A learning optimization method for large-scale flight recovery

Abstract

The application relates to a learning optimization method for large-scale flight recovery, belongs to the technical field of air operation scheduling optimization under disturbance, and solves the problems of low overall search efficiency and insufficient solution set quality of a multi-population evolution algorithm for flights in the prior art, and comprises the following steps: constructing a multi-objective flight recovery problem model based on a space-time network; reading flight data; initializing a double population; processing individual constraints and quality evaluation in a sub-population; performing crossover in the sub-population; performing mutation in the sub-population; performing cross-population information interaction and generating offspring; updating and evolving the sub-population; updating a global non-dominated solution set; adaptively regulating the size of the double population; performing termination judgment and outputting an optimization result.

Description

Technical Field

[0001] This invention relates to the field of air traffic operation scheduling optimization technology under disturbances, and specifically to a learning optimization method for large-scale flight recovery. Background Technology

[0002] With the continuous growth in demand for civil aviation transportation, airlines, under the constraints of limited fleets and operational resources, generally adopt highly optimized flight schedules to improve operational efficiency and economic benefits. However, in actual operation, such highly coupled operational plans are often affected by factors such as aircraft mechanical failures and severe weather, which can easily lead to widespread flight cancellations and delays, resulting in significant economic losses and management pressure. Airlines need to readjust flight takeoff and landing times, aircraft assignment relationships, and execution sequences within a given recovery time window, and obtain large-scale flight recovery solutions that can meet multiple optimization objectives.

[0003] Flight operations are subject to a variety of complex operational constraints. Among these, aircraft maintenance constraints limit the availability of some aircraft within specific time periods, exacerbating the shortage of transport capacity. Airport capacity constraints limit the number of takeoffs and landings that an airport can operate at different times, which can easily lead to the propagation of flight delays. These constraints overlap, giving the flight recovery problem a high-dimensional, strongly coupled, and strongly constrained combinatorial optimization characteristic, posing significant challenges to practical solutions.

[0004] In large-scale flight recovery problems with strong multi-objective constraints, traditional single-population search often struggles to handle complex constraints while simultaneously considering the trade-offs between different optimization objectives. To alleviate multi-objective conflicts and improve solution set diversity, multi-population co-evolutionary methods have gained increasing attention. These methods perform parallel optimization on multiple subpopulations, with different populations focusing on improving different objectives. Simultaneously, the populations cooperate and share information, thereby improving the solution efficiency of multi-objective, strongly constrained combinatorial optimization problems to a certain extent.

[0005] The key to multi-population evolutionary algorithms lies in the interaction between individuals within the population and the rational allocation of computational resources. In existing multi-population evolutionary methods, information interaction between populations often relies on simple rules for individual exchange, which can easily lead to the propagation of invalid information or search redundancy. At the same time, the use of fixed population size or preset resource allocation ratios can easily result in the waste of computational resources, thereby limiting further improvements in overall search efficiency and solution set quality.

[0006] Therefore, there is a need in the field for improved optimization methods for large-scale flight recovery to achieve highly efficient collaborative optimization. Summary of the Invention

[0007] To address the problems existing in the prior art, the present invention aims to provide a learning optimization method for large-scale flight recovery. This method achieves efficient collaborative optimization of delay and cost objectives by constructing a collaborative search mechanism with different objective orientations; and improves solution efficiency under complex constraints through an adaptive resource regulation mechanism. Specifically, the proposed learning optimization method for large-scale flight recovery first decouples the search directions of multiple objectives by constructing parallel evolutionary populations with different objective orientations; then, it guides the collaborative evolution of different search directions through information interaction and adaptive regulation mechanisms among the populations. Through this optimization strategy, the method can efficiently solve the multi-objective flight recovery problem while satisfying aircraft maintenance and airport capacity constraints.

[0008] The specific technical solution of the present invention is as follows: A learning-based optimization method for large-scale flight recovery includes: S1: Construct the flight operation process as a multi-objective flight recovery problem model based on spatiotemporal networks; S2: Flight data reading, reads flight sets, aircraft sets, aircraft maintenance plans, airport takeoff and landing capacity per unit time, and information on aircraft malfunctions or airport capacity reduction within the recovery time window; S3: Dual-population initialization. Based on the read flight data, dual-population initialization is performed to construct the initial individual sets of the delay-oriented subpopulation and the cost-oriented subpopulation, respectively, providing an initial search starting point for subsequent iterative evolution. S4: Individual constraint processing and quality assessment within subpopulations, respectively constraining and assessing flight plan individuals in delay-oriented and cost-oriented subpopulations; S5: Crossover within subpopulations. Perform crossover operations in both the delay-oriented subpopulation and the cost-oriented subpopulation until a set number of offspring are generated. Then, add the generated offspring individuals to the corresponding subpopulations to obtain the delay-oriented subpopulation and the cost-oriented subpopulation after the crossover operation. S6: Intrapopulation mutation. Perform mutation operations on offspring individuals in the delayed-direction subpopulation and the cost-direction subpopulation after the crossover operation, respectively, to obtain the delayed-direction subpopulation and the cost-direction subpopulation after the mutation operation. S7: Cross-population information exchange and offspring generation. Through the cross-population information exchange mechanism, search information is exchanged between the delayed-direction subpopulation and the cost-oriented subpopulation after the mutation operation to generate a cross-population offspring set, which in turn constitutes the delayed-direction subpopulation and the cost-oriented subpopulation after cross-population interaction. S8: Subpopulation update and evolution. Perform update and evolution operations on the delayed-directed subpopulation and cost-oriented subpopulation after cross-population interaction to form the next generation of delayed-directed subpopulation and cost-oriented subpopulation. S9: Update the global non-dominated solution set to obtain the global non-dominated solution set for the current iteration round; S10: Adaptive regulation of dual population size based on Q-learning; S11: Termination judgment and optimization result output. If the preset termination condition is met, the iteration process ends and the current optimization result is output; otherwise, return to S4 to execute the next iteration.

[0009] Preferably, in S1: The spatiotemporal network consists of a set of airport time nodes and a set of flight arcs. Each node in the set of airport time nodes represents a takeoff or arrival event at a specific time point at a certain airport, and each arc in the set of flight arcs represents a flight or aircraft's transfer connection between flights. The established multi-objective flight recovery problem model based on spatiotemporal networks includes: The optimization objectives include minimizing the airline's overall recovery costs and minimizing overall flight delays; The constraints include flow balance constraints for aircraft at each airport node, ensuring that each flight is assigned to at most one aircraft, guaranteeing that the number of passengers carried by each aircraft in each cabin class does not exceed its corresponding seating capacity limit, constraints on the maximum number of landing and taking off flights allowed at each airport per unit time, and guaranteeing that the cumulative flight time of each aircraft between two planned maintenance sessions does not exceed a safety threshold. Ensure that the flights allocated to each aircraft do not exceed its maximum flight range limit.

