An Airport Shuttle Bus Scheduling Method Based on Variable Neighborhood Search
By changing neighborhood search, the airport shuttle bus scheduling is optimized, and the unreasonable allocation of resources and flight delays caused by manual scheduling is solved, and efficient flight services are achieved.
Patent Information
- Application Number
- CN202310032743.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-10
- Publication Date
- 2025-08-01
- Estimated Expiration
- 2043-01-10
AI Technical Summary
The dispatch of existing airport shuttle buses mainly relies on manual decision-making, resulting in unreasonable resource allocation, especially during peak flights, which can easily cause flight delays and are inefficient.
Using a scheduling method based on variable neighborhood search, the objective function is constructed to minimize the weighted sum of tow periods of incoming and outgoing flights, and combined with timing relationships and non-preemptive constraints, the allocation and scheduling of shuttle vehicles are optimized.
It improves the efficiency of shuttle bus dispatch, rationally allocates resources, reduces flight delays, ensures that all passengers can be picked up and delivered in a timely manner, and avoids resource waste and dispatch conflicts.
Smart Images
Figure CN116070849B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field related to the scheduling of airport ground support vehicles, and more specifically, relates to a scheduling method for airport shuttle buses based on variable neighborhood search. Background Art
[0002] With the rapid development of the civil aviation industry, the contradiction between the growing number of flight takeoffs and landings and the limited ground support service resources has gradually become prominent. The number of aircraft and shuttle buses continues to increase, the utilization frequency of remote airport positions has greatly increased, and the untimely supply of ground support services has also become one of the important reasons for flight delays. Currently, the scheduling of shuttle buses at most airports still adopts the method of manual decision-making and manual operation. This scheduling method based on manual experience is short-sighted, does not consider the global optimal solution of shuttle bus scheduling, and has low efficiency. Especially during the peak periods of flight arrivals and departures and the occurrence of abnormal flights, vehicle resources are tense, the scheduling workload is large, and it may be difficult to obtain a feasible solution in a timely manner through manual scheduling, resulting in flight delays caused by unreasonable scheduling. Thus, there is an urgent need for a scientific and reasonable scheduling method in airports to effectively schedule shuttle buses. Summary of the Invention
[0003] In view of the above-mentioned defects or improvement requirements of the prior art, the present invention provides a scheduling method for airport shuttle buses based on variable neighborhood search, which can make full use of shuttle bus resources, reduce the tardiness time, and improve the scheduling efficiency and effect of shuttle buses.
[0004] To achieve the above object, according to one aspect of the present invention, a scheduling method for airport shuttle buses based on variable neighborhood search is provided. The method includes: S1: Number m shuttle buses and n flights respectively; S2: Construct an objective function with the goal of minimizing the weighted sum of tardiness for the shuttle services of inbound and outbound flights; S3: Evenly pre-allocate the shuttle tasks of n flights to m shuttle buses; S4: Calculate the objective function TAR0 in the case of pre-allocation and the tardiness time of each flight; S5: Change the shuttle task of the flight with the maximum tardiness time to other shuttle buses, recalculate the corresponding objective function TAR1 and the tardiness time of each flight respectively, and take the shuttle bus scheduling plan with the minimum objective function TAR1 as the first preferred plan; S6: Adopt the same method as in step S5, change the shuttle task of the flight with the maximum tardiness time in the first preferred plan to other shuttle buses, recalculate the corresponding objective function TAR2 and the tardiness time of each flight respectively, and take the shuttle bus scheduling plan with the minimum objective function TAR2 and less than the objective function TAR1 as the second preferred plan; S7: Optimize the shuttle buses corresponding to the flights with non-zero tardiness times in the second preferred plan in descending order of tardiness time until the objective function is minimized.
[0005] Preferably, if the passenger capacity of the flight in step S3 is greater than that of the shuttle bus, the flight is split into multiple flights with the goal of minimizing the number of split flights and ensuring that the passenger capacity on each flight is less than or equal to that of the shuttle bus.
[0006] Preferably, the expression of the objective function is:
[0007]
[0008] where PC is the weighted sum of delays of inbound and outbound flight shuttle services; Tar j is the service delay of flight j; ω1 is the weight of the inbound flight; Arr j is 1 if flight j is an inbound flight and 0 if flight j is an outbound flight; CT j is the service completion time of flight j; is 1 if shuttle bus k serves flight j after serving flight i and 0 if shuttle bus k does not serve flight j after serving flight i; is the driving time for shuttle bus k to go from serving the previous flight i to serving the current flight j; is 1 if shuttle bus k serves flight j and 0 if shuttle bus k does not serve flight j; EAT k is the time for the shuttle bus to arrive at the service location in advance; DT k is the stay time of shuttle bus k; is the distance between the arrival gate or boarding gate of flight j and the remote stand; v k is the driving speed of shuttle bus k; ω2 is the weight of the outbound flight; T j is the inbound and outbound time of flight j.
