An airport boarding gate assignment dynamic optimization method and system for improving transfer reliability

Abstract

The application discloses a kind of dynamic optimization method and system of airport boarding gate distribution considering flight delay condition to improve transfer reliability, it is related to airport ground resource scheduling and operation control technical field, including the following steps: with historical airport operation data as input, to predict flight arrival time using deep learning model based on.Based on the prediction result of machine learning, the application constructs the mixed integer linear programming MILP model with the minimum passenger boarding time and airport shuttle energy consumption as the target.In addition, the application designs a customized branch and price B&P algorithm and combines parallel elite genetic algorithm to solve the model.The dynamic optimization method in the application can reasonably allocate the boarding gate of each flight by the airport tower, maximize the utilization efficiency of the bridge and improve the robustness of scheduling, and can realize stable and reliable boarding gate allocation under the condition of flight delay, improve the quality of allocation scheme, reduce the impact of delay propagation, and reduce the negative effect on taxi efficiency.

Description

Technical Field

[0001] This invention belongs to the field of airport ground resource scheduling technology, and in particular relates to a dynamic optimization method and system for airport boarding gate allocation to improve transfer reliability. Background Technology

[0002] In recent years, the rapid growth of the civil aviation industry has led to an increasing scarcity of airport parking positions, especially those near jet bridges. With the continuous increase in the number of flights and the relatively lagging expansion of available parking capacity, flight delays have become a key factor affecting the operational efficiency of airports worldwide. The uncertainty of flight arrival times directly causes discrepancies between pre-allocated gate plans and actual operational conditions, leading to gate conflicts, affecting the normal arrival and departure of subsequent flights, and impacting ground service support, passenger transfers, and other aspects. Transfer passengers unable to connect to their connecting flights on time due to delays not only reduce passenger satisfaction but also incur additional costs for airlines, such as rebooking and compensation. Therefore, rationally allocating each parking position with limited gate resources, improving transfer reliability, maximizing jet bridge utilization, and enhancing passenger flow efficiency under flight delay conditions have become core challenges in airport operations management.

[0003] Currently, domestic and international scholars have achieved some research results on models and optimizations for the airport gate allocation problem. Seker and Noyan proposed a stochastic model to describe gate conflicts caused by the uncertainty of flight arrival / departure times; Castaing et al. introduced several robustness criteria related to flight schedule overlap and estimated the probability of each criterion based on historical delay data; Kim et al. proposed a gate allocation model with chance constraints; Cao et al. constructed a prediction-optimization framework, using a CNN-LSTM-Attention hybrid model to improve the accuracy of flight arrival time prediction in the prediction stage, and using an epsilon-constrained branch pricing algorithm to solve the dual-objective gate allocation model in the optimization stage.

[0004] Regarding solution algorithms, Cheng et al. compared the performance of heuristic methods such as genetic algorithms, simulated annealing, and tabu search on large airport instances; Li et al. and Hagspihl et al. proposed a column generation-based method; Bi et al. designed a branch pricing algorithm to improve the utilization rate of boarding bridges and added a certain probability heuristic search to each search node to accelerate the solution.

[0005] The research findings of the aforementioned scholars have contributed to the modeling and solution of the airport gate allocation problem. However, existing branch-and-price algorithms still face slow convergence when solving large-scale multi-objective gate allocation models. Although existing technologies attempt to incorporate heuristic search at each search node, their search strategies lack a systematic evaluation and differentiated processing mechanism for node potential, resulting in a significant waste of computational resources on ineffective exploration of low-potential nodes. Furthermore, no existing technology deeply integrates priority quantification evaluation methods based on solution space structure analysis with the branch-and-bound search process. How to efficiently identify high-potential search directions and quickly eliminate low-quality branches through systematic pruning strategies and priority ranking mechanisms during the branch-and-bound search process, thereby rapidly obtaining a gate allocation scheme that meets transfer reliability constraints under flight delay conditions, is a pressing technical challenge.

[0006] Based on the above reasons, this invention designs a dynamic optimization method and system for airport gate allocation to improve transfer reliability. Summary of the Invention

[0007] The purpose of this invention is to solve the problems in the prior art, and to propose a dynamic optimization method and system for airport gate allocation to improve transfer reliability.

[0008] This invention first discloses a dynamic optimization method for airport gate allocation to improve transfer reliability, comprising the following steps: Obtain the multi-objective gate allocation model to be solved. The multi-objective gate allocation model is used to describe the airport gate allocation problem. The multi-objective gate allocation model adopts the mixed integer linear model with multiple constraints (MILP). An elite genetic algorithm is used to solve the multi-objective gate allocation model to obtain an initial feasible solution, which is then used as the current global optimal solution. Construct a branch-bound search tree, take the root node of the multi-target boarding gate allocation model as the starting search node, and solve the linear slack subproblem corresponding to the current search node to obtain the relaxed solution; During the branch search iteration process, the current search node is eliminated or prioritized based on the pruning rule set; The branch-bound search tree is iteratively pruned and searched according to the pruning rule set until the search termination condition is met. The updated current global optimal solution is output as the optimal solution result of the multi-objective boarding gate allocation model to generate an airport boarding gate allocation scheme.

[0009] Secondly, the present invention provides a dynamic optimization system for airport gate allocation to improve transfer reliability, used in the above method, comprising: The model acquisition module is used to acquire the multi-objective gate allocation model to be solved, which describes the airport gate allocation problem. The initial solution generation module is used to solve the multi-objective gate allocation model using an elite genetic algorithm to obtain an initial feasible solution, and store the initial feasible solution as the current global optimal solution in the storage unit; The branch search module is used to construct a branch and bound search tree, taking the root node of the multi-target boarding gate allocation model as the starting search node, and solving the linear slack subproblem corresponding to the current search node to obtain a relaxed solution. The pruning decision module is used to make decisions on eliminating or prioritizing the current search node during the branch search iteration process; The iterative control and output module is used to iteratively prune and search the branch-bound search tree according to the decision result of the pruning decision module until the search termination condition is met. The updated current global optimal solution is output as the optimal solution result of the multi-objective boarding gate allocation model to generate an airport boarding gate allocation scheme.

