A two-stage robust optimization method for airport cluster timetable

Abstract

The application is suitable for the field of intelligent civil aviation, and provides a two-stage airport group timetable robust optimization method. According to the fixed hour capacity parameter, the dynamic allocation of the 15min capacity parameter and the uncertainty of the 5min capacity parameter of each airport, the method allocates the best time slot for each flight of each airport on the basis of the 15min capacity of each airport, meets the airport and waypoint capacity constraints, avoids the waste problem of traditional fixed coordination parameter flight timetable resource allocation, and provides technical support for multi-airport flight timetable compilation.

Description

Technical Field

[0001] This invention belongs to the field of intelligent civil aviation, and in particular relates to a two-stage robust optimization method for airport cluster timetables. Background Technology

[0002] With the continuous growth in air transport demand, the independent operation model of a single airport is no longer sufficient to meet the development needs of regional air transport networks. Airport clusters, as the core form of multi-airport collaborative operation, have become a key carrier for improving regional air transport efficiency. The core objective of airport cluster operation is to coordinate key parameters such as flight take-off and landing times and route allocation at each airport to avoid flight conflicts at shared waypoints, optimize the overall utilization of airspace and airport resources, and reduce the total cost of flight delays.

[0003] However, the allocation of timetable coordination parameters for airport clusters still relies heavily on the human experience of air traffic controllers. The decision-making process is easily influenced by non-quantifiable factors, leading to problems such as imbalanced allocation of time slots, wasted time slots, or congestion. Therefore, there is an urgent need to address the issue of automated generation and evaluation of airport cluster flight timetables based on artificial intelligence and big data.

[0004] Although existing models and algorithms provide some support for optimizing airport cluster operations, their coordination parameters are usually fixed and difficult to meet actual operational needs. This is because the core of airport cluster timetable optimization relies on the precise allocation of coordination parameters such as take-off and landing times, airway capacity, and flight intervals. These parameters are affected by factors such as sudden weather changes, air traffic fluctuations, and air traffic control. This requires that the coordination parameters be flexible and applicable to the uncertainties of airport cluster timetables.

[0005] As can be seen from the above, the current airport cluster flight schedule lacks a comprehensive design for the entire process of "parameter pre-allocation and dynamic adjustment". Some two-stage optimization schemes have not established a mechanism for the correlation between parameter uncertainty and stages, and cannot achieve dynamic adaptation between pre-allocated parameters and actual operating status. Summary of the Invention

[0006] The purpose of this invention is to provide a two-stage robust optimization method for airport group timetables, aiming to solve the technical problems existing in the prior art as identified in the background section.

[0007] This invention is implemented as follows: a two-stage robust optimization method for airport cluster timetables, comprising:

[0008] S1. Data Preparation: Collect and process the input data required for the model, covering all relevant operational elements within the airport network on a given operating day. Specifically, this includes: a set of all airports and waypoints and their attributes; planning information, acceptable time deviations, and flight paths for all arriving and departing flights; a set of time slots divided at different time granularities (hours, 15 minutes, 5 minutes); fixed capacity data for each airport at the hourly granularity, historical uncertain capacity data at the 5-minute granularity, and their probability distribution; and the maximum throughput capacity of each waypoint at the 5-minute granularity.

[0009] S2. Constructing a Two-Stage Robust Optimization Model: Based on the data prepared in S1, construct an integrated two-stage optimization model framework:

[0010] Phase 1 (Coordination Parameter Pre-allocation Model): Given the known hourly fixed capacity and 5-minute uncertain capacity probability distribution for each airport, the goal is to minimize the total occupied capacity by dynamically deciding the upper limit of arrival and departure capacity (i.e., coordination parameters) to be allocated to each airport in each 15-minute time period. This phase of decision-making must satisfy constraints on the total hourly capacity, the correlation between the sum of the 15-minute and 5-minute capacities, and the smoothness of capacity fluctuations.

[0011] The second stage (flight slot assignment model): Given the 15-minute capacity parameter from the first stage decision, and considering various uncertainties regarding the actual 5-minute capacity of each airport, the objective is to minimize the total deviation between all flight plans and assigned slots, assigning a specific 5-minute slot to each flight. This stage's decision must satisfy constraints such as each flight being assigned one and only one slot, flight assignment time deviation not exceeding the allowable range, the number of takeoffs and landings at each airport within each 5-minute slot not exceeding the actual capacity of that slot, and the number of flights passing through each waypoint within each 5-minute slot not exceeding its maximum capacity.