[0009] Preferably, the weight ω2 of the outbound flight is greater than the weight ω1 of the inbound flight, and ω1 + ω2 = 1.
[0010] Preferably, the actual start time of the flight shuttle service is not earlier than the planned service time. Therefore, the objective function satisfies the following timing relationship constraint conditions:
[0011]
[0012] where ST j is the service start time of flight j; CT i is the service completion time of flight i; T stop is the maximum time limit for the shuttle bus to stay at the current position after the service ends; Arr i is 1 if flight i is an inbound flight and 0 if flight i is an outbound flight; is the distance between the shuttle bus base and the remote stand where flight j is located; is the distance between the shuttle bus base and the arrival gate or boarding gate of flight j; is R i is the distance between the operating area where the remote stand is located and the remote stand where flight j is located; is R i is the distance between the operating area where the remote stand is located and the arrival gate or boarding gate of flight j; is the distance between the arrival gate or boarding gate of flight i and the remote stand where flight j is located; is the distance between the arrival gate or boarding gate of flight i and the arrival gate or boarding gate of flight j; is the distance between the remote stand where flight i is located and the remote stand where flight j is located; is the distance between the remote stand where flight i is located and the arrival gate or boarding gate of flight j; ψ is an infinite number; T j is the arrival and departure time of flight j; EAT k is the time when shuttle bus k arrives at the service position in advance.
[0013] Preferably, the shuttle bus can start serving the current flight only after serving the previous flight, so the objective function satisfies the non-preemptive scheduling constraint:
[0014]
[0015]
[0016] where ψ is an infinite number, ST j is the service start time of flight j; EAT k is the time when shuttle bus k arrives at the service position in advance; DT k is the residence time of shuttle bus k; CT i is the service completion time of flight i.
[0017] Preferably, the start time and end time constraints of the first flight served by the shuttle bus:
[0018]
[0019]
[0020] where is the driving time of shuttle bus k from the shuttle bus base to serve the current flight j; is the distance between the shuttle bus base and the remote stand where flight j is located; is the distance between the shuttle bus base and the arrival gate or boarding gate of flight j; ST j is the service start time of flight j; ψ is an infinite number; T j is the arrival and departure time of flight j; EATk is the time for the shuttle bus k to arrive at the service position in advance; ST j is the service start time of flight j; ψ is an infinite large number; T j is the arrival and departure time of flight j; EAT k is the time for the shuttle bus k to arrive at the service position in advance.
[0021] Preferably, the matching relationship that each flight can only be served by one shuttle bus is constrained as follows:
[0022]
[0023] Each shuttle bus must serve the first and the last tasks in the task sequence, so as to ensure that there are both previous flight and subsequent flight constraints for all flights in the task sequence of its shuttle bus:
[0024]
[0025]
[0026]
[0027]
[0028] The constraint on the service order of two adjacent tasks of the shuttle bus is as follows:
[0029]
[0030] The relationship constraint between two adjacent flights served by one shuttle bus is as follows:
[0031]
[0032] [[ID=4S]]
[0033]
[0034] Among them, being 1 means that the shuttle bus k serves flight i, and being 0 means that the shuttle bus k does not serve flight i; being 1 means that the shuttle bus k departs from the shuttle bus base; being 1 means that the shuttle bus k finally returns to the shuttle bus base; T j is the arrival and departure time of flight j; T i is the arrival and departure time of flight i; being 0 means that the first and the last tasks in the service task sequence are not adjacent tasks; being 1 means that the shuttle bus k serves flight i after serving flight j, and being 0 means that the shuttle bus k does not serve flight i after serving flight j.
[0035] Generally speaking, compared with the prior art by the above technical solution conceived by the present invention, a method for scheduling airport shuttle buses based on variable neighborhood search provided by the present invention has the following beneficial effects:
[0036] 1. This application takes the minimum weighted lateness of inbound flights and outbound flights as the optimization goal, and adopts a local search matching strategy to calculate and gradually optimize the shuttle bus scheduling plan. It can reasonably allocate shuttle buses for flights, avoid waste of shuttle bus resources, improve the scheduling efficiency of airport shuttle buses, effectively cope with the shortage of vehicle resources during peak hours at large airports, provide an achievable shuttle bus scheduling plan for the airport, and reduce flight delays caused by untimely airport ground shuttle services.
[0037] 2. This application splits flights that exceed the passenger capacity of the shuttle bus and imposes constraints, so as to more reasonably schedule the shuttle bus and ensure that all passengers can be picked up and dropped off in the first place.