[0010] The beneficial effects of this invention are as follows: The dynamic optimization method for airport gate allocation in this invention comprehensively considers multiple objectives such as walking distance for transit and direct passengers and energy consumption of airport shuttle buses. It improves the prediction accuracy of flight arrival time by introducing a deep learning prediction model, enhances the anti-interference ability against flight time uncertainty by constructing a robust correspondence model, and achieves efficient solution by combining a customized branch pricing algorithm with a parallel elite genetic algorithm. It can improve transit reliability, reduce passenger walking distance and bus energy consumption under limited gate resources, while ensuring the robustness and feasibility of the scheduling scheme under flight delay interference. Attached Figure Description

[0011] Figure 1 This is a flowchart of the present invention.

[0012] Figure 2 This is the layout of the departure level of Chengdu Tianfu International Airport in an embodiment of the present invention.

[0013] Figure 3 This is a satellite image of Chengdu Tianfu International Airport, as shown in an embodiment of the present invention.

[0014] Figure 4 This describes the airport parking space allocation process in an embodiment of the present invention.

[0015] Figure 5 This is the CNN-BiLSTM-Attention model structure used in this embodiment of the invention.

[0016] Figure 6This is a structural diagram of the random forest in an embodiment of the present invention.

[0017] Figure 7 This is a flowchart illustrating the workflow of the genetic algorithm in this embodiment of the invention.

[0018] Figure 8 This is a flowchart illustrating the branch pricing algorithm in an embodiment of the present invention.

[0019] Figure 9 This is a schematic diagram showing the distance between the airport boarding gate and the main entrance of the terminal building in an embodiment of the present invention.

[0020] Figure 10 This is a comparison chart of the convergence trends of the branch pricing algorithm and the genetic + branch pricing hybrid algorithm in the embodiments of the present invention.

[0021] Figure 11 This is a comparison chart of the convergence trends of the simulated annealing + branch pricing hybrid algorithm and the genetic algorithm + branch pricing hybrid algorithm in the embodiments of the present invention.

[0022] Figure 12 This is a sensitivity analysis diagram of the weight coefficient a1 in an embodiment of the present invention.

[0023] Figure 13 This is a comparison chart of the convergence trends of the simulated annealing + branch pricing hybrid algorithm and the branch pricing hybrid algorithm after 2000 optimizations in the embodiments of the present invention. Detailed Implementation

[0024] Reference Figures 1-13 A dynamic optimization method for airport gate allocation to improve transfer reliability. The method includes the following steps: S1: Obtain the multi-objective gate allocation model to be solved, which is used to describe the airport gate allocation problem; S2: The multi-objective gate allocation model is solved using an elite genetic algorithm to obtain an initial feasible solution, which is then used as the current global optimal solution. S3: Construct a branch-and-bound search tree, take the root node of the multi-target boarding gate allocation model as the starting search node, and solve the linear slack subproblem corresponding to the current search node to obtain the relaxed solution; S4: During the branch search iteration, the current search node is eliminated or prioritized based on the pruning rule set. The pruning rule set includes rules for pruning or retaining nodes based on the result of re-estimating the partial solution space of the node by calling the elite genetic algorithm, rules for pruning nodes based on the satisfaction of mandatory constraints by the candidate solutions of the node, and rules for prioritizing nodes and guiding the search order based on the search potential of the node. S5: Iteratively prune and search the branch-bound search tree according to the pruning rule set until the search termination condition is met. Output the updated current global optimal solution as the optimal solution result of the multi-objective boarding gate allocation model to generate an airport boarding gate allocation scheme.

[0025] In step S1, before obtaining the multi-target gate allocation model, a flight arrival time prediction step is also included, comprising: Acquire historical and real-time operational data of the airport. The operational data shall include at least the operational date, flight number, aircraft take-off and landing time, number of passengers, aircraft type, gate type and gate number for each flight. Based on the historical operational data, a time series prediction model is used to predict the actual arrival time of each flight, thereby obtaining the predicted arrival time; the predicted arrival time replaces the planned arrival time as the input parameter of the multi-target gate allocation model.

[0026] Preferredly, in this embodiment, the time series prediction model is a deep learning-based CNN-BiLSTM-Attention model, which predicts flight data based on historical data and actual operation conditions. In one feasible embodiment, all computations are performed on a Windows 11 operating system, using Python 3.9 as the programming language, and the computer configuration is: an AMD Ryzen 55600 6-core processor (3.50 GHz) and an NVIDIA GeForce RTX 4070 GPU. In the following text, "+" indicates a combination or integration of two algorithms. The model includes an input layer, convolutional layers, pooling layers, a bidirectional long short-term memory network layer, an attention mechanism layer, a fully connected layer, and an output layer. The convolutional and pooling layers are used to extract local features of flight operation data, the bidirectional long short-term memory network layer is used to capture bidirectional temporal dependencies, and the attention mechanism layer is used to assign weights to hidden states at different time steps. The specific implementation process of the model is as follows: The CNN-BiLSTM-Attention model consists of an input layer, a CNN layer, a BiLSTM layer, an attention mechanism layer, a fully connected layer, and an output layer. The input layer takes into account features including the flight date, flight number, aircraft arrival time, aircraft departure time, number of passengers, aircraft type, gate type, and gate number. The CNN layer extracts local features from the original input features, captures the changing patterns of flight operation data within a local time window through convolutional operations, and applies a non-linear activation function to obtain the output features of the convolutional layer to enhance feature representation. Pooling operations are then used to reduce the feature dimensionality while retaining local feature information crucial for aircraft arrival time prediction. Finally, a flattening layer transforms the two-dimensional feature mapping into a single layer. A 3D vector is input to a BiLSTM layer. The BiLSTM layer processes the input sequence simultaneously through forward and backward LSTM layers. At time step t, it captures the temporal dependencies in the flight operation data by connecting the forward and backward hidden states, making full use of contextual information from past and future time steps. The attention mechanism layer assigns different weights to the hidden states at different time steps, further enhancing the model's ability to capture key information and outputting a weighted feature vector. The fully connected layer integrates the weighted features output by the attention mechanism layer, mapping the features extracted by the previous layers to the output space of the prediction task through linear transformation and nonlinear activation functions. The output layer outputs the predicted flight arrival time, which serves as the input to the subsequent gate allocation optimization model. Secondly, in the model prediction process, the relevant feature data of the flight to be predicted is first input into the input layer. After forward propagation calculations through the aforementioned layers, the predicted flight arrival time is obtained. During model training, mean squared error is used as the loss function, and the backpropagation algorithm and Adam optimizer are used to update the network parameters to minimize the error between the predicted arrival time and the actual arrival time. Finally, the trained model is used to predict flight arrival times in real time, providing a basis for decision-making in airport gate allocation.