[0012] S3. Design an efficient solution algorithm to solve and evaluate the solution. For the complex two-stage robust optimization model constructed in S2, an iterative solution framework based on the column and constraint generation (C&CG) algorithm is designed. This algorithm approximates the optimal solution by repeatedly solving a master problem and multiple subproblems.

[0013] Main problem: Optimize capacity allocation in the first stage under a set of finite second-stage uncertainties, and consider the optimal response in the second stage under these scenarios, given the decision variables in the first stage.

[0014] Subproblem: Given the first-stage decision obtained from the main problem, find a new uncertain capacity scenario and its corresponding flight assignment scheme that makes the objective function of the second stage the worst (i.e., the total deviation is maximized).

[0015] Iteration and Convergence: The worst-case scenario found in the subproblem is added to the scenario set of the main problem, and the solution is recalculated. This process is repeated until the difference between the lower bound of the main problem and the upper bound of the subproblem is less than a preset convergence threshold, at which point the optimal solution that satisfies the robustness requirement is obtained.

[0016] A solution framework for the aforementioned algorithm was built using the Python programming language, and commercial mathematical optimization solvers such as Gurobi were used to quickly solve the main problem and subproblems. By setting different model parameters (such as capacity level and fluctuation constraint range), the model and algorithm were run to generate optimal airport group flight schedule schemes under various operating scenarios. Finally, the impact of different parameters on the optimization results (such as total allocated capacity and total flight deviation) was compared and analyzed, and sensitivity analysis was performed to provide quantitative support for practical decision-making.

[0017] The beneficial effects of this invention are:

[0018] This invention considers the spatial layout of an airport cluster network. Based on the traffic flow changes of arriving and departing flights at each airport and taking into account the capacity constraints of airports and waypoints, it dynamically allocates 15-minute capacity parameters for each airport based on the estimated arrival and departure times of any flight. This allocation is made while satisfying practical constraints such as the maximum deviation between planned and actual time slot allocation. It assumes that the hourly capacity parameter of each airport is fixed, while the 5-minute capacity parameter is uncertain. This allows any flight from each airport to be assigned to a corresponding time slot, providing data support for the refined management of airport cluster timetables dynamically generated based on flexible time slot coordination parameter changes. This invention enables the automatic generation of an executable airport cluster timetable based on flexible time slot coordination parameters of each airport, airport flight time distribution, and airport cluster network layout, providing technical support for intelligent daily management of airport cluster timetables. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a robust optimization method for flight schedules in a two-stage airport cluster, as provided in an embodiment of the present invention.

[0020] Figure 2 This is a flowchart illustrating the implementation of a two-stage airport cluster flight timetable optimization model provided in this embodiment of the invention.

[0021] Figure 3 The flowchart illustrates the implementation of an efficient algorithm for solving a two-stage airport group flight timetable optimization model, as provided in this embodiment of the invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be 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 illustrative and not intended to limit the invention.

[0023] like Figure 1 and Figure 2 As shown, a two-stage robust optimization method for airport cluster flight schedules includes the following steps:

[0024] S1. Data Preparation and Preprocessing

[0025] 1. Basic airport and flight information:

[0026] All airport assembly points are recorded as Any airport All arriving flights and all departing flights gathered Any flight The time slot number corresponding to the planned departure or arrival time is The maximum deviation between the planned and actual time slots is Its waypoints are .

[0027] 2. Waypoint and flight path information:

[0028] The set of all waypoints is denoted as waypoints airport All departing flights are recorded as waypoints airport All arriving flights are recorded as Waypoints With the airport The corresponding time slots for flight times are .

[0029] 3. Definition of Time Slot System:

[0030] The set of 288 5-minute time slots per day is denoted as Any 5-minute time slot The time slot number is An airport In any 5-minute time slot The uncertain capacity is denoted as A certain waypoint In any 5-minute time slot The maximum capacity is denoted as .

[0031] A 24-hour gathering is recorded as An airport At any hour The maximum capacity is denoted as .

[0032] Any hour The set of 4 15-minute time slots is Any 15-minute time slot The set of 3 5-minute time slots is .

[0033] 4. Determining capacity parameters:

[0034] Based on big data, analyze a certain airport In any 5-minute time slot Uncertain capacity Set of probabilities of different values And the probability scenarios of each value occurring. capacity .

[0035] S2. Construction of a Two-Stage Robust Optimization Model

[0036] Establish a time-segment coordination parameter allocation model for each airport at different scales. Assume that the hourly capacity parameter of each airport is fixed and the 5-minute capacity parameter is uncertain. Dynamically allocate the 15-minute capacity parameter of each airport to minimize the total usage capacity.