[0038] 3. This application establishes time sequence relationship constraints, non-preemptive scheduling constraints, start time and end time constraints of the first flight served by the shuttle bus, matching relationship constraints, etc., which ensure the rationality of shuttle bus scheduling and avoid shuttle bus scheduling conflicts. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 is a flowchart of the steps of the method for scheduling airport shuttle buses based on variable neighborhood search of this application;
[0040] Figure 2 is a flowchart of the variable neighborhood algorithm of this application;
[0041] Figure 3 is a layout diagram of the airport in the embodiment of this application;
[0042] Figure 4 is the neighborhood solution obtained by the first N1 neighborhood search;
[0043] Figure 5 In (a) of is the solution after inserting flight No. 3 into shuttle bus No. 1, and (b) is the solution after inserting flight No. 3 into shuttle bus No. 3;
[0044] Figure 6 is the service lateness after inserting flight No. 3 into shuttle bus No. 1;
[0045] Figure 7 In (a) of is the solution after inserting flight No. 8 into shuttle bus No. 1, and (b) is the solution after inserting flight No. 8 into shuttle bus No. 2;
[0046] Figure 8(a) is the solution after inserting flight 10 into shuttle bus 1, and (b) is the solution after inserting flight 10 into shuttle bus 3. Figure 9 (a) is the solution after inserting flight 8 into shuttle bus No. 1, (b) is the solution after inserting flight 8 into shuttle bus No. 2, (c) is the solution after inserting flight 10 into shuttle bus No. 1, and (d) is the solution after inserting flight 10 into shuttle bus No. 3.
[0047] Figure 10 (a) is the solution after inserting Flight 2 into shuttle bus No. 1, (b) is the solution after inserting Flight 2 into shuttle bus No. 2, (c) is the solution after inserting Flight 5 into shuttle bus No. 1, and (d) is the solution after inserting Flight 5 into shuttle bus No. 2; (e) is the solution after inserting Flight 9 into shuttle bus No. 1, (f) is the solution after inserting Flight 9 into shuttle bus No. 2, (g) is the solution after inserting Flight 8 into shuttle bus No. 1, and (h) is the solution after inserting Flight 8 into shuttle bus No. 2;
[0048] Figure 11 is the local optimal solution after searching N5 neighborhoods, that is, Figure 10 The corresponding solution in (f);
[0049] Figure 12 This is the Gantt chart of the final solution. DETAILED DESCRIPTION
[0050] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
[0051] The airport shuttle bus scheduling problem can be described as follows: there are m shuttle buses at the airport and n remote-parking flights that require shuttle bus service, including real flights and virtual flights (if the number of passengers on a flight exceeds the maximum passenger capacity of the shuttle bus and multiple shuttle buses are needed, virtual flights will be introduced). The shuttle bus scheduling problem is to assign a shuttle bus to each flight so that all ferry missions are completed on time as much as possible and the total delay is minimized.
[0052] The estimated departure / arrival time of each remote stand flight i is T i , the remote stand number is R i , the departure / arrival gate number is G i The maximum passenger capacity of shuttle bus k is Cap k , the driving speed is v kFor each remote stand flight i, the time when the shuttle bus must arrive is defined as the planned service time SerT of the flight. i According to the regulations of the Civil Aviation Administration, the shuttle bus must arrive at the designated position 5 minutes before passenger boarding and alighting. Therefore, the pre-departure / pre-arrival time T of the shuttle bus relative to flight i is set. i The time required to arrive in advance is E. A T k When passengers board and alight from the shuttle bus, the waiting time of the shuttle bus is DT. k Virtual flights numbered 0 and n + 1 with a task time of 0 are introduced as the first and last tasks in the flight task sequence.
[0053] The scheduling problem of airport shuttle buses can be modeled as an unrelated parallel machine scheduling problem by regarding the shuttle buses as machines and the remote stand flights as jobs. The main difference between the airport shuttle bus scheduling problem and the parallel machine scheduling problem is that in the airport shuttle bus scheduling problem, the order in which the shuttle buses serve the flights is determined by the arrival and departure times of the flights, and the travel time of each shuttle bus when serving a flight is uncertain, which depends on the order in which the shuttle buses serve the flights.
[0054] When solving this problem, the following assumptions need to be made:
[0055] (1) The maximum passenger capacity and speed of all shuttle buses are the same;
[0056] (2) All shuttle buses are available and there will be no breakdowns;
[0057] (3) Allowing shuttle buses to arrive in advance;
[0058] (4) Not considering the path planning and congestion problems of the shuttle buses;
[0059] (5) The initial positions of all shuttle buses are at the base, and they all depart from the base to serve the first flight respectively;
[0060] (6) The final positions of all shuttle buses are at the base, and all shuttle buses return to the base after serving the last flight;
[0061] (7) After the current task of the shuttle bus is completed, if the interval time between waiting at the current position until the start time of the next task exceeds the time limit, the shuttle bus must go to the operation area or the base in the remote stand area where it is located, and the start time of the next task will be recalculated from the current position.
[0062] Specifically, as Figure 1 shown, the airport shuttle bus scheduling method based on variable neighborhood search of the present application includes the following steps S1 to S7.
[0063] S1: Number m shuttle buses and n flights respectively.