[0027] This embodiment collects historical flight data from Chengdu Tianfu International Airport. This airport is one of China's busiest airports, serving 54.91 million passengers and handling 378,798 aircraft takeoffs and landings in 2024. The historical data is used to predict future flight allocations. Figure 2 A schematic diagram of the departure level of Chengdu Tianfu International Airport (based on...) Figure 3 (Satellite imagery). In the image, red-numbered gates are for flights to Hong Kong, Macau, Taiwan, and international flights, while black-numbered gates are for domestic flights. The dataset used in the actual case study includes: aircraft landing and departure times, the number of passengers distinguishing between transit and non-transit destinations, aircraft types, and transit connections between flights, as detailed in Table 1. The model output is a gate and apron allocation scheme for multiple aircraft types. Figure 5A diagram illustrating the airport parking stand allocation process is provided to help understand the allocation logic between boarding gates and remote parking stands. For prediction, 87.5% of the data was used as the training set, and 12.5% ​​as the validation set. Table 2 presents the prediction results for the eighth day based on seven days of flight data (number of flights, total number of passengers, number of transit passengers). Figure 4 The diagram shows the architecture of the CNN-BiLSTM-Attention model. This model combines convolutional layers, a bidirectional long short-term memory network, and an attention mechanism to effectively improve the prediction accuracy of flight arrival times. Furthermore, Table 3 compares the prediction accuracy of the random forest and CNN-BiLSTM-Attention models, showing that the proposed model outperforms the random forest in terms of MAE, MAPE, MSE, RMSE, and ACC. (Multi-objective weight coefficients are also shown.) The initial values ​​were set to 0.5, 0.25, and 0.25 respectively.

[0028] Table 1:

[0029] Table 2:

[0030] Table 3:

[0031] Furthermore, the decision variables of the multi-objective gate allocation model include at least: allocation variables that characterize the relationship between flights and gate allocation, transfer indicator variables that characterize the connection relationship between transit passengers between flights, and jet bridge type variables that characterize whether a gate is equipped with a jet bridge. The objective function of the multi-objective gate allocation model includes at least: the cost of transfer walking distance for transit passengers within the terminal, the cost of boarding and disembarking walking distance for direct passengers, and the energy consumption cost of airport shuttle buses. This can be achieved in the following ways: Through formula This refers to the cost item representing the walking distance for transit passengers within the terminal building.

[0032] in, It refers to the collection of aircraft owned by the airport. This indicates the assembly point for arriving at the airport. Indicates the assembly of aircraft taking off. This represents the set of all boarding gates. Indicates boarding gate and The distance between them This indicates the distance from the airport's main entrance to the boarding gate. The distance quantifies the allocation of remote parking positions and contact parking aprons. Indicates the distance from the remote parking stand to the boarding gate. distance, Indicates from airplane arrive Number of connecting passengers It's a binary variable, if the airplane There is a connecting flight If the number of passengers is 1, then the value is 1; otherwise, it is 0. It is a binary variable, if the airplane If assigned to a gate without a jet bridge, the value is 1; otherwise, it is 0.

[0033] Through formula This indicates the cost item for walking distances between boarding and disembarking for direct passengers.

[0034] Time-related costs are represented by equivalent travel distance. Indicates airplane The number of passengers who do not need to transfer. It is a binary variable, such as a gate. If the flight is occupied, the value is 1; otherwise, it is 0.

[0035] Through formula This indicates the energy consumption cost of airport shuttle buses.

[0036] in, This indicates the average energy efficiency of airport shuttle buses for each flight passenger transported.

[0037] Furthermore, by transforming multiple objectives into a single-objective function, different weighting coefficients are assigned to each objective from the perspectives of different decision-makers, using the formula... To determine the gate assigned to each flight, the corresponding passenger walking distance, and the energy consumption of the airport shuttle bus, among which, , .

[0038] Preferably, involving each aircraft Assigned to parking position Assignment variables Transit passenger indicator variables between aircraft Flight arrival time With departure time Number of passengers on airplanes In addition to variables related to airport shuttle bus energy consumption, the following constraints are set: Each aircraft is assigned exactly one parking space, that is:

[0039] Each parking space can be occupied by a maximum of one aircraft during the same operating period. ; Large aircraft can only be assigned to large parking stands (including stands with jet bridges and remote stands without jet bridges), that is:

[0040] in, It is a binary variable; if it refers to a large aircraft, the value is 1; otherwise, it is 0. This represents a small set of parking spaces. This represents a large group of aircraft; the occupancy times of any two flights assigned to the same parking position do not overlap, that is:

[0041] If the plane With airplane If there are transit passengers, the number of transit passengers shall not exceed the number of passengers on the aircraft. The total number of passengers and not exceeding the number of passengers on the aircraft The passenger capacity, i.e.:

[0042] in, Indicates from airplane Transfer to airplane The number of transit passengers; Indicates airplane The total number of passengers.

[0043] The arrival time of the aircraft must be earlier than its departure time, that is... ; The number of passengers that each gate can serve per day is limited to a maximum, namely:

[0044] in, It is a binary variable; if the boarding gate... Assigned to aircraft If the result is positive, then it equals 1; otherwise, it equals 0. This indicates the maximum number of passengers the gate can serve; the number of transit passengers that each flight can accommodate is limited to this maximum value, i.e.:

[0045] in, Indicates the maximum passenger capacity; Airport shuttle bus energy consumption is capped to increase the use of aircraft parking spaces with jet bridges, namely:

[0046] in, This indicates the maximum permissible energy consumption for airport shuttle buses; For aircraft operating continuously at the airport, the departure time intervals remain within a predetermined range, i.e.:

[0047] in, and These represent the minimum and maximum allowed time intervals, respectively. The minimum time interval between consecutive aircraft at the same parking position satisfies:

[0048] when and ,in, This indicates the minimum allowed time interval; the parking time for each aircraft shall not exceed the maximum value, i.e. ,in, Indicates the maximum permitted parking time; if the aircraft With airplane If there are transit passengers, then the plane Arrival time earlier than flight The departure time, i.e. ; To meet airport operational requirements, a certain number of aircraft must be allocated to parking positions without jet bridges, that is:

[0049] in, It is a binary variable, if the airplane If the aircraft is assigned a parking position without a jet bridge, the value is 0; otherwise, it is 1. The minimum number of jet bridge-less parking spaces required by the airport; small aircraft can be assigned to any type of parking space, i.e., if the aircraft If it is small, then for all allow .