[0010] Preferably, S3 includes: S3.1: Generate individuals in the delay-oriented subpopulation and the cost-oriented subpopulation. Individuals in the delay-oriented subpopulation and the cost-oriented subpopulation are flight plan individuals. Set the initial size of the delay-oriented subpopulation and the cost-oriented subpopulation. S3.2: Disturbance information labeling and flight recovery scheme coding, taking each flight plan individual as a flight recovery scheme; establishing a flight set, for each flight plan individual in the delay-oriented sub-population and cost-oriented sub-population, based on information such as aircraft malfunction and airport capacity reduction, labeling the disturbed flights in the flight plan individual to obtain the set of disturbed flights corresponding to the flight plan individual; coding each flight plan individual includes the flight, the aircraft assigned to the flight, and the offset of the adjusted departure time of the flight from the original departure time.

[0011] Preferably, S4 includes: S4.1: Establish constraint types and priority classification, including establishing local constraints and global constraints. Local constraints include flight connection time constraints, flight range constraints, maximum allowable delay constraints, and aircraft capacity constraints. Global constraints include aircraft maintenance constraints and airport capacity constraints. The priority is set to execute local constraints first, and then global constraints. S4.2: Local constraint repair based on aircraft path; All flights are assigned to corresponding aircraft, forming a flight execution sequence for each aircraft; For each sequence, check the flight connection time constraints, flight range constraints, maximum allowable delay constraints, and aircraft capacity constraints in sequence. For flights that violate flight connection time constraints, the flight will be delayed until the earliest time that meets the flight connection time constraints. For flights that violate flight range constraints or maximum allowable delay constraints, the flight will be cancelled directly. For flights that violate aircraft capacity constraints, the cost of refunds will be calculated for passengers exceeding the capacity as a penalty. S4.3: Fixes for aircraft maintenance constraints; S4.4: Fixes for airport capacity constraints; S4.5: Individual assessment, calculate the delay target and cost target values ​​for the individual flight plans obtained after the repair based on the two optimization objectives in the multi-objective flight recovery problem model.

[0012] Preferably, in step S5, crossover operations are performed in the delay-oriented subpopulation and the cost-oriented subpopulation in the current iteration round, respectively, including: Within the delay-oriented or cost-oriented subpopulation in the current iteration round, two parent individuals are selected using the binary tournament selection operator. The PMX crossover operator is executed on the parent generation to obtain offspring, and this process is repeated until a preset number of offspring are generated. The generated offspring individuals are added to the corresponding subpopulations to obtain the delayed-directed subpopulations and cost-directed subpopulations after the crossover operation.

[0013] Preferably, in step S6, the following mutation operations are performed on the offspring individuals in the delayed-direction subpopulation and the cost-direction subpopulation after the crossover operation, respectively: S6.1: Establish a set of delay direction operators and a set of neighborhood operators, including time shift compression operator, delay state rearrangement operator, and high-delay flight cancellation operator; S6.2: Establish a cost-oriented operator set, including a neighborhood operator set such as the insertion cancellation operator, the exchange cancellation operator, and the assignment aircraft rescheduling operator; S6.3: Establish a hill-climbing local search mutation framework and execute a hill-climbing local search process for each offspring individual to be mutated; S6.4: Output the mutation results, obtaining the delayed-directed subpopulation and the cost-directed subpopulation after the mutation operation.

[0014] Preferably, in step S7, the following cross-population information exchange operations are performed on the delayed-direction subpopulation and the cost-direction subpopulation after the mutation operation: S7.1: Parent selection: Select one parent individual from each of the delayed-direction subpopulation and the cost-direction subpopulation using the roulette wheel selection operator to obtain two parent individuals; S7.2: Parent generation comparison and primary / secondary parent generation determination. For the two selected parent generation individuals, calculate their evaluation values ​​under the cost target and the delay target respectively, and compare and determine the cost primary parent generation, cost secondary parent generation, delay primary parent generation, and delay secondary parent generation. S7.3: Cost-oriented crossover stage, with the cost-oriented parent generation as the main force, performs a structure-preserving crossover operation to obtain cost-oriented offspring individuals; S7.4: Delayed-direction crossover stage, with delayed parent generation as the main driver, adopts the same structured crossover mechanism as the cost-oriented stage, and uses the delay index as the retention basis to obtain delayed-direction offspring individuals; S7.5: Generation of offspring set. Repeat steps S7.1–S7.4 until the number of offspring individuals generated reaches the preset scale, forming a cross-population offspring set, which in turn constitutes the delayed-direction subpopulation and cost-direction subpopulation after cross-population interaction.

[0015] Preferably, in step S8, the following update evolution operations are performed on the delayed-direction subpopulation and the cost-direction subpopulation after cross-population interaction, respectively: S8.1: Subpopulation candidate set construction: Based on the current delayed-directed subpopulation, cost-oriented subpopulation, and cross-population offspring set, construct delayed-directed subpopulation update candidate set and cost-oriented subpopulation update candidate set; S8.2: The feasible solution-first non-dominated sorting principle is used to perform fast non-dominated sorting on the obtained delayed-directed subpopulation update candidate set and cost-directed subpopulation update candidate set to obtain a series of non-dominated layers; S8.3: Crowding degree calculation. For individuals with the same priority obtained in S8.2, the crowding degree distance between individuals is further calculated. Individuals with higher crowding degree have higher priority when selected, thus obtaining the updated priority ranking of all individuals in each candidate set. S8.4: Subpopulation update, the reordered individuals are selected in sequence to fill the current delay-oriented subpopulation and cost-oriented subpopulation, to obtain the next generation of delay-oriented subpopulation and cost-oriented subpopulation.

[0016] Preferably, S9 includes: S9.1: Constructing the candidate solution set: Combine the set of offspring within the delayed-directed subpopulation, the set of offspring within the cost-directed subpopulation, and the set of offspring across subpopulations in the current iteration round with the global non-dominated solution set of the previous iteration round to obtain the candidate solution set for the current round. S9.2: Non-dominated solution screening and feasibility priority processing: calculate the dominance relationship for all individuals in the candidate solution set of the current round, and the resulting non-dominated solutions constitute the global non-dominated solution set of the current iteration round; S9.3: Subpopulation search contribution statistics, obtaining the improvement of the global hypervolume by the current delay-oriented subpopulation and cost-oriented subpopulation.

[0017] Preferably, S10 includes: S10.1: Establish basic size constraints; S10.2: Determine the direction of scale control; S10.3: Determine the scale control step size and control strategy; S10.4: Optimize state definition and Q table settings; S10.5: Select step size based on historical experience; S10.6: Update subpopulation size; S10.7: Reward Calculation and Q-Value Update.