[0037] Establish a time-segment coordination parameter allocation model for different airports at different scales:

[0038] Decision variable: any airport Every hour Any 15-minute time slot The allocation of inbound and outbound capacity parameters and .

[0039] Objective function: All airports within 24 hours The minimum total capacity for arriving and departing flights is allocated within 15 minutes. .

[0040] Constraints:

[0041] (1) , indicating any airport Every hour of The sum of the arrival and departure flight capacities allocated within 15 minutes is less than its maximum capacity. .

[0042] (2) , indicating any airport Every hour Any 15-minute time slot The deviation between the sum of the arrival and departure flight capacities allocated to the airport and its average capacity is within [ ]. ]Inside.

[0043] (3)0

[0044] Establish an airport group timetable optimization model

[0045] Decision variables: Represents any airport A certain flight Should it be allocated to a 5-minute time slot? .

[0046] Objective function: to pursue the various airports The deviation between the planned and actual arrival and departure time slots for all flights is the smallest, i.e. .

[0047] Constraints:

[0048] (1) , indicating any airport Any flight It must be assigned to a unique time slot.

[0049] (2) , indicating any airport Any flight The planned and actual arrival / departure time slot deviations must be within [the specified range]. Within.

[0050] (3) , indicating any airport All flights Assigned to a time slot The quantity does not exceed its capacity .

[0051] (4) , indicating any waypoint From all airports All arriving and departing flights Assigned to a time slot The quantity does not exceed its capacity .

[0052] (5)0 , indicating any airport Every hour Any 15-minute time slot The sum of the allocated arrival and departure flight capacity is less than three consecutive 5-minute time slots. Uncertain capacity sum.

[0053] S3. Efficient solution algorithm and solution calculation

[0054] Construct a two-stage ensemble model for optimizing flight schedules for airport clusters, considering adaptive coordination parameter allocation:

[0055] For a certain airport in the second-stage model In any 5-minute time slot Uncertain capacity Based on big data mining, it determines the probability of occurrence for each value. Corresponding capacity is Construct a set of probabilities of different values ​​occurring. Based on the above, the first and second stage models are integrated into one model, as shown below.

[0056] ;

[0057] ;

[0058] The constraints are:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] 0

[0066] like Figure 3 The diagram shown illustrates an embodiment of the present invention, illustrating the implementation flowchart of an efficient algorithm for solving a two-stage airport group flight timetable optimization model, comprising:

[0067] Step 1: Prepare basic data, such as: Flights, etc.

[0068] Step 2: Set different parameter data for model constraints, such as , wait.

[0069] Step 3: Algorithm initialization, including:

[0070] Set the number of iterations ;

[0071] , ;

[0072] Set convergence threshold .

[0073] Step 4: During the number of iterations At that time, the decision variables of the first-stage model of the main problem are solved based on Gurobi. and Based on this, obtain its objective function. Meanwhile, in the first phase of decision-making and Below, we use the second-stage model based on Gurobi to solve subproblems to find arbitrary uncertain scenarios. The best solution Obtain its objective function .

[0074] Step 5: If Then stop iterating. and This is the optimal solution. If the target value is optimal, proceed to step 6; otherwise, let... , will new scene join in get Return to step 4.

[0075] Step 6: Establish different parameters , and optimization results and The contrast and combination, such as , ( and If you want to continue comparing the differences in optimization results for different parameters, return to step 2; otherwise, visualize the results.

[0076] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0077] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A two-stage robust optimization method for airport cluster timetables, characterized in that, The method includes: S1. Obtain all flight data for the day and record airport information, waypoints, and route information; S2. Construct a two-stage airport cluster flight timetable optimization model that considers adaptive coordination parameter allocation. In the first stage, the 15-minute capacity parameter of each airport is dynamically optimized and allocated based on a fixed hourly capacity framework. A coordination parameter allocation model that aims to minimize the total used capacity is established. In the second stage, considering the uncertainty of the 5-minute capacity parameter, an airport cluster timetable optimization model that aims to minimize the deviation between the planned and actual arrival and departure time slots of all flights is established. Under the condition of satisfying the capacity constraints of airports and waypoints, time slots are allocated to each flight at each airport. S3. Solve the two-stage airport cluster flight timetable optimization model, find the optimal solution under different conditions, and perform sensitivity analysis.