[0050] Furthermore, the above constraints transform the multi-objective gate allocation model into a mixed-integer linear model (MILP). Based on this, the predicted arrival and departure times of flights are further treated as deterministic parameters to establish a prior deterministic MILP model. By introducing boundary parameters for arrival and departure time deviations and robustness constraints, a robust correspondence model is constructed to enhance the model's resistance to unpredictable disturbances and optimize the schedulability of the timetable under uncertain conditions. By introducing the deviation variable of flight arrival and departure times, a robust correspondence model for airport gate allocation considering timetable uncertainty is constructed. Maximum delay time is defined based on historical data. The actual arrival time Compared with the actual departure time Defined as:

[0051] in, and Representing deviation variables; defining the budget uncertainty set based on the Bertsimas–Sim framework. ,Right now:

[0052] ,in, Indicates the maximum delay time. This indicates the maximum number of flights that can experience severe delays simultaneously. , For binary variables (0 indicates on-time flight, 1 indicates delay); budget parameters Controlling the degree of conservatism of the solution: when The model degenerates into a deterministic case. The larger the value, the more flights can experience the worst-case deviation simultaneously, resulting in a more conservative solution. To enhance robustness to timetable deviations, a min-max formula is used to modify the original objective function in S2. Rewritten to minimize the worst-case operating cost, i.e.:

[0053] in,

[0054] This indicates the penalty for time deviation; The model is configured with the following robust correspondence constraints to ensure that all operational constraints are still satisfied under worst-case bias: consecutive flights and The takeoff intervals satisfy the given upper and lower limits, that is:

[0055] The time interval between consecutive flights at the same parking position shall not be less than the minimum safe separation, that is:

[0056] The time each flight spends at its designated parking space shall not exceed the maximum allowable value, i.e.:

[0057] The number of passengers served at each gate is limited by its maximum capacity, namely:

[0058] The number of transit passengers that each flight can accommodate is limited to a maximum value, namely:

[0059] The energy consumption of airport shuttle buses shall not exceed the permitted upper limit, that is:

[0060] The model is configured with robust budget parameters. Deviation variables , and binary variables , The corresponding constraints.

[0061] The initial solution can be obtained by using the elite genetic algorithm PGA based on parallel computing to solve the above MILP model, specifically including the following steps: Define the maximum number of generations of the population during population initialization. The system randomly initializes individuals to form an initial population and randomly selects a flight-gate allocation scheme; individuals are represented using integer encoding and binary variables. , and Each individual is divided into three parts: the first part indicates the number of passengers boarding, disembarking, and transferring for each aircraft; the second part indicates the assigned boarding gate and whether it is equipped with a jet bridge; and the third part indicates the size category of the assigned boarding gate. Perform fitness calculations based on Calculate the fitness value of each individual in the population to evaluate and update the flight gate allocation scheme; Using the roulette wheel method, individuals with high fitness values ​​are selected as parents for crossover and mutation operations; at the same time, the individual with the highest fitness value in each generation is identified as an elite individual and ensured that it is directly inherited by the next generation. New individuals are generated from selected elite parent individuals by exchanging and recombining some genes from two parent individuals, so that the offspring inherit the characteristics of both parents. New gate allocation schemes are generated through cross-pollination, forming new populations; In the mutation operation, the genes of new individuals are changed with a certain probability to maintain population diversity, that is, some flights are reassigned to other gates; in the evaluation step, each individual represents a complete gate allocation scheme, and the objective function value of each individual is calculated accordingly. If the maximum number of iterations is reached, the parallel elite genetic algorithm terminates; otherwise, it returns to the fitness calculation step for a new round of iterations; the individual with the highest fitness value is selected as the final boarding gate allocation scheme, and the result is exported to a CSV file.

[0062] First, after obtaining the initial feasible solution, a branch-and-bound search tree is constructed, using the root node of the mixed-integer linear programming model as the starting search node. The linear relaxation subproblem corresponding to the current search node is solved, and after relaxing the integer constraints, the corresponding linear programming problem is solved to obtain the relaxed solution and its corresponding objective function value. A branching strategy is used to accelerate the search for integer feasible solutions in the MILP, including: during the branch search iteration process, decisions are made to eliminate or prioritize the current search node based on a pruning rule set, which contains three rules: First pruning rule: Obtain the objective function value corresponding to the relaxed solution of the current search node. If the objective function value is worse than the objective function value of the initial feasible solution, then call the elite genetic algorithm to re-evaluate the partial solution space represented by the current search node. If the re-evaluation result is worse than the current global optimal solution, then determine that the current search node and all its child nodes do not contain better feasible solutions and perform pruning and removal. If the re-evaluation result is equal to the current global optimal solution, then retain the current search node and allow continued branching to avoid missing feasible solutions that are as good as the global optimal solution. This is because the re-evaluation result being equal to the current optimal solution means that there may be other feasible solutions with the same quality as the known optimal solution in the solution space of this node. These equally good solutions also have application value in the actual airport boarding gate allocation scenario. Second pruning rule: Extract candidate solutions corresponding to the current search node, and check whether the candidate solutions violate the preset mandatory constraints in the multi-objective boarding gate allocation model; if any of the mandatory constraints are violated, the current search node and all its child nodes are determined to be infeasible regions, and pruning is performed. The preset mandatory constraints include at least the following: Parking time constraints:

[0063] in That is the departure time of plane J. It is the arrival time of plane A. If the plane With airplane If there are transit passengers, then the plane Arrival time earlier than flight Departure time constraints:

[0064] To meet airport operational requirements, a certain number of aircraft must be allocated to parking positions without jet bridges:

[0065] in It is every airplane Assigned to parking position Assignment variables, It is an indicator variable for transit passengers between aircraft. It is a binary variable, if the airplane If the machine is assigned a parking space without a jet bridge, the value is 0; otherwise, it is 1. This refers to the minimum number of jet bridge-less parking spaces required by the airport.