[0018] Compared with the prior art, the learning optimization method for large-scale flight recovery provided by the embodiments of the present invention has at least the following advantages: With the optimization objectives of minimizing airline recovery costs and minimizing overall flight delays, and considering constraints such as aircraft maintenance and airport capacity, a flight recovery optimization model is constructed. A learning-based evolutionary intelligent optimization method is proposed, which achieves decoupled optimization of multi-objective search directions by constructing delay-oriented and cost-oriented populations. A cross-population information interaction and fusion mechanism is designed to generate candidate solutions that take into account the characteristics of different optimization objectives through combination operators. Furthermore, an adaptive population size control mechanism based on reinforcement learning is introduced to dynamically allocate computational resources according to the contributions of different populations during the search process. This method can efficiently solve the flight recovery problem under complex constraints, achieving rapid and efficient optimization of large-scale flight recovery schemes. Attached Figure Description

[0019] Figure 1 In an embodiment of a learning optimization method for large-scale flight recovery provided according to an embodiment of the present invention, a flight network diagram is provided, wherein the vertical layers represent time and the horizontal axis represents airports.

[0020] Figure 2In an embodiment of a learning optimization method for large-scale flight recovery provided according to an embodiment of the present invention, an initial flight schedule is provided.

[0021] Figure 3 In an embodiment of a learning optimization method for large-scale flight recovery provided according to an embodiment of the present invention, the time-line representation of flight schedules is described. Detailed Implementation

[0022] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0023] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein. Therefore, the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0024] Figure 1-3 Together they showcased a small-scale flight operation network consisting of 5 airports, 7 flights, and 3 aircraft. Figure 1 This is a time-space representation of a flight network, where vertical layers represent time, horizontal time slices show the relative geographical locations of airports, and arrows represent flights between airports, containing both time and space information. Flights with the same linear shape are operated by the same aircraft. Figure 2 for Figure 1 The initial flight schedule corresponding to the flight operation network in the middle, where, For flight numbers, OD indicates the departure and arrival airports. For the scheduled departure time of the flight, This refers to the aircraft number operating the flight. Figure 3 for Figure 1 The flight operation network in the image corresponds to the Time-Line representation, where arrows represent flights between airports, containing both time and spatial information. Flights with the same linear shape indicate that they are operated by the same aircraft.

[0025] The following is a reference appendix Figure 1-3A learning optimization method for large-scale flight recovery according to an embodiment of the present invention is described in detail. This method constructs a multi-objective flight recovery problem model based on a spatiotemporal network. Firstly, a dual-population optimization framework and target-specific search operators within each population are designed to decouple the search directions for multiple objectives. Secondly, an optimization information exchange mechanism between subpopulations is designed to improve the optimization quality of flight recovery schemes through high-quality optimization information sharing. Thirdly, a Q-learning-based adaptive adjustment mechanism for subpopulation size is designed to adjust the next-generation population size of the subpopulations based on the optimization status and historical search contributions of the two subpopulations, achieving a reasonable allocation of computational resources and improving the optimization speed / efficiency of flight recovery schemes.

[0026] Symbol explanation:

[0027] According to an embodiment of the present invention, a learning optimization method for large-scale flight recovery is provided, the specific steps of which are as follows.

[0028] S1: Construct a multi-objective flight recovery problem model based on a spatiotemporal network. The flight operation process is abstracted into a directed spatiotemporal network to uniformly describe the flight time sequence relationships, aircraft paths, and airport capacity constraints.

[0029] This spatiotemporal network can be composed of a set of airport time nodes and a set of flight arcs. Each node in the set of airport time nodes represents a takeoff or arrival event at a specific time point for a certain airport, and each arc in the set of flight arcs represents a connecting flight or aircraft between flights.

[0030] During the construction of the spatiotemporal network, the operational capacity of airports can be discretized. For any airport within a given time period, the maximum number of landings and takeoffs allowed can be set to reflect the capacity limitations of the airport in different time periods.

[0031] In addition, an auxiliary source node and an auxiliary sink node can be introduced for each aircraft in the spatiotemporal network. The auxiliary source node represents the aircraft's initial position at the start of the recovery period and is connected to the first flight departure node that the aircraft can execute. The auxiliary sink node represents the aircraft's terminateable position at the end of the recovery period, thus fully depicting the aircraft's execution path within the recovery window. Furthermore, aircraft subsets can be defined based on the aircraft manufacturer, specific model, and cabin configuration to describe the penalties incurred in cases of mismatched aircraft parking.

[0032] The following model for the multi-objective flight recovery problem is established based on spatiotemporal networks:

[0033] Equation (1) aims to minimize the overall recovery cost of the airline. The first three terms represent flight delay cost, flight cancellation cost, and flight operation cost, respectively, while the last three terms represent the penalty cost caused by mismatched aircraft parking locations. Specifically, flight delay cost is related to the flight delay time, flight type, and the number of passengers who have booked seats on the flight; flight cancellation cost is also related to the flight type and the number of passengers; flight operation cost is related to the type of aircraft operating the flight and the flight time; and aircraft parking non-compliance cost is related to the severity of the parking mismatch. Equation (2) further aims to minimize the overall flight delay and is used to measure the operational efficiency of the recovery plan. Equations (3)-(5) give the flow balance constraints of the aircraft at each airport node to ensure that the execution path of each aircraft in the spatiotemporal network is continuous and complete. Equation (6) ensures that each flight can be assigned to at most one aircraft for execution. Equation (7) ensures that the number of passengers carried by each aircraft in each cabin class does not exceed its corresponding seat capacity limit, thereby avoiding passenger overflow. Equations (8) and (9) respectively limit the maximum number of landing and taking off flights allowed at the airport per unit time to reflect airport capacity constraints. Equation (10) ensures that the cumulative flight time of each aircraft between two planned maintenance operations does not exceed a safety threshold. Finally, Equation (11) ensures that the flights allocated to each aircraft do not exceed its maximum flight range limit. Equation (12) indicates that the variable for allocating aircraft to flights is a 0-1 variable. In addition, other operational constraints, including minimum turnaround time, transfer time, maximum allowable delay, and maintenance schedule, are implicitly processed during the spatiotemporal network generation stage and can be detected or corrected during the solution process using the proposed algorithm.

[0034] S2: Flight data read, reads the set of flights within the recovery time window. Airplane assembly Aircraft maintenance plan Airport takeoff and landing capacity per unit time Information such as aircraft malfunctions or airport capacity reductions.

[0035] S3: Dual Population Initialization. Based on the flight data reading results from step S2, dual population initialization is performed to construct initial individual sets for both the delay-oriented subpopulation and the cost-oriented subpopulation, providing an initial search starting point for subsequent iterative evolution.

