011] Therefore, how to quickly and efficiently perform real-time (online) scheduling of bus vehicles in the bus operation scenario where the vehicle driving time is uncertain, as a key issue in the field of intelligent transportation, still exists. Summary of the Invention

[0012] Aiming at the problems existing in the above-mentioned prior art, the present invention provides a bus vehicle online scheduling method, which can quickly make high-quality vehicle scheduling decisions in the scenario where the vehicle driving time is not fixed, thereby reducing the bus operation cost and improving the service quality.

[0013] The bus vehicle online scheduling method of the present invention includes a bus vehicle online scheduling controller and a parameter optimization method. A vehicle type dynamic converter and a vehicle selector are set in the controller.

[0014] The controller combines the departure schedules of the two control points of each bus line, reorders all time points according to the departure time, and makes point-by-point decisions in the order of time points; at each time point, the controller obtains the real-time operating status of the vehicle and inputs the information into the vehicle type dynamic converter and the vehicle selector.

[0015] The vehicle type dynamic converter makes real-time decisions on the vehicle type and status and sends them to the vehicle selector; the vehicle type dynamic converter divides the working status of the vehicle into three types: working state, sleeping state, and out-of-service state, and the vehicle types include short-distance buses, long-distance buses, and peak-hour buses.

[0016] The vehicle selector makes a selection of the departing vehicle, including: determining the vehicles in the working state among the control points where the current departure time is located as candidate vehicles; if there is only one candidate vehicle, select this vehicle to depart; when there are at least two candidate vehicles, calculate the priority value of each candidate vehicle, and select the vehicle with the maximum priority value to depart; the priority value is calculated by comprehensively considering the remaining trip tasks of the vehicle, the continuous rest time, and whether it is the last trip.

[0017] The parameter optimizer optimizes the parameters of the controller. The parameter optimizer uses an intelligent optimization algorithm to optimize the parameters of the controller offline. The parameters of the controller include α, β, γ, δ; α, β, γ are the parameters set when calculating the priority value of the candidate vehicle, and δ is the rest duration threshold set when converting a short-distance bus into a sleeping peak-hour bus.

[0018] The vehicle selector calculates the priority value S i of the candidate vehicle v i in the following way:

[0019]

[0020] where α, β, γ are parameters; Γ i represents the remaining number of trips of v i ; G i represents the remaining working duration of v i ; B i represents the rest duration of v i since the end of the last trip; L i represents whether v i has only the last trip left:

[0021]

[0022] For short-distance buses and peak-hour buses, Γ i = M - E i , G i = T W - W i ;

[0023] For long-distance buses, Γ i = 2M - E i , G i = 2T W - W i ;

[0024] T W is the maximum working time, and M is the maximum number of trips.

[0025] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0026] (1) The method of the present invention combines the real-time control idea of the controller with the intelligent optimization algorithm and applies it to the real-time (online) bus vehicle scheduling problem. In the actual bus vehicle scheduling scenario, it realizes real-time online departure scheduling according to the real-time running information of the vehicle, without being affected by random factors such as traffic congestion. At the same time, the method of the present invention is also applicable to offline bus vehicle scheduling.

[0027] (2) The method of the present invention realizes the function of real-time scheduling of vehicles by statistically analyzing the real-time running information of the vehicles. The method can online schedule several vehicles to cover each time point on the departure schedule under the condition of satisfying all scheduling constraints. The method of the present invention can reduce the bus operation cost and improve the service quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a schematic diagram of the trip of a bus vehicle;

[0029] Figure 2 is a schematic diagram of the implementation of the online scheduling method of the bus vehicle of the present invention;

[0030] Figure 3 is a schematic diagram of the process of the online scheduling controller of the bus vehicle of the present invention for vehicle scheduling. DETAILED DESCRIPTION OF THE INVENTION

[0031] The present invention will be further described in detail below with reference to the drawings and embodiments.

[0032] During the actual bus operation, at any given moment, the vehicle information of the bus line control points CP1 (CP2) can be obtained in real time. For example: the number of vehicles parked at the CP, the number of each vehicle, the rest time, the driving time, the number of completed trips, etc. Based on this real-time vehicle information, a vehicle can be selected to depart from this moment, that is, use this vehicle to execute the trip corresponding to this moment. If such a decision is made at all departure moments, then each moment in the timetable will be covered by a vehicle trip, thus forming a vehicle scheduling plan. Therefore, the bus vehicle online scheduling method designed by the present invention generates a vehicle scheduling plan by making decisions at each moment, without having to generate the entire vehicle scheduling plan in advance and then execute the scheduling plan, but online schedules the vehicles according to the real-time information of the vehicles in the CP.

