Two-stage multi-runway departure flight ordering method based on collaborative promotion

Abstract

The invention provides a collaborative two-stage multi-runway departure flight ordering method, which is specially designed for relieving the congestion problem of a multi-runway airport in a peak period, ensures that the departure process of the flight is more efficient, and accords with scientific planning. The method comprises the following steps: constructing a multi-runway dynamic push-out rate control model to determine an optimal queuing threshold value of a taxiway; constructing a flight ordering and assigning model with the goal of minimizing flight delay and operation cost; and proposing a continuous Markov chain-based interactive whale algorithm, and carrying out flight push-out sequence and runway resource allocation. According to the method, the departure flight taxiing amount of the airport scene can be accurately identified, taxiway waiting time caused by runway occupation after the flight is launched is reduced, the actual significance is achieved for improving the flight punctuality rate and improving the overall airport operation efficiency, and the current green aviation development concept is met.

Description

Technical Field

[0001] The technical scope of the present invention is the optimization of airport operation scheduling, which belongs to the technical field of airport ground operation management, and specifically relates to a collaboratively launched two-stage multi-runway departure flight sequencing method. Background Art

[0002] Faced with the growing demand for air transport, limited airport capacity resources have become an important factor restricting the development of the civil aviation industry. As the problem of limited airport capacity becomes increasingly prominent, the level of civil aviation safety margin has been reduced under the condition that the total number of flights continues to operate at a high level, and the efficiency of airport surface operations has been challenged. In response to this, some domestic hub airports have taken hardware measures such as adding runways, but the contradiction between demand and capacity has not been resolved. Therefore, how to scientifically dispatch departing flights, make full use of limited airport resources, and effectively improve the quality of flight services has become a key issue in promoting the development of civil aviation airports.

[0003] In the research field, relevant scholars have conducted a lot of research on the scheduling methods of arriving and departing flights, but most of them focus on improving models and algorithms on a single resource, including parking space allocation, pushback control, taxi path planning, taxi time prediction, runway assignment, etc., such as the Chinese patents with application publication numbers CN117854331A and CN117789541A. In addition, related research on pushback rate control has not been verified in multi-runway systems. For random and dynamically complex airport environments, the above research shows certain limitations, and multi-resource collaborative scheduling has become a key measure to improve airport operating efficiency. Therefore, studying a dynamic scheduling method that conforms to the characteristics of multi-runway airports has important theoretical and practical significance for optimizing airport surface operations, improving flight punctuality, and promoting green and sustainable development. Summary of the invention

[0004] Purpose of the invention: To overcome the shortcomings of the prior art, an innovative method for dynamic scheduling of departing flights is provided, which regards the scheduling process of departing flights as the coordinated optimization of pushback control and runway assignment. Combined with the flight plan of incoming flights, the present invention aims to achieve the coordinated optimization of pushback control and runway assignment in the scheduling process of departing flights, in order to improve the efficiency of airport operations, reduce flight delays, and improve the quality of flight services.

[0005] The technical solution for achieving the purpose of the present invention is:

[0006] The present invention provides a collaboratively launched two-stage multi-runway departure flight sequencing method, namely, dynamic launch control in continuous time and integrated scheduling of flight sequencing and runway assignment, and is optimized through two stages. The first stage: By minimizing the taxiway queue waiting cost and the penalty for gate occupancy, the launch control threshold is optimized to ensure that the launch control threshold can alleviate the airport congestion problem. The second stage: from the perspective of airports, airlines and passengers, taking into account flight delay costs and environmental impacts, an integrated scheduling model with the goal of minimizing flight delays and minimizing operating costs is constructed, and a continuous-time Markov chain optimized whale algorithm is introduced to realize the flight launch order and the allocation of runway resources, further improving the runway utilization and the departure efficiency of flights. The process is as follows: Figure 1 shown.