[0036] S3.1: Generation of individuals in the delay-oriented subpopulation and the cost-oriented subpopulation. Individuals in the delay-oriented subpopulation and the cost-oriented subpopulation are flight plan individuals. Each flight plan individual can be coded to include the flight, the aircraft assigned to the flight, and the offset of the adjusted departure time from the original departure time.

[0037] Let the initial size of each subpopulation be... Construct the initial delayed-direction subpopulation. With initial cost-oriented subpopulation And make both the size consistent:

[0038] In both subpopulations, an individual with an initial flight plan was placed. and generate the rest respectively. Individual flight schedules allow for:

[0039]

[0040] in, This represents the individual flight plan participants in the initial delay guidance subpopulation obtained through random generation. This represents the individual flight plans in the initial cost-oriented subpopulation obtained through random generation, ensuring the diversity of the initial solution set; when generating random flight plan individuals, the aircraft assignment relationship can be randomly perturbed, and the takeoff time offset is set to 0.

[0041] S3.2: Disturbance information labeling and flight recovery plan coding, with each flight plan as a flight recovery plan.

[0042] Establish flight aggregation For any individual flight plan in the delay-oriented subpopulation and the cost-oriented subpopulation. Based on disturbance information such as aircraft malfunctions and reduced airport capacity, the disturbed flights in the individual flight schedule are marked, thus obtaining the set of disturbed flights in the individual flight schedule. ,in This indicates the total number of flights.

[0043] Furthermore, the flight plan individuals in the two populations were sequentially coded as follows: ,in Indicates flight The assigned aircraft Indicates flight The offset of the adjusted takeoff time compared to the original takeoff time.

[0044] S4: Individual Constraint Processing and Quality Assessment within Subpopulations. In each iteration, constraints and quality assessments are performed on individuals in both the delay-oriented and cost-oriented subpopulations. Infeasible flight recovery solutions are first modified into feasible solutions that meet operational constraints, while minimizing the negative impact on solution quality during the modification process.

[0045] S4.1: Establish constraint types and priority divisions.

[0046] In response to the various operational constraints involved in flight resumption, the repair process comprehensively considers the following six types of constraints: (1) Flight connection time constraints: Minimum turnaround time must be met between adjacent flights operated by the same aircraft; (2) Flight range constraint: The flight distance shall not exceed the maximum range of the assigned aircraft; (3) Maximum allowable delay constraint: Flight delays shall not exceed the preset maximum allowable delay threshold; (4) Aircraft capacity constraints: The number of passengers on a flight shall not exceed the aircraft’s seating capacity; (5) Aircraft maintenance constraints: The aircraft must complete the planned maintenance at the designated airport and within the specified time window; (6) Airport capacity constraints: The number of takeoffs and landings at an airport during any time interval shall not exceed the capacity limit.

[0047] Among them, constraints (1)–(4) are local constraints; constraints (5)–(6) are global constraints.

[0048] Regarding the priority of constraints, the repair strategy can be executed in the order of "local first, then global", that is, first execute constraints (1)-(4), and then execute constraints (5)-(6).

[0049] S4.2: Local constraint repair based on aircraft path.

[0050] First, based on the aircraft assignment relationship All flights are assigned to corresponding aircraft, forming a flight execution sequence for each aircraft. For any given aircraft... Let its flight sequence be And sorted according to the planned departure times. Indicates the first An airplane, Indicates the first One flight, Indicates flight The offset of the adjusted takeoff time compared to the original takeoff time.

[0051] Subsequently, for each sequence, the constraints of flight connection time, flight range, maximum allowable delay, and aircraft capacity are checked in turn.

[0052] In the cost-oriented subgroup and the delay-oriented subgroup, for flights that violate the flight connection time constraint, the flight will be delayed until the earliest time that meets the flight connection time constraint. For flights that violate the route constraint or the maximum allowable delay constraint, the flight will be cancelled directly. For flights that violate the aircraft capacity constraint, the refund cost will be calculated as a penalty for passengers exceeding the capacity.

[0053] S4.3: Fixes for aircraft maintenance constraints.

[0054] Regarding aircraft maintenance constraints, check whether the flight sequence of each aircraft can reach the maintenance airport and complete the maintenance task within the specified time window. If there is a conflict between the aircraft's flight time and the maintenance time window, adjust the departure time of the conflicting flights to avoid the maintenance time window; if the maximum flight time or maintenance accessibility requirements still cannot be met after adjustment, cancel the relevant flights.

[0055] S4.4: Fixes for airport capacity constraints.

[0056] After completing the local constraint repair based on aircraft paths, the airport capacity constraints are further examined. Let the airport set be... The set of time intervals is If the meeting is at any of the airports in the airport group Any time interval in the set of time intervals If the number of flights taking off or landing exceeds the airport's capacity limit during a given time period, it is considered a capacity conflict at that airport. Flights taking off or landing during this conflicting time period constitute a capacity conflict flight set. Adjustments are made to this capacity conflict flight set based on the principle of minimizing cascading delays.

[0057] Specifically, flights within the capacity conflict set are sorted from lowest to highest according to the number of subsequent flights required for each designated aircraft, and then adjusted sequentially. During adjustment, differentiated repair preference strategies can be adopted for different subgroups. For example, for the delay-oriented subgroup, a flight cancellation strategy can be used to obtain a feasible solution with less overall delay; for the cost-oriented subgroup, a flight delay strategy is prioritized to adjust flights to within the time range that meets takeoff and landing capacity constraints, keeping flights running as much as possible and reducing the high costs of flight cancellations. When delay repair is not feasible, flight cancellation is executed. This process is repeated until all airport capacity constraints are met.

[0058] S4.5: Individual assessment.

[0059] In this step, after the constraint repair is completed, the delay target and cost target values ​​are calculated for the feasible individuals obtained after repair according to formulas (1) and (2) in the multi-objective flight recovery problem model, respectively, for subsequent non-dominated ranking and evolutionary selection. Both objective functions in the multi-objective flight recovery problem model are evaluated based on the repaired flight recovery scheme to ensure that the target values ​​reflect the quality of the truly executable operation scheme.

[0060] S5: Crossover within the subpopulation, resulting in a delayed-directed subpopulation and a cost-directed subpopulation after the crossover operation.

[0061] In each iteration, at this step, a crossover operation is performed within both the delay-oriented subpopulation and the cost-oriented subpopulation. This represents the current iteration round number. Specifically, it can be executed as follows: First, select two individuals from the subpopulation using a binary tournament selection operator. and As the parent generation, the PMX crossover operator is then executed on the parent generation to obtain offspring. This process is repeated until offspring are generated in both the delay-oriented and cost-oriented offspring populations, respectively. and Each offspring is added to its corresponding subpopulation, resulting in a deferred-directed subpopulation and a cost-directed subpopulation after the crossover operation. These subpopulations then participate in subsequent mutation operations and the subpopulation update and evolution process.