[0033] As Figure 2 shown, the bus vehicle online scheduling method of the present invention designs a bus vehicle online scheduling controller and a parameter optimizer. Among them, the bus vehicle online scheduling controller makes real-time decisions. At each departure moment, the controller selects a suitable departure vehicle in real time according to the vehicle information in the CP. In order to enable the controller to make decisions in chronological order, the departure timetables of CP1 and CP2 are merged, and all moments are reordered according to the departure time. The controller makes point-by-point decisions in the order of the moments. The parameter optimizer is used to optimize the controller parameters.

[0034] The bus vehicle online scheduling controller converts the vehicle type in real time at each departure moment, selects a suitable vehicle to execute the departure task at the current moment, and issues a get-off work order in a timely manner. A Vehicle Type Convector (VTC) and a Vehicle Selector (VS) are set in the bus vehicle online scheduling controller. The controller obtains the bus operation information in real time. In the embodiment of the present invention, a bus operation simulation environment is built, and the controller obtains the real-time operation status and information of the vehicles from it, such as the location of the vehicle, the vehicle number, the vehicle type, whether it has been put into work, the working duration, the rest duration, the number of completed trips (shifts), etc. The Vehicle Type Convector makes real-time decisions on the vehicle type according to the bus vehicle information, such as short-haul buses, long-haul buses, peak-hour buses. The Vehicle Selector selects the departure vehicle according to the real-time vehicle information and the converted vehicle type.

[0035] (1) The implementation of the Vehicle Type Convector is described as follows.

[0036] In vehicle scheduling, different vehicle types need to be considered, including short-haul buses, peak-hour buses, long-haul buses, etc., to meet the passenger transport demands during different periods. Generally speaking, the maximum working hours of long-haul buses are twice that of short-haul buses (peak-hour buses). The working hours of peak-hour buses are divided into two working periods, the morning peak and the evening peak, and the interval between them is not counted as working hours. The peak-hour bus can stop operating for a period of time after the morning peak period and complete the remaining journey during the evening peak period. In the present invention, the working states of vehicles are divided into three types: "working state", "sleeping state" and "out-of-service state". A vehicle type dynamic converter is designed to determine the vehicle type according to the vehicle state and the current vehicle information. Vehicles in the "working state" in the CP can be selected for departure; vehicles in the "sleeping state" will not be selected for departure until they are awakened; vehicles in the "out-of-service state" will not be selected for departure or awakened.

[0037] The vehicle type dynamic converter performs vehicle type and state conversion according to the following rules:

[0038] (a) Initialize a new vehicle as a short-haul bus in the "working state": If there are no vehicles in the "working state" and "sleeping state" in the current CP at the current time point, a new vehicle needs to be added. The state of the new vehicle is set to the working state and the type is set to a short-haul bus.

[0039] (b) Convert to a peak-hour bus in the "sleeping state": If the number of completed trips E of the short-haul bus is an even number and the rest duration B after the last trip reaches the threshold δ, that is, E mod 2 = 0 and B ≥ δ, then it is converted into a peak-hour bus in the "sleeping state". Among them, the threshold δ is a parameter. At this time, the duration B is the time during the large interval period in the middle of the peak-hour bus and is not counted as working hours.

[0040] (c) Convert to a short-haul bus in the "sleeping state": If a short-haul bus in the "working state" meets one of the following conditions: 1) W ≥ T W ; 2) H ≥ T H ; 3) The current number of completed trips E is equal to the maximum number of trips M, then its "working state" is converted to the "sleeping state". The calculation formula for M is:

[0041]

[0042] Where T a represents the average one-way time of the line. W is the current total working hours of the vehicle, and T W is the maximum working time. H is the current total driving hours of the vehicle, and T H is the maximum driving time.

[0043] (d) Wake up the "sleeping state" vehicle: If there is no "working state" vehicle in the CP and there is a "sleeping state" vehicle, wake up the vehicle with the longest sleep time. If the awakened vehicle is a short shuttle bus, convert it into a "working state" long shuttle bus; if the awakened vehicle is a peak-hour vehicle, convert its state into the "working state".