[0066] The third pruning rule: For search nodes not eliminated by the first or second pruning rule, calculate the priority coefficient of the node according to the priority coefficient calculation model; in the branch-bound search queue, sort the search nodes according to the value of the priority coefficient, and prioritize branch exploration for nodes with high priority coefficients. Specifically, the priority coefficient calculation model involves dividing the partial solution space S represented by the current search node into a non-optimal solution subspace. Subspace of suboptimal solutions and optimal solution subspace ; Define binary variables Used to label candidate solutions Whether it is a non-optimal solution; if the solution is not optimal, the value is 0, otherwise it is 1. Define binary variables Used to label candidate solutions Whether it is a suboptimal or optimal solution; if the solution is suboptimal, the value is 0, otherwise it is 1. Calculated using the following mathematical model:

[0067] in is the branch priority coefficient, and its value is positively correlated with the probability that the partial solution space represented by the current search node contains a high-quality feasible solution.

[0068] In the process of constructing the branch-bound search tree, the root node of the multi-target boarding gate allocation model is used as the starting search node, and the linear relaxation subproblem corresponding to the current search node is solved to obtain the relaxation solution. At the same time, during the branch search iteration process, the current search node is eliminated or prioritized based on the pruning rule set. The decision is to iteratively prune and search the branch-bound search tree according to the pruning rule set until the search termination condition is met. The above solution method is named the branch-and-price algorithm (B&P). Its core idea is to decompose the original main problem into smaller, restricted main problems to improve iteration efficiency. The method includes the main problem and the pricing subproblem, and specifically includes the following steps: First, define a “column” as a feasible flight-gate assignment sequence; The high-quality upper bound of the original problem is obtained by using the elite genetic algorithm PGA combined with parallel computing. Based on this, the initial column of the restricted master problem is generated, and the restricted master problem is used as the root node of the branch and bound tree. Secondly, the pricing subproblem is solved based on the column generation algorithm. New columns are continuously generated from the restricted subproblem and added to the main problem, and this iterative process is repeated. If the optimal solution of the linear relaxation problem is an integer solution, the solution is saved and an attempt is made to update the global upper bound. Otherwise, the pruning condition is checked to remove fractional solutions. If the pruning condition is not met, a branching operation is performed to generate a new search node and add it to the branch and bound tree for subsequent iterations. Finally, for each search node in the branch and bound tree, column generation and branch and bound operations are continuously performed until all nodes have been visited; the algorithm is then terminated according to the pruning condition and converges to the optimal solution. The solution method for the pricing subproblem is as follows: The goal of the pricing subproblem is to generate candidate columns with negative test numbers (i.e., flight-gate allocation schemes) and replace them in the constrained main problem, thereby identifying potential gate allocation schemes and expanding the search space; enumerate the test numbers of all feasible columns until they are all strictly positive, at which point it indicates that there are no more columns that can improve the objective value, and the main problem has reached its optimum. Each newly generated allocation scheme from the pricing subproblem is used for objective function evaluation and branch decision, and these newly generated potential allocation schemes constitute new columns in the column generation process; To explore the solution space and efficiently solve the pricing subproblem, the following constraints, tailored for the flight gate exchange process, are introduced into the serial subproblem: Ensure that any allocation exceeding the allowed distance is considered infeasible:

[0069] in, This indicates the maximum permissible distance between the gates assigned to connecting flights; Ensure that it is assigned to any gate The workload does not exceed its capacity limit:

[0070] in, This indicates the maximum capacity, defined based on the maximum permissible workload for each gate. The above two constraints ensure that after the boarding gate is adjusted, the newly assigned boarding gate for the flight still meets operational requirements and compatibility constraints: ,

[0071] The following constraints are imposed to allow exchanges only between flights that are sufficiently close in time, in order to ensure the practical feasibility of gate-to-gate exchanges:

[0072] in, This indicates the maximum permissible time interval between the departure or arrival of two flights that can share the same gate; To facilitate the allocation of adjacent gates to consecutive flights, especially those involving transit passengers, thereby reducing long-distance transfers within the terminal and improving overall transfer reliability, the following constraints are given:

[0073]

[0074] The following constraints represent the minimum value that limits the main problem:

[0075] Among them, flights Assigned to boarding gate The cost is denoted as The corresponding dual variable is denoted as The pricing problem is solved by explicitly enumerating pairs of flights and gates to calculate the test number, rather than solving structured subproblems such as shortest paths with resource constraints, in order to simplify implementation and improve feasibility.

[0076] To accelerate the above algorithm, the following two formulas in the original model are restated:

[0077]

[0078] The minimum connection time for transit passengers is reformulated, and auxiliary variables are introduced. Replace the original variable , and parameters The goal of minimizing the distance for direct passengers is rephrased as:

[0079]

[0080] in, Total number of flights; only The decision variables are set as follows, which reduces the solution dimension of the branch-price algorithm compared to the original model; the other constraints remain unchanged.

[0081] This invention conducts experiments with a fixed number of iterations (200 times) on data of different scales to systematically evaluate the algorithm performance. Specific rules are as follows: the capabilities of the elite genetic algorithm PGA and the exact algorithm B&P are evaluated on small, medium, and large-scale flight data, respectively; both PGA and B&P terminate after 200 iterations. The results of performing an additional 2000 iterations are shown below. Figure 10The commercial solver Gurobi was used as a benchmark. However, Gurobi failed to solve cases with insufficient memory when the number of flights exceeded 50. Except for four small-scale instances (F30g8, F35g9, F40g12, and F45g13), all others exceeded this limit. Medium-scale instances had 120-175 flights, and large-scale instances had 200-490 flights, far exceeding Gurobi's solving capacity. Therefore, Gurobi was not used in subsequent examples. This invention compares the solution quality (optimization rate) and computational efficiency (CPU time) of PGA and B&P at small, medium, and large scales. PGA generates 100 individuals per generation, for a total of two generations. Its workflow is as follows... Figure 7 As shown; B&P performs 200 iterations, and the workflow of its branch pricing algorithm is as follows. Figure 8 As shown, both algorithms can solve cases at various scales, but their computational performance differs significantly. The optimization rate is calculated using the following formula:

[0082] in The target value for the initial scheme is given. If the actual timetable is unreliable, a random allocation scheme will be used. This is the optimized target value.