[0062] S6: Variation within the subpopulation.

[0063] In each iteration, at this step, mutation operations are performed on offspring individuals within the delayed-directed subpopulation and the cost-directed subpopulation after the crossover operation, respectively, resulting in the mutated delayed-directed subpopulation and the cost-directed subpopulation. To focus on optimizing different objectives within different populations (i.e., optimizing the delay objective for the delayed-directed subpopulation and the cost objective for the cost-directed subpopulation), differentiated sets of neighborhood search operators can be used for the delayed-directed subpopulation and the cost-directed subpopulation.

[0064] S6.1: Establish a set of delay direction operators.

[0065] The goal of delay-directed subpopulation is to reduce the overall delay level and suppress delay propagation. Establishing a neighborhood operator set includes: Operator D1: Time-shifting compression operator; randomly selects a set of flights and halves the delay of flights within the set.

[0066] Operator D2: Delay state rearrangement operator; randomly selects several aircraft and performs a reordering operation on all flights in their flight sequence. Change to 0.

[0067] Operator D3: High-delay flight cancellation operator; First, select aircraft based on total delay time, using the total delay as a weighting factor; the longer the delay time, the higher the probability of selection. Then, randomly remove one flight from the selected aircraft's schedule; the probability of removal increases as the individual flight's delay time increases.

[0068] S6.2: Establish a set of cost-oriented operators.

[0069] The goal of the cost-oriented subpopulation is to reduce recovery costs and maintain flight operations as much as possible. The set of neighborhood operators includes: Operator C1: Insert Cancelled Flight Operator; Sort cancelled flights in descending order of cancellation cost. The higher the cancellation cost, the higher the probability of selection. After selection, insert it into the aircraft's list of executed flights at a position that satisfies the location continuity requirement.

[0070] Operator C2: Exchange canceled flight operator; sort canceled flights from highest to lowest cancellation cost, with higher cancellation costs having a higher probability of selection. After selection, exchange the selected flight with a flight in the aircraft's scheduled flight list, ensuring that the location is continuous.

[0071] Operator C3: Assign aircraft swap operator; randomly select two aircraft that pass through the same airport at the same time. If they belong to the same manufacturer and model, then swap the subsequent flight sequences of these two aircraft.

[0072] S6.3: Establish a hill-climbing local search mutation framework.

[0073] For each offspring individual to be mutated in the delay-oriented subpopulation and the cost-oriented subpopulation, perform the following hill-climbing local search procedure: 1) Record the current evaluation value of the solution; 2) Randomly select an operator from the preset neighborhood operator set to generate candidate solutions; 3) Perform a feasibility check on the candidate solutions. If they are not feasible, the repair mechanism in step S4 shall be used to repair them. 4) If the new solution obtained is an improvement over the recorded value in any goal-oriented evaluation, then accept the mutation; otherwise, reject it and try the next operator. 5) Repeat steps 2)-4) until the maximum number of neighborhood attempts is reached or the number of consecutive unimproved attempts reaches the threshold, then output the mutated individual.

[0074] S6.4: Output of mutation results.

[0075] Perform the above hill-climbing local search mutation on the crossover individuals in both subpopulations to obtain the delayed offspring set of the mutated subpopulations. With cost-oriented subpopulation offspring set The resulting mutant individuals will be used as candidate inputs for subsequent steps S7 (cross-population information interaction and offspring generation) and S8 (subpopulation update and evolution).

[0076] S7: Cross-population information exchange and offspring generation. Through the cross-population information exchange mechanism, search information is exchanged between the delayed-direction subpopulation and the cost-oriented subpopulation after crossover and mutation operations, generating offspring that take into account the characteristics of different optimization objectives.

[0077] In each iteration, at this step, search information can be exchanged between the delay-oriented subpopulation and the cost-oriented subpopulation through a cross-population information exchange mechanism. An elite-preserving cross-population crossover operator is used to generate offspring individuals. The key structure of the parent solution is reorganized in the cost-oriented stage and the delay-oriented stage, respectively, thereby generating offspring that take into account the characteristics of different optimization objectives.

[0078] S7.1: Parent selection.

[0079] In each round of cross-population operation, one individual is selected from the parent individuals of the current delayed-direction subpopulation and one individual from the parent individuals of the cost-direction subpopulation using a roulette wheel selection operator. The selection probability of an individual is related to its fitness.

[0080] Suppose that the first subpopulation individual The probability of selection is:

[0081] in, For individuals The weight of a can be obtained by mapping its ranking level under the corresponding objective.

[0082] This method yields parent individuals from the two current subpopulations respectively:

[0083] in, , These are the two parent individuals selected.

[0084] S7.2: Parent generation comparison and determination of primary and secondary parents.

[0085] For the two selected parent individuals and Calculate the evaluation values ​​for each under the cost target and the delay target respectively, and compare their relative advantages and disadvantages: Under the cost objective, individuals with better evaluation scores are designated as the cost parent generation. Another is cost-assisted parent generation ; Under the delay objective, individuals with better evaluation scores are designated as the delay parent generation. Another is to delay the adoption of paternal lineage. .

[0086] S7.3: Cost-oriented crossover stage. Cost-driven parent generation. The primary method is to perform a structure-preserving crossover operation. The specific process is as follows: 1) Represent the Lord Father According to aircraft assignment Divided into several aircraft execution routes (flight sequences); 2) Calculate the flight cancellation cost for each flight route to measure the route's importance to the cost objective; 3) Randomly generate a retention ratio parameter. And select the one with the largest cost contribution. The aircraft path is directly inherited to the offspring, among which The total number of aircraft paths in the parent generation; 4) For the unfilled portions in the offspring generation, follow the method of supplementing the parent generation. The corresponding segments in the code are sequentially filled with the corresponding flight routes, and duplicates are skipped. 5) For flight routes inherited from their parent, the departure time offset. Direct inheritance; for newly introduced flight paths from the auxiliary parent generation, the departure time offset is initialized to 0.

[0087] Through the above steps, a cost-oriented offspring individual is obtained. Its structure preserves key components of low-cost recovery solutions to the greatest extent possible.

[0088] S7.4: Delaying the crossover phase. This delays the main parent generation. This phase is led by a structured, cross-functional mechanism similar to the cost-oriented phase, but retains delay indicators as the basis for reliance. The specific process is as follows: 1) Represent the Lord Father Aircraft routes are defined according to aircraft assignment relationships; 2) Calculate the cumulative delay level for each path and select the critical paths with the lowest delays; 3) Use the same retention ratio parameters as in step S7.3. To minimize the delay Inheritance can be passed down to offspring via a single path; 4) For the remaining unfilled portions, follow the parent-child relationship. The corresponding segments should be used to supplement the flight routes, and duplication should be avoided; 5) Inherit the takeoff time offset of the main parent path, and initialize the takeoff time offset of the other paths to 0.