[0044] (e) The peak-hour vehicle stops working: If a peak-hour vehicle in the "working state" meets one of the following conditions: 1) W≥T W ; 2) H≥T H ; 3) E = M, then the peak-hour vehicle stops working and its state becomes the "out-of-service state".

[0045] (f) The long shuttle bus stops working: If a long shuttle bus in the "working state" meets one of the following conditions: 1) W≥2T W ; 2) H≥2T H ; 3) E = 2M, then the long shuttle bus stops working and its state becomes the "out-of-service state".

[0046] (g) The line ends operation: After completing the scheduling tasks at all time points, convert the vehicles still in the "working state" into the "out-of-service state", and convert the long shuttle buses and peak-hour vehicles in the "sleeping state" into the short shuttle buses in the "out-of-service state".

[0047] (2) The implementation of the vehicle selector is described as follows.

[0048] VS selects a vehicle to depart in real time according to the vehicle information of the CP at the current departure time point and the vehicle type and state output by the VTC. Suppose at a certain departure time point, there are C vehicles v1, v2,..., v c in the CP, and m vehicles are in the working state. The selection mechanism of VS is designed as follows:

[0049] (1) When there is only one working vehicle v i (m = 1) in the CP, VS directly arranges for v i to complete the journey at the current time point.

[0050] (2) When there are at least two working vehicles in the CP (m≥2), VS needs to select the most reasonable vehicle from the m candidate vehicles according to the vehicle information to cover this time point. Therefore, the present invention calculates the priority value S i (1≤i≤C) of each vehicle v i according to the following formula:

[0051]

[0052] where α, β, γ are parameters; Γ i represents the remaining journey number of v i ; G i represents vi Remaining working hours; B i Denote v i Resting hours since the end of the last trip; L i Denote v i Whether there is only the last trip left:

[0053]

[0054] VS selects the priority value S from m candidate vehicles i The vehicle with the maximum value departs from this time point (covering this time point).

[0055] (III) Implementation description of the parameter optimizer.

[0056] The parameter optimizer gradually optimizes the controller parameters according to the results of several offline simulation vehicle scheduling, improving its control effect. In the present invention, the designed parameter optimizer uses intelligent optimization algorithms to offline optimize 4 parameters of the controller: α, β, γ, δ. The intelligent optimization algorithms include particle swarm optimization (PSO), genetic algorithm (GA), simulated annealing, etc. Each set of parameters can form a controller. Then, use this controller to perform online scheduling in the simulation environment to obtain a scheduling plan. Use the performance evaluation value of this scheduling plan as the evaluation value of this set of parameters. The present invention uses the following index f to evaluate a vehicle scheduling plan and the corresponding controller parameters:

[0057] f = μ1×Q + μ2×P (4)

[0058] Wherein, Q and P respectively represent the number of vehicles with an even number of trips and the number of vehicles with an odd number of trips in the vehicle scheduling plan; μ1 and μ2 are coefficients, which can be set according to the actual needs of the bus company.

[0059] When in use, for the bus vehicle online scheduling method of the present invention, first use an intelligent optimization algorithm, such as the particle swarm optimization algorithm PSO, to offline optimize the parameters of the controller, and secondly use the optimized controller for real-time scheduling. As Figure 3 shown, a specific process for the bus vehicle online scheduling method of the present invention to implement vehicle scheduling is as follows:

[0060] Step 1, obtain the departure schedule, and obtain all current bus vehicle operation information, including vehicle number, vehicle location, vehicle type, whether it has been put into work, resting hours, driving hours, working hours, number of completed shifts, etc. Suppose there are a total of time points in the departure schedule.