[0083] Comparing PGA and B&P on small-scale instances. Although the expected performance is generally average, both algorithms obtain efficient solutions in a relatively short time. Table 4 shows the input data for small-scale instances (number of flights, number of passengers, number of gates). Table 5 shows the optimization results of PGA and B&P, including optimization rate and computation time. Under the 200-iteration limit, B&P struggles to converge. Only in instances F30g8, F35g9, F40g12, F45g13, F55g15, and F70g18 does B&P achieve a higher optimization rate than PGA. In terms of computation time, PGA is consistently shorter than B&P. For example, in instance F75g19, PGA takes 50.49 seconds, while B&P takes 110.42 seconds. Figure 9 (a) is the runtime schedule for the small-scale instance “F30g9”.

[0084] Table 4:

[0085] Table 5:

[0086] As the number of flights, gates, and passengers increases, the computation time for both algorithms after 200 iterations inevitably increases. However, the optimization rate of PGA remains stable even with larger datasets. Table 6 shows the input data for medium-sized datasets, and Table 7 shows the corresponding optimization results. Notably, in instance F130g33, PGA's optimization rate reaches 36.02%, exceeding all small-scale instances. This indicates that PGA has good scalability, and the solution quality is almost unaffected by the increase in problem size. Conversely, B&P's performance declines with increasing scale: the optimization rate at 200 iterations decreases. For example, in F125g33, B&P's optimization rate is 13.82%, which is the best value for medium-sized datasets, but still lower than all small-scale cases. Moreover, in all medium-sized instances, B&P's optimization performance is inferior to PGA, and its convergence time is longer. Figure 9 (b) Flight configuration diagram for the medium-sized instance “F175g37”.

[0087] Table 6:

[0088] Table 7:

[0089] As shown in Table 8, with the further increase in the number of flights, B&P's optimization performance is significantly worse than PGA's at the same number of iterations, while its computation time is much longer (see Table 9 for details). This indicates that as the number of flights and gates increases, the number of transit passengers also increases. This is because when the number of flights reaches a certain threshold, airports tend to operate as hubs, and hub airports naturally have a higher proportion of transit passengers than non-hub airports. In example F200g70, the optimization times for PGA and B&P are 161.47 seconds and 322.42 seconds, respectively, a difference of 160.95 seconds. In example F490g77, PGA takes 452.27 seconds, while B&P takes 1146.51 seconds, a difference of 694.24 seconds. It is evident that the more flights there are, the longer each iteration of B&P requires. Simultaneously, the optimization rate of B&P decreases from 9.62% in F200g70 to 3.69% in F480g77. This indicates that as the problem size increases, the performance of B&P continuously declines, failing to converge effectively within a fixed 200 iterations. This is because as the number of flights increases, the airport may upgrade from a regional airport to a hub, leading to higher transfer rates and increased problem complexity. The increase in transfer passengers also dramatically increases the number of variables and constraints in the network, expanding the solution space and making algorithm optimization more difficult. In the AGAP problem, while PGA cannot guarantee global optimum, it is insensitive to the number of flights. Therefore, this invention proposes a hybrid strategy: first, PGA performs an efficient local search to quickly obtain a high-quality initial solution; then, B&P performs global optimization. This approach ensures both efficiency and quality.

[0090] Table 8:

[0091] Table 9:

[0092] Furthermore, Figure 10 The performance of the standalone B&P algorithm and the PGA+B&P hybrid algorithm was compared, and the results were demonstrated from four aspects: target convergence trend, shuttle bus travel distance, walk distance of the boardwalk, and shuttle bus energy consumption. Figure 10 (a) shows that the objective values ​​of both methods decrease with increasing iterations, but PGA+B&P converges faster and exhibits a more pronounced optimization trajectory. B&P alone remains unstable after 200 iterations, ultimately performing significantly worse than the hybrid method. The lower final objective value of PGA+B&P demonstrates the effectiveness of PGA as an initial strategy. The hybrid method provides both a high-quality initial solution and guides B&P towards a better solution space, accelerating convergence and improving the quality of the final solution. Figure 10 Figures (b), 10(c), and 10(d) show the changes in walking distance for direct passengers, transfer time for transit passengers, and shuttle bus energy consumption over 200 iterations. The overall trend is improving, but not a monotonous decline. Specifically, Figure 10 (d) The shuttle bus energy consumption of PGA+B&P shows an increasing trend, indicating a trade-off or constraint conflict in the model. Table 10 shows the optimization rates of B&P and PGA+B&P after 200 iterations. The main objective function value of PGA+B&P is 16.54% higher than that of B&P alone, further verifying the advantages of the hybrid method in optimization quality and convergence efficiency. Therefore, when PGA provides the initial solution for B&P, the convergence speed of B&P is faster than that of B&P alone.

[0093] Table 10:

[0094] To explore the potential advantages of different algorithm combinations, this invention designs two hybrid strategies: SA+B&P and PGA+B&P. Figure 11 The comparison results are presented. Figure 11 (a) shows that SA+B&P has strong optimization capabilities in the early iterations, but the improvement speed slows down significantly in the later stages and eventually stagnates. PGA+B&P, although its early improvement is slightly slower, maintains stability and continuous optimization throughout the process, ultimately achieving better results. Figure 11Tables (b), (c), and (d) show the changes in direct passenger distance, transfer passenger time, and shuttle bus energy consumption under the two schemes during 200 iterations. PGA+B&P outperforms SA+B&P in both transfer passenger walking distance and shuttle bus energy consumption. SA+B&P performs better in terms of direct passenger walking time. Table 11 shows that the optimization efficiency of the main objective function of PGA+B&P is 1.49% higher than that of SA+B&P, and it converges faster. Therefore, in this AGAP model, PGA+B&P outperforms SA+B&P in both convergence speed and optimization efficiency. The extended experiment increased the number of iterations to 2000, with a maximum running time of 10 hours. The results are shown in Table 11. Figure 13 .

[0095] Table 11:

[0096] To examine the impact of sub-objective weights on gate allocation results, this invention adjusts the weight coefficient for transit passengers. . Figure 12 (a) Shows that the objective function is... The sensitivity is nonlinear: As the value increased from 0.1 to 0.3, the target value continued to decrease. When the value increases from 0.3 to 0.8, the target value rises. Overall, the target value is... At the largest, in It is the smallest. Figure 12 (b), (c), and (d) respectively demonstrate the three sub-targets following Trends in transit passenger sub-destinations Maximum time, Minimum time; direct passenger sub-targets at Maximum time, Minimum time; shuttle bus energy consumption target is Maximum time, It is at its minimum. It is worth noting that when... At that time, the optimization results for both transit and direct passengers were close to their respective minimum values, indicating that the weight could effectively balance the objectives of the two types of passengers. Therefore, the objective function in It reaches its optimal state at that time.