[0089] This generates a delayed misdirection to offspring individuals. Its structure prioritizes retaining key components from low-delay solutions.

[0090] S7.5: Generation of child sets.

[0091] In a single crossover operation, two offspring individuals are obtained. Steps S7.1–S7.4 are repeated until the number of offspring individuals reaches the preset target. Forming cross-population offspring sets The offspring individuals then enter step S8, subpopulation renewal and evolution, and participate in the next stage of evolutionary selection.

[0092] S8: Subpopulation Update and Evolution. In this step, update and evolution operations can be performed on the delay-oriented subpopulation and the cost-oriented subpopulation respectively to form the next generation of delay-oriented subpopulation and cost-oriented subpopulation. This step is based on fast non-dominated sorting of feasible solutions, ensuring that the subpopulation size is controlled while maintaining the quality and diversity of the solution set.

[0093] S8.1: Construction of candidate sets for subpopulations.

[0094] The current number In this generation, the parent set of the delayed-direction subpopulation and the parent set of the cost-oriented subpopulation are respectively... and .

[0095] In this round of iteration, each subpopulation generates its internal offspring set through crossover and mutation operations, denoted as the delayed-direction subpopulation's internal offspring set. With cost-oriented subpopulation and offspring set Simultaneously, in conjunction with the current round, a cross-population offspring set is generated in step S7. Construct candidate sets for delayed-directed and cost-oriented subpopulation updates respectively:

[0096]

[0097] in, Indicates the first Cost-oriented subpopulation update candidate set in round-by-round iteration Indicates the first The delayed round of iteration guides the candidate set of the subpopulation to be updated.

[0098] S8.2: Non-dominated sorting of candidate sets prioritizing feasible solutions.

[0099] The obtained update candidate set and Perform quick non-dominated sorting on each candidate set to obtain a sorted-priority updated candidate set. The sorting process employs the feasible solution-dominated principle, using the candidate set as the basis for the sorting. For example, the dominance relationship between each pair of individuals in the candidate set is defined as follows: 1) If an individual Individuals as feasible solutions If it is an infeasible solution, then the individual Dominant Individual ; 2) If an individual With individuals If both solutions are feasible, then a non-dominated comparison is performed based on the two objective functions of the two individuals; 3) If an individual With individuals If both solutions are infeasible, then the degree of constraint violation of the two individuals is compared, and the individual with the smaller degree of violation dominates the other individual.

[0100] The above assessment of individual feasibility can be performed based on the results of constraint repair and inspection in step S4.

[0101] S8.3: Crowding Calculation.

[0102] For individuals with the same priority obtained in S8.2, the crowding distance between individuals is further calculated to measure the sparsity of their distribution in the target space. Individuals with higher crowding have higher priority in selection, thus obtaining the updated priority ranking of all individuals in each candidate set.

[0103] S8.4: Subpopulation update.

[0104] Let the first In the round of iteration, the current sizes of the delay-oriented subpopulation and the cost-oriented subpopulation are respectively and .Establish Delayed guidance of subpopulation in round iteration Cost-oriented subpopulation First and All are initialized to empty. Then, individuals are selected from the corresponding candidate sets according to the priorities calculated in previous steps S8.2 and S8.3 to fill the subpopulation. The process stops when the number of selected individuals reaches the corresponding size limit, thus forming the next generation of subpopulation.

[0105] It should be noted that the upper limit of the corresponding size of the two subpopulations in step S8 is determined by the current evolutionary state, and the specific adjustment strategy will be given in step S10, which is based on Q-learning for adaptive control of the size of the two subpopulations; in this step, the subpopulation update evolution is performed according to the predetermined size.

[0106] S9: Global Non-Dominated Solution Set Update, obtaining the global non-dominated solution set for the current iteration. In this step, the global non-dominated solution set can be constructed and updated, and all candidate flight recovery schemes generated during the current iteration can be uniformly summarized and evaluated.

[0107] S9.1: Construction of candidate solution set.

[0108] No. The candidate solutions generated in the round of iterations include: the set of offspring generated by the delayed misdirection of the subpopulation's internal evolution. The set of offspring produced by the internal evolution of a cost-oriented subpopulation and the set of offspring generated through cross-population information exchange in step S7. .

[0109] Compare the above candidate solutions with the previous generation's globally non-dominated solution set. Merge to form the first Candidate solution set of round iteration .

[0110] S9.2: Screening of non-dominated solutions and prioritizing feasibility, for the candidate solution set in the current round. The dominance relationships of all individuals are calculated, and the resulting non-dominated solutions constitute the global non-dominated solution set for the current iteration round.

[0111] In this step, the current set of candidate solutions can be... For all individuals in S8.2 and S8.3, calculate the dominance relationship, extract all non-dominated solutions, and obtain the first... The updated global non-dominated solution set ,in This indicates a non-dominated solution extraction operation.

[0112] S9.3: Subpopulation search contribution statistics, obtaining the improvement of the global hypervolume by the current delay-oriented subpopulation and cost-oriented subpopulation.

[0113] In this step, the newly generated child solutions (i.e.) can be used as a basis. , and ), for the two subpopulations in the 1st The search contributions during each generation were statistically analyzed. Specifically, the contributions could be categorized according to the origin of the primary parent generation during cross-population processes. Divided into a set of offspring generated primarily by the parent generation based on delayed guidance of individuals. And the set of offspring generated primarily by cost-oriented individuals from the parent generation. With the first Substitute global non-dominated solution set Based on this, the improvement in global hypervolume for the two subpopulations is calculated as follows:

[0114]

[0115] in, For the selected reference point, use The worst values ​​of all individuals on both objectives are used as the coordinates of a reference point. Represents a set The set of non-dominated solutions in Denotes the set of non-dominated solutions Relative to reference point The excess volume value.

[0116] The search contribution mentioned above is used to reflect the role of the two subpopulations in improving the quality of multi-objective solution sets in the current generation, and serves as the basis for subsequent computational resource adjustment.

[0117] S10: Adaptive regulation of dual population size based on Q-learning.

[0118] In this step, after updating the global non-dominated solution set and obtaining the search contribution of each subpopulation in the current generation, the size of the delay-oriented subpopulation and the cost-oriented subpopulation can be adaptively adjusted based on the search contribution feedback, so as to achieve dynamic allocation of computing resources among different search directions. It should be noted that S10.1 and S10.3 in this part are only executed in the first iteration, and the remaining parts are executed sequentially in each iteration.

[0119] S10.1: Establish basic size constraints.