[0064] The ferries and flights are numbered for indexing. In this embodiment, i and j are the indices of flights, where i, j = 1, 2,..., n, k is the index of the ferry, k = 1, 2,..., m, n is the number of flights, and m is the number of ferries.
[0065] S2: Construct an objective function with the goal of minimizing the weighted sum of delays in the ferry services for inbound and outbound flights.
[0066] The expression of the objective function is as follows:
[0067]
[0068] Among them, PC is the weighted sum of delays in the ferry services for inbound and outbound flights; Tar j is the service delay of flight j; ω1 is the weight of inbound flights; Arr j is 1 indicating that flight j is an inbound flight and 0 indicating that flight j is an outbound flight; CT j is the service completion time of flight j; is 1 indicating that ferry k serves flight j after serving flight i and 0 indicating that ferry k does not serve flight j after serving flight i; is the travel time for ferry k to go from serving the previous flight i to serving the current flight j; is 1 when ferry k serves flight j and 0 when ferry k does not serve flight j; EAT k is the time when the ferry arrives at the service location in advance; DT k is the stay time of ferry k; is the distance between the arrival gate or boarding gate of flight j and the remote stand; v k is the travel speed of ferry k; ω2 is the weight of outbound flights; T j is the arrival / departure time of flight j.
[0069] In a further preferred solution, the weight ω2 of outbound flights is greater than the weight ω1 of inbound flights, and ω1 + ω2 = 1. Because for outbound flights, if the ferry arrives at the remote stand later than the inbound time of the flight, there will be a delay in the ferry service for the flight at this time, resulting in passengers having to wait for some time for the ferry to arrive. For outbound flights, if the ferry finishes transporting passengers, that is, the completion time of the ferry service is later than the scheduled departure time of the flight, there will be a delay in the ferry service for the flight at this time, which will lead to flight delays. For example, the weight of outbound flights can be set to 0.8 and the weight of inbound flights can be set to 0.2.
[0070] Due to requirements such as the time sequence and matching relationship between ferries and flights, to avoid scheduling conflicts, the following constraint relationships need to be established.
[0071] The actual start time of the flight transfer service is not earlier than the planned service time. Therefore, the objective function satisfies the following timing relationship constraint conditions:
[0072]
[0073]
[0074] where ST j is the service start time of flight j; CT i is the service completion time of flight i; T stop is the maximum time limit for the shuttle bus to stay at the current position after the service ends; Arr i is 1 indicating that flight i is an inbound flight and 0 indicating that flight i is an outbound flight; is the distance between the shuttle bus base and the remote stand where flight j is located; is the distance between the shuttle bus base and the arrival gate or boarding gate of flight j; is R i the distance between the operating area where the remote stand is located and the remote stand where flight j is located; is R i the distance between the operating area where the remote stand is located and the arrival gate or boarding gate of flight j; is the distance between the arrival gate or boarding gate of flight i and the remote stand where flight j is located; is the distance between the arrival gate or boarding gate of flight i and the arrival gate or boarding gate of flight j; is the distance between the remote stand where flight i is located and the remote stand where flight j is located; is the distance between the remote stand where flight i is located and the arrival gate or boarding gate of flight j; ψ is an infinite large number; T j is the arrival / departure time of flight j; EAT k is the time for shuttle bus k to arrive at the service location in advance.
[0075] The shuttle bus can start serving the current flight only after serving the previous flight. Therefore, the objective function satisfies the non-preemptive scheduling constraint:
[0076]
[0077]
[0078] where ψ is an infinite large number, ST j is the service start time of flight j; EAT k is the time for shuttle bus k to arrive at the service location in advance; DT k is the stay time of shuttle bus k; CT i is the service completion time of flight i.
[0079] Constraints on the start time and end time of the first flight served by the shuttle bus:
[0080]
[0081]
[0082]
[0083] Among them, is the driving time for shuttle bus k to go from the shuttle bus base to serve the current flight j; is the distance between the shuttle bus base and the remote stand where flight j is located; is the distance between the shuttle bus base and the arrival gate or boarding gate of flight j; ST j is the service start time of flight j; ψ is an infinitely large number; T j is the arrival and departure time of flight j; EAT k is the time for shuttle bus k to arrive at the service location in advance.
[0084] The matching relationship constraint that each flight can only be served by one shuttle bus is:
[0085]
[0086] Each shuttle bus must serve the first and last tasks in the task sequence, thereby ensuring that there are preceding flights and subsequent flight constraints for all flights in the task sequence of its shuttle bus:
[0087]
[0088]
[0089]
[0090]
[0091] The constraint on the service order of two adjacent tasks of the shuttle bus is:
[0092]
[0093] The relationship constraint between two adjacent flights served by one shuttle bus is:
[0094]
[0095]
[0096]
[0097] Among them, being 1 indicates that the shuttle bus k serves flight i, and being 0 indicates that the shuttle bus k does not serve flight i; being 1 indicates that the shuttle bus k departs from the shuttle bus base; being 1 indicates that the shuttle bus k finally returns to the shuttle bus base; T j is the arrival and departure time of flight j; T i is the arrival and departure time of flight i; being 0 indicates that the first task and the last task in the service task sequence are not adjacent tasks; being 1 indicates that the shuttle bus k serves flight i after serving flight j, and being 0 indicates that the shuttle bus k does not serve flight i after serving flight j.