[0097] This embodiment further evaluates the constructed robust model by introducing timetable perturbations at different levels. Based on This study examines the performance of the robust corresponding model under disturbances and the optimization capability of the algorithm under uncertainty. It assumes that flight schedule disturbances follow a normal distribution, adjusting the mean and standard deviation to simulate the magnitude and range of delays. The disturbance level ranges from an average delay of 10 minutes per flight to an average delay of 20 minutes. Table 12 summarizes the robust optimization results. From F10g5 to F20g20, the objective value shows an upward trend due to the penalty term. The optimization rate increases with increasing delay. Table 12 shows the optimization rates of PGA+B&P on instances F10g5 to F20g20. The greatest improvement is reflected in the penalty term: the optimization rate of the penalty value in F10g10 is as high as 91.01%. When the average delay is less than 20 minutes, delay uncertainty has the greatest impact on optimization performance. F10g5 and F10g10 have the same average delay (10 minutes), but the latter has greater delay variability, and the optimization effect is significantly reduced. When the average delay reaches 20 minutes, the impact of uncertainty on optimization performance weakens, and the optimization results tend to stabilize. The optimization rates of instances F20g5, F20g10, F20g15, and F20g20 are 18.71%, 22.65%, 18.19%, and 21.60%, respectively, all stabilizing at around 20%. This indicates that at higher delay levels, the optimization gain is no longer sensitive to changes in disturbance intensity.

[0098] Table 12:

[0099] Table 13:

[0100] In summary, this invention addresses the dynamic optimization problem of airport gate allocation, which requires the rational allocation of each gate, maximizing the utilization of jet bridges and remote gates, and ensuring efficient operation and passenger satisfaction. First, it collects flight operation dates, flight numbers, departure and arrival times, passenger numbers, aircraft types, and gate types and numbers. Then, it constructs a multi-objective allocation model, uses a CNN-BiLSTM-Attention model to predict flight arrival times, establishes a robust correspondence model to handle timetable uncertainty, and employs a customized branch-price algorithm combined with a parallel elite genetic algorithm to solve the problem, thereby obtaining the optimal gate allocation scheme for each flight, minimizing passenger walking distance and shuttle bus energy consumption. Compared with existing technologies, this invention comprehensively considers transfer reliability, timetable uncertainty, and multi-objective trade-offs, enabling more accurate and robust control of gate allocation, improving airport operational efficiency, and reducing shuttle bus energy consumption.

[0101] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative and not exhaustive. All modifications within the scope of this invention or its equivalents are included in this invention.

Claims

1. A dynamic optimization method for airport gate allocation to improve transfer reliability, characterized in that, Includes the following steps: Obtain the multi-objective gate allocation model to be solved. The multi-objective gate allocation model is used to describe the airport gate allocation problem. The multi-objective gate allocation model adopts the mixed integer linear model with multiple constraints (MILP). An elite genetic algorithm is used to solve the multi-objective gate allocation model to obtain an initial feasible solution, which is then used as the current global optimal solution. Construct a branch-bound search tree, take the root node of the multi-target boarding gate allocation model as the starting search node, and solve the linear slack subproblem corresponding to the current search node to obtain the relaxed solution; During the branch search iteration, the current search node is eliminated or prioritized based on the pruning rule set. The pruning rule set includes rules for pruning or retaining nodes based on the result of re-estimating the partial solution space of the node by calling the elite genetic algorithm, rules for pruning nodes based on the satisfaction of mandatory constraints by the candidate solutions of the node, and rules for prioritizing nodes and guiding the search order based on the search potential of the node. The branch-bound search tree is iteratively pruned and searched according to the pruning rule set until the search termination condition is met. The updated current global optimal solution is output as the optimal solution result of the multi-objective boarding gate allocation model to generate an airport boarding gate allocation scheme.

2. The method according to claim 1, characterized in that, The pruning rule set specifically includes: First pruning rule: Obtain the objective function value corresponding to the relaxed solution of the current search node. If the objective function value is worse than the objective function value of the initial feasible solution, call the elite genetic algorithm to re-evaluate the partial solution space represented by the current search node. If the re-evaluation result is worse than the current global optimal solution, determine that the current search node and all its child nodes do not contain a better feasible solution and perform pruning and removal. Second pruning rule: Extract candidate solutions corresponding to the current search node, and check whether the candidate solutions violate the preset mandatory constraints in the multi-objective boarding gate allocation model; if any of the mandatory constraints are violated, the current search node and all its child nodes are determined to be infeasible regions and are pruned and removed. The third pruning rule: For search nodes that have not been removed by the first or second pruning rule, calculate the priority coefficient of the node according to the priority coefficient calculation model; in the branch and bound search queue, sort the search nodes according to the value of the priority coefficient, and prioritize branch exploration for nodes with high priority coefficients.

3. The method according to claim 2, characterized in that, In the first pruning rule, when the elite genetic algorithm is invoked to re-evaluate the partial solution space represented by the current search node, if the re-evaluation result is equal to the current global optimal solution, the current search node is retained and further branching is allowed. The search termination condition is that all search nodes have been visited or pruned. The elite genetic algorithm is a genetic algorithm or a simulated annealing algorithm. The objective function of the multi-objective gate allocation model includes at least the passenger walking distance cost and the shuttle bus energy consumption cost. The re-evaluation result and the global optimal solution in the first pruning rule are compared based on the comprehensive cost value of the objective function.

4. The method according to claim 2, characterized in that, The priority coefficient calculation model specifically involves dividing the partial solution space S represented by the current search node into a non-optimal solution subspace. Subspace of suboptimal solutions and optimal solution subspace ; Define binary variables Used to label candidate solutions Whether it is a non-optimal solution; if the solution is not optimal, the value is 0, otherwise it is 1. Define binary variables Used to label candidate solutions Whether it is a suboptimal or optimal solution; if the solution is suboptimal, the value is 0, otherwise it is 1. Calculated using the following mathematical model: in is the branch priority coefficient, and its value is positively correlated with the probability that the partial solution space represented by the current search node contains a high-quality feasible solution.