[0120] In this step, the first... The sizes of the generational delay-oriented subpopulation and the cost-oriented subpopulation are respectively and ,Regulation + Meanwhile, to ensure that each subpopulation possesses basic search capabilities, the size of any subpopulation is constrained to be no less than [a certain value]. .

[0121] S10.2: Determine the direction of scale control.

[0122] Based on the search contribution obtained in step S9.3, calculate the contribution ratio of the delayed-direction subpopulation in the current iteration round:

[0123] in, It is a preset, extremely small positive number. When A value greater than 0.5 indicates that the delayed-direction offspring population contributes significantly to the current generation, and more computing resources should be allocated to the next generation; when... If the value is less than 0.5, the size of the cost-oriented subpopulation should be increased; when the two are close, the existing size allocation should be maintained.

[0124] S10.3: Determine the scale control step size and control strategy.

[0125] To avoid drastic fluctuations in subpopulation size between adjacent iterations, three size adjustment step sizes are introduced:

[0126] The adjustment range adopted in this generation is determined by a step size selection mechanism based on Q-learning.

[0127] S10.3: Optimize state definition and Q table settings.

[0128] In this step, the first can be defined The optimized state of the algorithm at the next iteration. It consists of the following two parts: 1) Contribution percentage range , hour, ; hour, ; hour, ; 2) Range of subpopulation size ratios Among them, the ratio of the size of the delayed-direction subpopulation to the cost-direction subpopulation. , hour, ; hour, ; hour, .in, .

[0129] The initial value of all state-step pairs is set to 0. Indicates step size, Indicates the state of algorithm optimization. Next, select the step size. The Q value.

[0130] S10.4: Select step size based on historical experience.

[0131] In this step, the current state can be used as a reference. Select the current step size Randomly select from three step sizes with a probability of 0.5; select with a probability of 0.5. Maximum step size.

[0132] S10.5: Update subpopulation size.

[0133] In this step, the population size can be updated based on the direction determined in step S10.2 and the step size selected in step S10.4. If the size of the delayed directional subpopulation should be increased, the following steps are performed:

[0134] If the cost-oriented subpopulation size should be increased, execute:

[0135] If it remains unchanged, then .

[0136] Then determined by the total size constraint:

[0137] The obtained total size is judged. If the updated total size violates the lower bound constraint, it is corrected according to the lower bound, and the size of another subpopulation is adjusted accordingly to keep the total size unchanged.

[0138] S10.6: Reward Calculation and Q-Value Update.

[0139] In this step, the first The hypervolume change of the globally non-dominated solution set is used as the immediate reward:

[0140] The state-step pair used in this iteration Update Q value:

[0141] in The learning rate can be set as needed.

[0142] S11: Termination Decision and Optimization Result Output. The output optimization results include the new takeoff and landing times for the flight, as well as the corresponding aircraft, which can be provided to the flight planning system for airlines to adjust flight resource allocation.

[0143] The current algorithm execution status is terminated. When the preset termination conditions are met, such as the maximum runtime or the upper limit of the optimization rounds, the iteration process ends and the optimization result is output. Otherwise, the next iteration is entered and the process returns to step S4 to continue the next iteration.

[0144] All of the above-mentioned optional technical solutions can be combined in any way to form optional embodiments of the present invention, and will not be described in detail here.

[0145] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order and method of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0146] It should be understood that the foregoing only illustrates some embodiments, and changes, modifications, additions, and / or variations can be made without departing from the scope and spirit of the disclosed embodiments. These embodiments are illustrative and not restrictive. Furthermore, the described embodiments relate to those currently considered most practical and preferred, and should be understood as not being limited to the disclosed embodiments, but rather intended to cover different modifications and equivalent arrangements included within the spirit and scope of those embodiments. Moreover, the various embodiments described above can be used in conjunction with other embodiments; for example, an aspect of one embodiment can be combined with an aspect of another embodiment to achieve yet another embodiment. Additionally, individual features or components of any given component can constitute another embodiment.

[0147] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A learning optimization method for large-scale flight recovery, characterized in that, include: S1: Construct the flight operation process as a multi-objective flight recovery problem model based on spatiotemporal networks; S2: Flight data reading, reads flight sets, aircraft sets, aircraft maintenance plans, airport takeoff and landing capacity per unit time, and information on aircraft malfunctions or airport capacity reduction within the recovery time window; S3: Dual-population initialization. Based on the read flight data, dual-population initialization is performed to construct the initial individual sets of the delay-oriented subpopulation and the cost-oriented subpopulation, respectively, providing an initial search starting point for subsequent iterative evolution. S4: Individual constraint processing and quality assessment within subpopulations, respectively constraining and assessing flight plan individuals in delay-oriented and cost-oriented subpopulations; S5: Crossover within subpopulations. Perform crossover operations in both the delay-oriented subpopulation and the cost-oriented subpopulation until a set number of offspring are generated. Then, add the generated offspring individuals to the corresponding subpopulations to obtain the delay-oriented subpopulation and the cost-oriented subpopulation after the crossover operation. S6: Intrapopulation mutation. Perform mutation operations on offspring individuals in the delayed-direction subpopulation and the cost-direction subpopulation after the crossover operation, respectively, to obtain the delayed-direction subpopulation and the cost-direction subpopulation after the mutation operation. S7: Cross-population information exchange and offspring generation. Through the cross-population information exchange mechanism, search information is exchanged between the delayed-direction subpopulation and the cost-oriented subpopulation after the mutation operation to generate a cross-population offspring set, which in turn constitutes the delayed-direction subpopulation and the cost-oriented subpopulation after cross-population interaction. S8: Subpopulation update and evolution. Perform update and evolution operations on the delayed-directed subpopulation and cost-oriented subpopulation after cross-population interaction to form the next generation of delayed-directed subpopulation and cost-oriented subpopulation. S9: Update the global non-dominated solution set to obtain the global non-dominated solution set for the current iteration round; S10: Adaptive regulation of dual population size based on Q-learning; S11: Termination judgment and optimization result output. When the preset termination condition is met, the iteration process ends and the current optimization result is output. Otherwise, return to S4 to execute the next iteration.

2. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, In S1: The spatiotemporal network consists of a set of airport time nodes and a set of flight arcs. Each node in the set of airport time nodes represents a takeoff or arrival event at a specific time point at a certain airport, and each arc in the set of flight arcs represents a flight or aircraft's transfer connection between flights. The established multi-objective flight recovery problem model based on spatiotemporal networks includes: The optimization objectives include minimizing the airline's overall recovery costs and minimizing overall flight delays; The constraints include flow balance constraints for aircraft at each airport node, ensuring that each flight is assigned to at most one aircraft, guaranteeing that the number of passengers carried by each aircraft in each cabin class does not exceed its corresponding seating capacity limit, constraints on the maximum number of landing and taking off flights allowed at each airport per unit time, and guaranteeing that the cumulative flight time of each aircraft between two planned maintenance sessions does not exceed a safety threshold. Ensure that the flights allocated to each aircraft do not exceed its maximum flight range limit.

3. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, S3 include: S3.1: Generate individuals in the delay-oriented subpopulation and the cost-oriented subpopulation. Individuals in the delay-oriented subpopulation and the cost-oriented subpopulation are flight plan individuals. Set the initial size of the delay-oriented subpopulation and the cost-oriented subpopulation. S3.2: Disturbance information labeling and flight recovery scheme coding, taking each flight plan individual as a flight recovery scheme; establishing a flight set, for each flight plan individual in the delay-oriented subgroup and the cost-oriented subgroup, according to the information of aircraft failure and airport capacity reduction, the disturbed flights in the flight plan individual are labeled to obtain the set of disturbed flights corresponding to the flight plan individual; Each flight plan individual code includes the flight, the aircraft assigned to that flight, and the offset of the adjusted departure time from the original departure time.

4. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, S4 include: S4.1: Establish constraint types and priority classification, including establishing local constraints and global constraints. Local constraints include flight connection time constraints, flight range constraints, maximum allowable delay constraints, and aircraft capacity constraints. Global constraints include aircraft maintenance constraints and airport capacity constraints. The priority is set to execute local constraints first, and then global constraints. S4.2: Local constraint repair based on aircraft path; All flights are assigned to corresponding aircraft, forming a flight execution sequence for each aircraft; For each sequence, check the flight connection time constraints, flight range constraints, maximum allowable delay constraints, and aircraft capacity constraints in sequence. For flights that violate flight connection time constraints, the flight will be delayed until the earliest time that meets the flight connection time constraints. For flights that violate flight range constraints or maximum allowable delay constraints, the flight will be cancelled directly. For flights that violate aircraft capacity constraints, the cost of refunds will be calculated for passengers exceeding the capacity as a penalty. S4.3: Fixes for aircraft maintenance constraints; S4.4: Fixes for airport capacity constraints; S4.5: Individual assessment, calculate the delay target and cost target values ​​for the individual flight plans obtained after the repair based on the two optimization objectives in the multi-objective flight recovery problem model.

5. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, In S5, crossover operations are performed in both the delay-oriented subpopulation and the cost-oriented subpopulation in the current iteration round, including: Within the delay-oriented or cost-oriented subpopulation in the current iteration round, two parent individuals are selected using a binary tournament selection operator. The PMX crossover operator is executed on the parent generation to obtain offspring, and this process is repeated until a preset number of offspring are generated. The generated offspring individuals are added to the corresponding subpopulations to obtain the delayed-directed subpopulations and cost-directed subpopulations after the crossover operation.

6. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, In S6, the following mutation operations are performed on offspring individuals in both the delayed-direction subpopulation and the cost-direction subpopulation after the crossover operation: S6.1: Establish a set of delay direction operators and a set of neighborhood operators, including time shift compression operator, delay state rearrangement operator, and high-delay flight cancellation operator; S6.2: Establish a cost-oriented operator set, including a neighborhood operator set such as the insertion cancellation operator, the exchange cancellation operator, and the aircraft reassignment operator; S6.3: Establish a hill-climbing local search mutation framework and execute a hill-climbing local search process for each offspring individual to be mutated; S6.4: Output the mutation results, obtaining the delayed-directed subpopulation and the cost-directed subpopulation after the mutation operation.

7. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, In S7, the following cross-population information exchange operations are performed on the delayed-directed subpopulation and the cost-directed subpopulation after the mutation operation: S7.1: Parent selection: Select one parent individual from each of the delayed-direction subpopulation and the cost-direction subpopulation using the roulette wheel selection operator to obtain two parent individuals; S7.2: Parent generation comparison and primary / secondary parent generation determination. For the two selected parent generation individuals, calculate their evaluation values ​​under the cost target and the delay target respectively, and compare and determine the cost primary parent generation, cost secondary parent generation, delay primary parent generation, and delay secondary parent generation. S7.3: Cost-oriented crossover stage, with the cost-oriented parent generation as the main force, performs a structure-preserving crossover operation to obtain cost-oriented offspring individuals; S7.4: Delayed-direction crossover stage, with delayed parent generation as the main driver, adopts the same structured crossover mechanism as the cost-oriented stage, and uses the delay index as the retention basis to obtain delayed-direction offspring individuals; S7.5: Generation of offspring set. Repeat steps S7.1–S7.4 until the number of offspring individuals generated reaches the preset scale, forming a cross-population offspring set, which in turn constitutes the delayed-direction subpopulation and cost-direction subpopulation after cross-population interaction.

8. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, In S8, the following update evolution operations are performed on the delayed-direction subpopulation and the cost-direction subpopulation after cross-population interaction, respectively: S8.1: Subpopulation candidate set construction: Based on the current delayed-directed subpopulation, cost-oriented subpopulation, and cross-population offspring set, construct delayed-directed subpopulation update candidate set and cost-oriented subpopulation update candidate set; S8.2: The feasible solution-first non-dominated sorting principle is used to perform fast non-dominated sorting on the obtained delayed-directed subpopulation update candidate set and cost-directed subpopulation update candidate set to obtain a series of non-dominated layers; S8.3: Crowding degree calculation. For individuals with the same priority obtained in S8.2, the crowding degree distance between individuals is further calculated. Individuals with higher crowding degree have higher priority when selected, thus obtaining the updated priority ranking of all individuals in each candidate set. S8.4: Subpopulation update, the reordered individuals are selected in sequence to fill the current delay-oriented subpopulation and cost-oriented subpopulation, to obtain the next generation of delay-oriented subpopulation and cost-oriented subpopulation.

9. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, S9 includes: S9.1: Constructing the candidate solution set: Combine the set of offspring within the delayed-directed subpopulation, the set of offspring within the cost-directed subpopulation, and the set of offspring across subpopulations in the current iteration round with the global non-dominated solution set of the previous iteration round to obtain the candidate solution set for the current round. S9.2: Non-dominated solution screening and feasibility priority processing: calculate the dominance relationship for all individuals in the candidate solution set of the current round, and the resulting non-dominated solutions constitute the global non-dominated solution set of the current iteration round; S9.3: Subpopulation search contribution statistics, obtaining the improvement of the global hypervolume by the current delay-oriented subpopulation and cost-oriented subpopulation.

10. The learning optimization method for large-scale flight recovery according to claim 1, characterized in that, S10 includes: S10.1: Establish basic size constraints; S10.2: Determine the direction of scale control; S10.3: Determine the scale control step size and control strategy; S10.4: Optimize state definition and Q table settings; S10.5: Select step size based on historical experience; S10.6: Update subpopulation size; S10.7: Reward Calculation and Q-Value Update.

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