[0098]
[0099]
[0100]
[0101]
[0102] Equations (18) to (21) are variable 0-1 constraints and parameter positive integer constraints.
[0103] Such as Figure 2 shown, the process steps of the variable neighborhood algorithm are generally as follows:
[0104] Step 1: Generate the initial solution x0; design the neighborhood structure set N r (r = 1, 2, 3, 4, 5) and the algorithm termination condition; the current solution x = x0.
[0105] Step 2: Let r = 1.
[0106] Step 3: Obtain the local optimal solution x1 in the N r neighborhood structure.
[0107] Step 4: If x1 is better than x, let x = x1, and go to Step 3; otherwise, let r = r + 1. If r ≤ 5, go to Step 3. If r > 5, go to Step 5.
[0108] Step 5: The algorithm stops and outputs the final solution x.
[0109] The specific algorithm design is as follows in steps S3 to S7. The present invention uses real number coding for encoding. The flight numbers (i ∈ {1, 2,..., n}) served by each shuttle bus (k = 1, 2,..., m) are arranged in sequence as the encoding substring of the shuttle bus. Encoding m shuttle buses can obtain m encoding substrings.
[0110] When each shuttle bus conducts the first shuttle service, the first trip of the shuttle bus starts from the base. For inbound flights, the first trip of the shuttle bus is from the base to the remote stand. For outbound flights, the first trip of the shuttle bus is from the base to the boarding gate. The calculation of the start and end times of the first shuttle service can be seen in formulas (2)-(5).
[0111] For subsequent shuttle services, the first trip of the shuttle bus is determined by the completion time of the previous task and the start time of the current task. If the interval time between them is less than or equal to 2 minutes, the first trip of the shuttle bus is from the end position of the previous task to the start position of the current task. Otherwise, the first trip of the shuttle bus is from the base or the rest area near the end position of the previous task to the start position of the current task. After determining the start time of the shuttle service, the end time can be calculated. The specific calculation can be seen in formulas (6)-(8).
[0112] Considering that the solution goal is to minimize the total service delay of the shuttle tasks of n flights, a random initialization is selected based on the idea of balanced allocation. The shuttle tasks of n flights are randomly assigned to m shuttle buses, but the number of tasks for each shuttle bus is balanced.
[0113] The smaller the value of the objective function, the larger the fitness function value of the individual, and the better the solution of the individual with higher fitness in the population.
[0114] Setting of neighborhood structure N1: From the delay Tar of the shuttle task of each flight i i calculate the total delay TAR of the shuttle tasks of all flights on each shuttle bus k Select the shuttle bus k1 with the largest total delay, and for the flight i1 with the largest delay among the shuttle tasks on it, move the shuttle task of flight i1 to the remaining m - 1 shuttle buses (1, 2,..., k1 - 1, k1 + 1,..., m) respectively to generate m - 1 neighborhood solutions.
[0115] Setting of neighborhood structure N2: From the delay Tar of the shuttle task of each flight i i select the flight i2 with the largest delay among all shuttle tasks. The shuttle task of flight i2 belongs to shuttle bus k2. Move the shuttle task of flight i2 to the remaining m - 1 shuttle buses (1, 2,..., k2 - 1, k2 + 1,..., m) respectively to generate m - 1 neighborhood solutions.
[0116] Setting of neighborhood structure N3: From the delay Tar of the shuttle task of each flight i i, select flight i3, which is the second most delayed among all ferry tasks, and the ferry task of flight i3 belongs to shuttle bus k3. Insert the ferry task of flight i3 into the remaining m-1 shuttle buses (1, 2, ..., k3-1, k3+1, ..., m) respectively, and generate m-1 neighborhood solutions.
[0117] Neighborhood structure N4 is set up by the delay Tar of the ferry task of each flight i i , select all the ferry tasks that are delayed TAR k The number of flights a≠0 constitutes the flight set The flight set F i The ferrying task of each flight in is moved to the remaining m-1 ferry vehicles, generating a×(m-1) neighborhood solutions.
[0118] Neighborhood structure N5 is set up by the delay Tar of the ferry task of each flight i i , calculate the total delay TAR of the ferry tasks of all flights on each ferry bus k , select shuttle bus k5 with the largest total delay, which has b flights to ferry. Then, move the ferry tasks of these b flights to the remaining m-1 shuttle buses (1, 2, ..., k5-1, k5+1, ..., m), generating b × (m-1) neighborhood solutions. A specific example is described below.