[0061] Step 2, Initialize the parameters of the intelligent optimization algorithm. In the embodiment of the present invention, the particle swarm optimization algorithm is adopted. The position vector of the particle corresponds to a set of controller parameters. Each particle represents a controller, and the fitness function value of the particle is the score of the vehicle scheduling plan generated by the corresponding controller as shown in formula (4). Set the initial value of the iteration number p to 0, and the upper limit of the iteration number is

[0062] Step 3, The controller corresponding to each particle calls the vehicle type dynamic converter and the vehicle selector to generate a vehicle scheduling plan, and score the scheduling plan, as Figure 3 shown in the left dotted box in. The process of generating and evaluating a vehicle scheduling plan is as follows:

[0063] (1) Starting from the first departure time point, that is, the current time k = 1, according to the vehicle information corresponding to the current time point, the controller calls the vehicle type converter to update the vehicle type, and then calls the vehicle selector to select the departure vehicle;

[0064] (2) Update the vehicle information and continue to select the vehicle for the next time point, that is, k is incremented by 1 at this time;

[0065] (3) Sequentially select the departure vehicles until the vehicle selection for the last time point is completed, that is, when a vehicle scheduling plan is generated;

[0066] (4) Score the vehicle scheduling plan through the evaluation function as shown in formula (4), and archive the scheduling plan and the score externally.

[0067] Step 4, Execute the parameter iteration optimization process, as Figure 3 shown in the right dotted box in. Loop and execute the above Step 3 until the scheduling stops after a certain number of times, and output the optimal controller parameters archived externally and the corresponding scheduling plan.

[0068] In the embodiment of the present invention, four parameters α, β, γ, δ of the PSO-optimized controller are utilized. Each particle is represented as a 4D vector, and the four dimensions respectively correspond to the parameters α, β, γ, δ. The 4D vector is the position vector. The position vector of the p-th particle x p of the population is represented as Its velocity vector v p is represented as x p Each particle of records its own best position (p-best) passed through and the corresponding evaluation value. The global best particle (g-best) is the particle with the optimal evaluation value in history.

[0069] The update formulas for the velocity and position vectors of the particle are as follows:

[0070]

[0071]

[0072] where d ∈ {1, 2, 3, 4}; ω represents the inertia weight; δ1 and δ2 represent the acceleration coefficients; and are random real numbers within the range of [0, 1]; is the d-th dimension of the p-best of the p-th particle; is the d-th dimension of the g-best.

[0073] The process of optimizing the PSO controller parameters is as follows:

[0074] Step 1: There are N particles in the initial population. Randomly initialize the velocity and position of each particle.

[0075] Step 2: Evaluate all the particles in the population. Each particle is decoded into a set of controller parameters α, β, γ, δ, and then a vehicle scheduling scheme is generated using the controller assigned with these parameters. Calculate the evaluation value of the particle through formula (4).

[0076] Step 3: Initialize the p-best of each particle to its current position and the g-best to the current population's optimal particle.

[0077] Step 4: Update the velocity and position of each particle according to formulas (5) and (6) respectively.

[0078] Step 5: Evaluate all the particles in the population by (4).

[0079] Step 6: For each particle, if the current evaluation value of the particle is better than the p-best, its p-best is updated to the current position of the particle. If the particle is better than the g-best, then the g-best is updated to this particle.

[0080] Step 7: Go to and execute Step 4 until the number of iterations reaches the maximum value. At this time, the g-best is the optimized parameter, representing the optimized controller.

[0081] Except for the technical features described in the specification, they are all well-known technologies to those skilled in the art. The present invention omits the description of well-known components and well-known technologies to avoid redundancy and unnecessarily limit the present invention. The implementation manners described in the above embodiments do not represent all the implementation manners consistent with the present application. Based on the technical solution of the present invention, various modifications or deformations that can be made by those skilled in the art without creative labor are still within the protection scope of the present invention.