2. The method according to claim 1, characterized in that, S1 specifically includes: Record all airport assembly points as Then any airport All arriving flights Gathering with all departing flights In China, any flight The planned departure and arrival times correspond to the time slot numbers as follows: The maximum deviation between the planned departure and arrival times and the actual time slots is: The flight's waypoints are ; Let the set of all waypoints be . waypoints airport All departing flights are recorded as waypoints airport All arriving flights are recorded as Waypoints With the airport The corresponding time slots for flight times are ; The set of all 5-minute time slots throughout the day is denoted as Any 5-minute time slot The time slot number is Any airport In any 5-minute time slot The uncertain capacity is denoted as Waypoints In any 5-minute time slot The maximum capacity is denoted as ; Let the set of hours for the whole day be denoted as Any airport At any hour The maximum capacity is denoted as ; Record any hour The complete set of 15-minute time slots within is Any 15-minute time slot The complete set of 5-minute time slots in the data is as follows: ; Dig any airport In any 5-minute time slot Uncertain capacity Set of probabilities of different values And the probability scenarios of each value occurring. capacity .

3. The method according to claim 1, characterized in that, The establishment of a coordination parameter allocation model that aims to minimize total usage capacity specifically includes: Establish a time-sharing coordination parameter allocation model for each airport at different scales. Assume that the hourly capacity parameter for each airport is fixed, while the 5-minute capacity parameter is uncertain. Dynamically allocate the 15-minute capacity parameter for each airport to minimize the total utilized capacity. Specifically: Set any airport Every hour Any 15-minute time slot The allocated entry capacity parameters are as follows The off-site capacity parameter is ; With all airports 24 hours Based on the condition of minimizing the total capacity of arriving and departing flights within 15 minutes, coordinate parameters for different time periods at various scales are constructed for each airport. Coordination parameter allocation model: objective function The goal is to minimize the 15-minute arrival and departure capacity parameters for all airports at different times of the hour. Apply constraints, including: For any airport Apply every hour of The sum of the arrival and departure flight capacities allocated within 15 minutes is less than the maximum capacity. The constraints, namely: ; For any airport Apply every hour Any 15-minute time slot The deviation between the sum of the allocated arrival and departure flight capacities and the average capacity is within [[ The constraints within ], namely: .

4. The method according to claim 1, characterized in that, The aforementioned establishment of an airport group timetable optimization model that aims to minimize the deviation between planned and actual arrival / departure time slots for all flights specifically includes: Set any airport Any flight Should it be allocated to a 5-minute time slot? The result is That is: if the flight Assigned to time slots ,but Otherwise, the flight Not allocated to time slots ,but ; With each airport Given the condition of minimizing the deviation between the planned and actual arrival and departure time slots of all flights, an airport group timetable optimization model is constructed: Objective function The goal is to minimize the deviation between the arrival and departure flight schedules and the actual flight slots at all airports. Apply constraints, including: For any airport any flight Add a constraint that must be assigned to a unique time slot, namely: ; For any airport any flight The discrepancy between the planned and actual arrival / departure time slots for added flights must be within [the specified range]. Constraints within ], namely: ,Right now: ; For any airport All flights in Add to assign to any time slot The quantity does not exceed the capacity The constraints, namely: ; For any waypoint From all airports All arriving and departing flights Assigned to a certain time slot The quantity does not exceed its capacity ,Right now: For any airport Every hour Any 15-minute time slot The sum of the allocated arrival and departure flight capacity is less than three consecutive 5-minute time slots. Uncertain capacity The sum, that is: 0 .

5. The method according to claim 4, characterized in that, Solving the two-stage airport cluster flight timetable optimization model specifically includes: S31. Set the number of iterations. Initialize any airport In any 5-minute time slot Uncertain capacity Set of probabilities of different values The probability of each of its possible values Corresponding capacity is Set a convergence threshold ; S32, in the number of iterations At that time, the main problem is fixed in the current scenario set. Solve for the decision variables of the first-stage model. and Determine its lower bound. : ； The constraint condition is that the coordination parameter allocation model is in the number of iterations. Restrictions: S33. Solve the sub-problems of the second stage. The model for the second stage sub-problems is in the current iteration number. Phase One Decision and Next, search for the worst-case, uncertain scenario. Solution Determine its upper bound. : ； The constraint is that the airport group timetable optimization model has a certain number of iterations. Restrictions: ， ， ， ； 0 S34, if If the iteration stops, then take... and This is the optimal solution. The optimal objective value is obtained; if the convergence condition is not met... Then the new scene join in get ; S35, Order Then return to S32 to repeat.

6. The method according to claim 1, characterized in that, The algorithm for finding the optimal solution under different scenarios uses Python to build an algorithm framework for optimizing flight schedules for two-stage airport clusters. Based on Gurobi, it gradually approximates the upper and lower bounds of the solutions to the main and subproblems in each iteration, generating the optimal solution under different scenarios.

Images