[0119] S3: Evenly pre-allocate the ferrying tasks of n flights to m shuttle buses.
[0120] If the passenger capacity of the flight is greater than the passenger capacity of the shuttle bus, the flight will be split into multiple flights with the goal of minimizing the number of split flights and ensuring that the passenger capacity of each flight is less than or equal to the passenger capacity of the shuttle bus.
[0121] This embodiment is described by taking 3 shuttle buses and 6 remote-parking flights as an example. The airport layout is as follows: Figure 3 As shown in Table 1, the original data is as follows:
[0122]
[0123]
[0124] Table 1
[0125] Since the maximum passenger capacity of the shuttle bus is 80, it is necessary to introduce virtual flights and split all flights with more than 80 passengers. For a flight with 174 passengers, it is split into 3 flights with 60, 60, and 54 passengers respectively. For a flight with 150 passengers, it is split into 2 flights with 75 and 75 passengers respectively. For a flight with 106 passengers, it is split into 2 flights with 53 and 53 passengers respectively. In this way, the passenger capacity of all flights after splitting does not exceed 80, meeting the matching relationship constraint, and each flight can only be served by one shuttle bus.
[0126] Number the tasks of the 10 flights after splitting to obtain Table 2 as follows.
[0127]
[0128] Table 2
[0129] To make the task quantity of each shuttle bus balanced, that is, one shuttle bus serves 4 flights, and the other two shuttle buses each serve 3 flights. Based on the idea of balanced distribution of task quantity, randomly assign the shuttle tasks of 10 flights to 3 shuttle buses to obtain the initial solution x0 as Figure 4 .
[0130] Among them, Shuttle Bus No. 1 serves the remote stand flights numbered 4, 7, and 10 in sequence, Shuttle Bus No. 2 serves the remote stand flights numbered 1, 3, and 6 in sequence, and Shuttle Bus No. 3 serves the remote stand flights numbered 2, 5, 9, and 8 in sequence. In addition, when Shuttle Bus No. 1 goes to serve Flight No. 10, there will be a delay of 0.2×25 min; when Shuttle Bus No. 2 goes to serve Flight No. 3, there will be a delay of 0.8×8 min, and when Shuttle Bus No. 3 goes to serve Flight No. 8, there will be a delay of 0.2×15 min. The objective function value of this initial solution is 14.4 min.
[0131] Then perform local search in the neighborhood of this initial solution.
[0132] S4: Calculate the objective function TAR0 in the case of pre-allocation and the delay time of each flight;
[0133] Let x = x0, r = 1, and perform local search in the set neighborhood structure N1.
[0134] Calculate that the total delays of the shuttle tasks of all flights on Shuttle Bus No. 1, Shuttle Bus No. 2, and Shuttle Bus No. 3 are 0.2×25 min, 0.8×8 min, and 0.2×15 min respectively. Select Shuttle Bus No. 2 with the largest total delay, and among the shuttle tasks on it, select Flight No. 3 with the largest delay, and move the shuttle task of Flight No. 3 to the other 2 shuttle buses respectively to generate 2 neighborhood solutions, and obtain the neighborhood solution set of x as Figure 4Among the solution set of \(x\) and its neighborhood, the solution with the minimum objective function value for the ferry task of Flight 3 moved to Ferry 1 is the neighborhood solution with the optimal fitness value, that is Figure 5 the solution marked by the black box in Figure 5 , denoted as \(x1\)
[0135] Let \(x = x1\), and repeat the search within the neighborhood structure of \(N1\). After reaching the local optimum within the neighborhood structure of \(N1\), the result is as Figure 6 , that is, Ferry 1 serves the remote stand flights numbered 3, 4, and 7 in sequence, Ferry 2 serves the remote stand flights numbered 1, 6, and 10 in sequence, and Ferry 3 serves the remote stand flights numbered 2, 5, 9, and 8 in sequence. In addition, when Ferry 2 goes to serve Flight 10, there will be a delay of \(0.2×14\) minutes; when Ferry 3 goes to serve Flight 8, there will be a delay of \(0.2×14\) minutes.
[0136] S5: Change the ferry task of the flight with the maximum delay time to other ferries, recalculate the corresponding objective function \(TAR1\) and the delay time of each flight respectively, and take the ferry plan with the minimum objective function \(TAR1\) as the first preferred plan.
[0137] \(r = 2\), change the operator, and search within the set neighborhood structure of \(N2\).
[0138] Select Flight 8 with the maximum delay among all ferry tasks, move the ferry task of Flight 8 from Ferry 3 to the other 2 ferries respectively, generate 2 neighborhood solutions, and obtain the neighborhood solution set of \(x\) as Figure 7 . Among the solution set of \(x\) and its neighborhood, the solution with the minimum objective function value is \(x\), that is, \(x\) is the neighborhood solution with the optimal fitness value, denoted as \(x2\). After the search, \(x2\) is equal to \(x\), that is, the local optimum is reached within the neighborhood structure of \(N2\).