Claims

1. An online scheduling method for a bus vehicle, characterized in that, This method regards each departure time point on the departure schedule as a decision point, and uses a controller to select a vehicle from the control points to depart at this departure time point; The inputs of the controller are: the real-time information of all vehicles within the control points at the current moment, including: the working time, rest time, and the number of completed trips of the vehicles; the output of the controller is: select a vehicle to depart at this departure time point; Use the controller to make online decisions point by point for all time points in the departure schedule, so that each time point in the schedule is covered by a vehicle trip, thereby forming a bus vehicle scheduling plan; The controller includes a vehicle type converter and a vehicle selector; the controller merges the departure schedules of the two control points of each bus line, sorts all time points in ascending order of time, and makes point-by-point decisions in the order of time points; at each time point, input the real-time operation status and information of the vehicle into the vehicle type converter and the vehicle selector; the vehicle type converter makes real-time decisions on the vehicle type and status and sends them to the vehicle selector; the vehicle type converter divides the working status of the vehicle into three types: working state, dormant state, and out-of-service state, considering three vehicle types: short-distance buses, long-distance buses, and peak-hour buses; the vehicle selector is used to select a vehicle to depart, and the process is as follows: regard the vehicles in the working state within the control points at the current departure time as candidate vehicles; if there is only one candidate vehicle, select this vehicle to depart; if there are at least two candidate vehicles, calculate the priority value of each candidate vehicle, and select the vehicle with the largest priority value to depart; the priority value is calculated by comprehensively considering the remaining trip tasks of the vehicle, the continuous rest time, and whether it is the last trip; The described vehicle selector calculates the priority value S of the candidate vehicle v i as follows: i in the following manner: where α, β, γ are parameters; Γ i represents the remaining number of trips of v i ; G i represents the remaining working hours of v i ; B i represents the rest duration of v i since the end of the last trip; L i represents whether v i has only the last trip left: For short shuttle buses and peak-hour buses, Γ i = M - E i , G i = T W - W i ; For long-distance buses, Γ i = 2M - E i , G i = 2T W - W i ; T W is the maximum working time, and M is the maximum number of trips; The vehicle type converter makes real-time decisions on the vehicle type and status, including: (a) If there are no vehicles in the working state and dormant state at the control point where the current bus line is located, add a new vehicle to this bus line, set the status of the new vehicle to the working state, and the type to the short-distance bus; (b) If the number of completed trips E of the short-distance bus is an even number, and the rest duration B after executing the last trip reaches the threshold δ, then convert this short-distance bus into a dormant peak-hour bus; (c) If the short-distance bus in the working state meets one of the following three conditions, it is converted into a dormant short-distance bus; 1) The current total working hours W of the vehicle ≥ T W ; T W is the maximum allowable working time of the vehicle; 2) The current total driving duration H of the vehicle ≥ T H ; T H is the maximum allowable driving time of the vehicle; 3) The number of completed trips E of the current vehicle is equal to the maximum number of trips M; where the calculation formula of M is: Among them, T a represents the average one-way time of this bus line; (d) If there are no vehicles in the working state and there are dormant vehicles at the control point where the current bus line is located, wake up the vehicle with the longest dormant time; if the awakened vehicle is a short-distance bus, convert this vehicle into a working long-distance bus; if the awakened vehicle is a peak-hour bus, convert the status of this vehicle into the working state; (e) If the peak-hour bus in the working state meets one of the following three conditions, the peak-hour bus stops working and the status becomes the out-of-service state; 1) W ≥ T W ; 2) H ≥ T H ; 3) E = M; (f) If the long-distance bus in the working state meets one of the following three conditions, the long-distance bus stops working and the status becomes the out-of-service state; 2) W ≥ 2T W ; 2) H ≥ 2T H ; 3) E = 2M; (g) After completing the scheduling tasks for all time points on the bus line, convert the vehicles in the working state to the out-of-service state, and convert the long-haul buses and peak-hour buses in the sleep state to short-haul buses in the out-of-service state; Use a parameter optimizer to optimize the parameters of the controller.

2. The method according to claim 1, wherein The real-time operating status and information of the vehicles include the positions of the vehicles on the bus line, vehicle numbers, vehicle types, whether they have been put into work, working hours, rest hours, and the number of completed trips.

3. The method according to claim 1, wherein The parameter optimizer uses an intelligent optimization algorithm to optimize the parameters of the controller offline. The parameters of the controller include α, β, γ, δ; α, β, γ are the parameters set when calculating the priority value of the candidate vehicle, and δ is the rest duration threshold set when converting the short-haul bus to a sleep state peak-hour bus.

4. The method according to claim 3, wherein When the parameter optimizer uses an intelligent optimization algorithm to optimize the parameters of the controller offline, it performs online scheduling for each set of controller parameters in a simulation environment to obtain a scheduling plan, and evaluates the vehicle scheduling plan and the corresponding controller parameters through the index f: f = μ1×Q + μ2×P where Q and P represent the number of vehicles with an even number of trips and the number of vehicles with an odd number of trips in the vehicle scheduling plan, respectively; μ1 and μ2 are preset coefficients; the lower the value of the index f, the higher the quality of the vehicle scheduling plan.

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