5. The method according to claim 1, characterized in that, The search strategy for the branch-bound search tree also includes: At the root node of the branch-bound search tree, the initial feasible solution obtained by the elite genetic algorithm is directly bound to the current global optimal solution; In subsequent iterations, when the objective function value of the linear relaxation solution of any search node is better than the current global optimum and satisfies the integer condition, the current global optimum is updated with the complete solution of that search node.

6. The method according to claim 1, characterized in that, Before obtaining the multi-target gate allocation model, a flight arrival time prediction step is also included: Acquire historical and real-time operational data of the airport. The operational data shall include at least the operational date, flight number, aircraft take-off and landing time, number of passengers, aircraft type, gate type and gate number for each flight. Based on the historical operational data, a time series prediction model is used to predict the actual arrival time of each flight, obtaining the predicted arrival time. The predicted arrival time replaces the planned arrival time as the input parameter of the multi-target gate allocation model. The time series prediction model is a deep learning-based CNN-BiLSTM-Attention model, which includes an input layer, convolutional layers, pooling layers, a bidirectional long short-term memory network layer, an attention mechanism layer, a fully connected layer, and an output layer. The convolutional and pooling layers are used to extract local features of the flight operation data, the bidirectional long short-term memory network layer is used to capture bidirectional temporal dependencies, and the attention mechanism layer is used to assign weights to hidden states at different time steps.

7. The method according to claim 1, characterized in that, The decision variables of the multi-objective gate allocation model include at least: allocation variables that characterize the relationship between flights and gate allocation, transfer indicator variables that characterize the connection relationship between transit passengers between flights, and jet bridge type variables that characterize whether a gate is equipped with a jet bridge. The objective function of the multi-objective gate allocation model includes at least: the cost of transit passengers' walking distance within the terminal, the cost of boarding and disembarking passengers' walking distance, and the energy consumption cost of airport shuttle buses, wherein: Through formula This refers to the cost item representing the walking distance for transit passengers within the terminal building. in, It refers to the collection of aircraft owned by the airport. This indicates the assembly point for arriving at the airport. Indicates the assembly of aircraft taking off. This represents the set of all boarding gates. Indicates boarding gate and The distance between them This indicates the distance from the airport's main entrance to the boarding gate. The distance quantifies the allocation of remote parking positions and contact parking aprons. Indicates the distance from the remote parking stand to the boarding gate. distance, Indicates from airplane arrive Number of connecting passengers It is a binary variable. It is a binary variable. Through formula This indicates the cost item for walking distances between boarding and disembarking for direct passengers. Time-related costs are represented by equivalent travel distance. Indicates airplane The number of passengers who do not need to transfer. It is a binary variable, such as a gate. If the flight is occupied, the value is 1; otherwise, it is 0. Through formula This indicates the energy consumption cost of airport shuttle buses. in, This indicates the average energy efficiency of airport shuttle buses for each flight passenger transported. By assigning different weighting coefficients to each objective, multiple objectives are transformed into a single objective function, using the formula... To determine the gate assigned to each flight, the corresponding passenger walking distance, and the energy consumption of the airport shuttle bus, among which, , .

8. The method according to claim 6, characterized in that, The preset mandatory constraints include at least the following: Parking time constraints: in That is the departure time of plane J. It is the arrival time of plane A. If the plane With airplane If there are transit passengers, then the plane Arrival time earlier than flight Departure time constraints: To meet airport operational requirements, a certain number of aircraft must be allocated to parking positions without jet bridges: in It is every airplane Assigned to parking position Assignment variables, It is an indicator variable for transit passengers between aircraft. It is a binary variable, if the airplane If the machine is assigned a parking space without a jet bridge, the value is 0; otherwise, it is 1. This refers to the minimum number of jet bridge-less parking spaces required by the airport.

9. The method according to claim 7, characterized in that, Treating the predicted arrival and departure times as deterministic parameters, a priori deterministic MILP model is established. By introducing boundary parameters for arrival and departure time deviations and robustness constraints, a robust correspondence model is constructed. Under uncertainty, the schedulability of the timetable is optimized. Introducing the flight arrival and departure time deviation variable, a robust correspondence model for airport gate allocation considering timetable uncertainty is constructed, including: Maximum delay time is defined based on historical data. The actual arrival time Compared with the actual departure time Defined as: in, and Representing deviation variables; defining the budget uncertainty set based on the Bertsimas–Sim framework. ,Right now: in, Indicates the maximum delay time. This indicates the maximum number of flights that can experience severe delays simultaneously. , For binary variables; budget parameters Controlling the degree of conservatism of the solution: when When the model degenerates into a deterministic case, the min-max formula is used for the original objective function. Rewritten to minimize the worst-case operating cost, i.e.: in, This indicates the penalty for time deviation; The following robust correspondence constraints are set to ensure that all operational constraints are still satisfied under worst-case deviations: consecutive flights and The takeoff intervals satisfy the given upper and lower limits, that is: The time interval between consecutive flights at the same parking position shall not be less than the minimum safe separation, that is: The time each flight spends at its designated parking space shall not exceed the maximum allowable value, i.e.: The number of passengers served at each gate is limited by its maximum capacity, namely: The number of transit passengers that each flight can accommodate is limited to a maximum value, namely: The energy consumption of airport shuttle buses shall not exceed the permitted upper limit, that is: in, For robust budget parameters, , It is a binary variable.

10. A dynamic optimization method for airport gate allocation to improve transfer reliability, characterized in that, For implementing any one of the methods as claimed in claims 1 to 9, comprising: The model acquisition module is used to acquire the multi-objective gate allocation model to be solved, which describes the airport gate allocation problem. The initial solution generation module is used to solve the multi-objective gate allocation model using an elite genetic algorithm to obtain an initial feasible solution, and store the initial feasible solution as the current global optimal solution in the storage unit; The branch search module is used to construct a branch and bound search tree, taking the root node of the multi-target boarding gate allocation model as the starting search node, and solving the linear slack subproblem corresponding to the current search node to obtain a relaxed solution. The pruning decision module is used to make decisions on eliminating or prioritizing the current search node during the branch search iteration process; The iterative control and output module is used to iteratively prune and search the branch-bound search tree according to the decision result of the pruning decision module until the search termination condition is met. The updated current global optimal solution is output as the optimal solution result of the multi-objective boarding gate allocation model to generate an airport boarding gate allocation scheme.

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