[0139] S6: Adopt the same method as in step S5, change the ferry task of the flight with the maximum delay time in the first preferred plan to other ferries, recalculate the corresponding objective function \(TAR2\) and the delay time of each flight respectively, and take the ferry plan with the minimum objective function \(TAR2\) and less than the objective function \(TAR1\) as the second preferred plan;
[0140] Let \(x = x2\), \(r = 3\), change the operator, and search within the set neighborhood structure of \(N3\).
[0141] Select Flight 10 ranked second in descending order of delay among all ferry tasks, move the ferry task of Flight 10 from Ferry 2 to the other 2 ferries respectively, generate 2 neighborhood solutions, and obtain the neighborhood solution set of \(x\) as Figure 8Among x and its neighborhood solution set, the solution with the minimum objective function value is x, that is, x is the neighborhood solution with the optimal fitness value, which is denoted as x3. The obtained x3 after search is equal to x, that is, the local optimum is reached within the N3 neighborhood structure.
[0142] S7: Optimize the shuttle buses corresponding to the flights with non-zero delay times in the second preferred plan in descending order of delay time until the objective function is minimized.
[0143] Let x = x3, r = 4, change the operator, and search within the set N4 neighborhood structure.
[0144] Select flights 10 and 8 with non-zero delay times among all shuttle tasks. Move the shuttle task of flight 10 from shuttle bus 2 to the other 2 shuttle buses respectively to generate 2 neighborhood solutions; move the shuttle task of flight 8 from shuttle bus 3 to the other 2 shuttle buses respectively to generate 2 neighborhood solutions; the neighborhood solution set of x is as Figure 9 Among x and its neighborhood solution set, the solution with the minimum objective function value is x, that is, x is the neighborhood solution with the optimal fitness value, which is denoted as x4. The obtained x4 after search is equal to x, that is, the local optimum is reached within the N4 neighborhood structure.
[0145] Let x = x4, r = 5, change the operator, and search within the set N5 neighborhood structure.
[0146] Select shuttle bus 3 with the largest total delay. Move all the shuttle tasks on it. Move the shuttle tasks of flight 2, flight 5, flight 9, and flight 8 to shuttle bus 1 and shuttle bus 2 respectively to obtain 8 neighborhood solutions of x. The neighborhood solution set is as Figure 10 Among x and its neighborhood solution set, the solution obtained by moving the shuttle task of flight 9 to shuttle bus 2 is the neighborhood solution with the optimal fitness value, that is Figure 10 the solution marked by the black box in, which is denoted as x5.
[0147] Let x = x5, repeat the search within the N5 neighborhood structure. After reaching the local optimum within the N5 neighborhood structure, the result is as Figure 11 。
[0148] r = 6, reaching the algorithm stop condition, output x = x5, as Figure 11 , that is, shuttle bus 1 serves the remote stand flights numbered 3, 4, and 7 in sequence, shuttle bus 2 serves the remote stand flights numbered 1, 9, 6, and 10 in sequence, and shuttle bus 3 serves the remote stand flights numbered 2, 5, and 8 in sequence. In addition, when shuttle bus 2 goes to serve flight 10, there will be a delay of 0.2×14 min.
[0149] The final shuttle bus scheduling result is:
[0150] The task list of the No. 1 shuttle bus is as shown in Table 3 below:
[0151]
[0152] Table 3
[0153] The task list of the No. 2 shuttle bus is as shown in Table 4 below:
[0154]
[0155]
[0156] Table 4
[0157] The task list of the No. 3 shuttle bus is as shown in Table 5 below:
[0158]
[0159] Table 5
[0160] Figure 12 For the Gantt chart of the final solution, the black dashed vertical lines thereon represent the scheduled departure / arrival times of flights, the white blocks represent the flights that receive the shuttle service on time, and the black blocks represent the flights with a delay in the shuttle service. The times corresponding to the start and end positions of the blocks are the departure time and the end time of the shuttle bus service. Above the blocks are the actual numbers of the flights and the positions of the shuttle bus after the shuttle service for that flight.
[0161] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
Claims
1. An airport shuttle bus scheduling method based on variable neighborhood search, characterized in that, The method includes: S1: Number m shuttle buses and n flights respectively; S2: Construct an objective function with the goal of minimizing the weighted sum of delays of inbound and outbound flight shuttle services; S3: Evenly pre-assign the shuttle tasks of n flights to m shuttle buses; S4: Calculate the objective function TAR0 in the case of pre-assignment and the delay time of each flight; S5: Change the shuttle task of the flight with the maximum delay time to other shuttle buses, recalculate the corresponding objective function TAR1 and the delay time of each flight respectively, and take the shuttle plan with the minimum objective function TAR1 as the first preferred plan; S6: In the same way as step S5, change the shuttle task of the flight with the maximum delay time in the first preferred plan to other shuttle buses, recalculate the corresponding objective function TAR2 and the delay time of each flight respectively, and take the shuttle plan with the minimum objective function TAR2 and less than the objective function TAR1 as the second preferred plan; S7: Optimize the shuttle buses corresponding to the flights with non-zero delay times in the second preferred plan in descending order of delay time until the objective function is minimized; The expression of the objective function is: Among them, PC is the weighted sum of delays of the shuttle services for inbound and outbound flights; Tar j is the service delay of flight j; ω1 is the weight of inbound flights; Arr j is 1 if flight j is an inbound flight and 0 if flight j is an outbound flight; CT j is the service completion time of flight j; is 1 if shuttle bus k serves flight j after serving flight i and 0 if shuttle bus k does not serve flight j after serving flight i; is the travel time for shuttle bus k to serve the current flight j after serving the previous flight i; is 1 if shuttle bus k serves flight j and 0 if shuttle bus k does not serve flight j; EAT k is the time for the shuttle bus to arrive at the service location in advance; DT k is the dwell time of shuttle bus k; is the distance between the arrival or boarding gate of flight j and the remote stand; v k is the driving speed of shuttle bus k; ω2 is the weight of outbound flights; T j is the arrival and departure time of flight j.
2. The method according to claim 1, wherein In step S3, if the passenger capacity of a flight is greater than that of a shuttle bus, the flight is split into multiple flights with the goal of minimizing the number of split flights and the passenger capacity of each flight being less than or equal to that of the shuttle bus.
3. The method according to claim 1, wherein The weight ω2 of the outbound flight is greater than the weight ω1 of the inbound flight, and ω1 + ω2 = 1.
4. The method according to claim 1, characterized in that The actual start time of the flight shuttle service is not earlier than the planned service time. Therefore, the objective function satisfies the following timing relationship constraint conditions: Among them, ST j is the service start time of flight j; CT i is the service completion time of flight i; T stop is the maximum time limit for staying at the current position after the shuttle bus service ends; Arr i If it is 1, it means flight i is an inbound flight, and if it is 0, it means flight i is an outbound flight; is the distance between the shuttle bus base and the remote stand where flight j is located; is the distance between the shuttle bus base and the arrival gate or boarding gate of flight j; is R i is the distance between the operating area where the remote stand is located and the remote stand where flight j is located; is R i is the distance between the operating area where the remote stand is located and the arrival gate or boarding gate of flight j; is the distance between the arrival gate or boarding gate of flight i and the remote stand where flight j is located; is the distance between the arrival gate or boarding gate of flight i and the arrival gate or boarding gate of flight j; is the distance between the remote stand where flight i is located and the remote stand where flight j is located; is the distance between the remote stand where flight i is located and the arrival gate or boarding gate of flight j; ψ is an infinite large number; T j is the arrival and departure time of flight j; EAT k is the time when shuttle bus k arrives at the service position in advance.
5. The method according to claim 1 or 4, characterized in that, The shuttle bus can start serving the current flight only after serving the previous flight. Therefore, the objective function satisfies the non-preemptive scheduling constraint: where ψ is an infinite number, ST j is the service start time of flight j; EAT k is the time for shuttle bus k to arrive at the service location in advance; DT k is the residence time of shuttle bus k; CT i is the service completion time of flight i.
6. The method according to claim 1, characterized in that, The start time and end time constraints of the first flight served by the shuttle bus: Among them, is the driving time for the shuttle bus k to go from the shuttle bus base to serve the current flight j; is the distance between the shuttle bus base and the remote stand where the flight j is located; is the distance between the shuttle bus base and the arrival gate or boarding gate of the flight j; ST j is the service start time of the flight j; ψ is an infinite large number; T j is the arrival and departure time of the flight j; EAT k is the time for the shuttle bus k to arrive at the service location in advance.
7. The method according to claim 1, characterized in that, The matching relationship constraint that each flight can only be served by one shuttle bus: Each shuttle bus must serve the first and last tasks in the task sequence, so as to ensure that there are previous and subsequent flights for all flights in the task sequence of its shuttle bus: The constraint on the service order of two adjacent tasks of the shuttle bus: The relationship constraint between two adjacent flights served by one shuttle bus: Among them, being 1 means that the shuttle bus k serves flight i, and being 0 means that the shuttle bus k does not serve flight i; being 1 indicates that the shuttle bus k departs from the shuttle bus base; being 1 indicates that the shuttle bus k finally returns to the shuttle bus base; T j is the arrival and departure time of flight j; T i is the arrival and departure time of flight i; being 0 means that the first task and the last task in the service task sequence are not adjacent tasks; being 1 means that the shuttle bus k serves flight i after serving flight j, and being 0 means that the shuttle bus k does not serve flight i after serving flight j.
Citation Information
Patent Citations
Route recommendation method and electronic device
CN110457606A
Airport ferry vehicle scheduling method based on two-stage optimization
CN114330842A