[0007] The specific steps include:

[0008] 1. Phase 1: Taking the airport's departing flights throughout the day as the research object, further optimize the linear dynamic pushback control strategy, adjust the pushback probability according to the current taxiway queue status, and allow flights to wait at the parking stand in a timely manner. In order to improve the runway utilization rate, consider the impact of parking stand occupancy on the bay area turnover rate, minimize the taxiway waiting cost and parking stand waiting penalty as the objective function setting, and seek the optimal threshold for pushback control under the multi-service station queue system, as follows:

[0009] 1-1 Objective function:

[0010]

[0011] Formula (1) is the objective function, which represents the phase 1 cost of all flights, which mainly includes two parts: the fuel consumption cost of the flight waiting on the taxiway and the penalty value of parking space occupancy. D is the departure flight assembly, and R is the runway assembly. represents the fuel cost per minute, in RMB / minute. For flight i that chooses runway r, W ir and G i They represent the taxiway waiting time and the gate waiting time, in minutes. Based on the existing settings, it is assumed that the fuel cost and penalty cost are equal when the parking stand waiting time is 30 minutes. When it exceeds 30 minutes, the penalty cost will increase rapidly due to the delay and exceed the fuel cost under the same time. Then the parking stand occupancy penalty coefficient

[0012] 1-2 Constraints:

[0013]

[0014] Formula (2) is the push-out rate constraint. Where n is the current queue length on the taxiway, that is, the number of flights on the ground; N is the taxiway queue threshold, which is an unknown variable. The purpose of this stage is to find the optimal N value;

[0015]

[0016] Formula (3) is the push interval constraint. i pushback represents the pushback request time, Δt represents the minimum safety interval between consecutive flights, and based on the model applicability, it is set that the two consecutive pushback flights in this stage must meet the average wake safety interval;

[0017] G i ≤G max (4)

[0018] Formula (4) is the parking space occupancy constraint. According to the operating rules of a large airport, a flight is considered “on time” if it is pushed out of the boarding gate within 30 minutes of the estimated departure time. Therefore, G max Set to 30 minutes;

[0019] 0≤n≤N min ≤N≤N max (5)

[0020] Formula (5) is the taxiway queue length constraint. The maximum taxiway queue length cannot be greater than the control threshold. The upper and lower limits of the N value are set to 30 and 1 respectively.

[0021] 2. According to the model principle and formula described in step 1, the optimization algorithm based on continuous time Markov chain (CMTC) is adopted, that is, based on a fixed service rate, the minimum cost under different taxiway queue length thresholds is searched by iterative loop. The specific implementation is as follows:

[0022] The first step is parameter initialization. Based on the first-come, first-served (FCFS) principle, all flights are sorted according to their pushback application time, and a pushback request sequence is generated to ensure that the flight sequence is processed according to the time priority principle. The initial value of the queue length and the mean value of the tail flow safety interval μ in the iterative algorithm are also initialized. ave , taxiway capacity and other key parameters are initialized.

[0023] Step 2: Taxiway capacity loop. Start the outer loop of taxiway capacity, where the capacity depends on the airport configuration. The purpose of this loop is to continuously update and simulate different taxiway queue length thresholds to find the optimal taxiing conditions when the taxiway capacity does not reach the configuration limit.

[0024] Step 3: Flight sequence loop. For each flight waiting to be pushed out, the system will make a judgment based on the current taxiway queue length n. When the taxiway queue length is less than the taxiway capacity described in step 2, the linear dynamic push-out method is used to control flight i. During this process, the service rate μ(n) = μ ave The setting of r is used to calculate the taxiway queue status at each moment. When the allowed push-out time interval is greater than or equal to μ(n) and meets the input requirements, (i+1) flights are allowed to enter the taxiway waiting queue. i Value exceeds G max , then the third step is interrupted and the second step is continued. This value of N is marked as infeasible.

[0025] The fourth step is to calculate the cost index. For each flight launch request, the simulation calculates the cost index under flight launch control and the cumulative cost C under the entire threshold N TN , which serves as the basis for selecting the optimal taxiway queuing threshold in the subsequent steps, and returns to the second step.

[0026] Step 5: Optimize and mark the optimal value. Step 2: After reaching the maximum taxiway capacity, for all C TN The optimal taxiway queue length W and its corresponding taxiway waiting time G and other parameter values ​​are compared and marked. The goal is to find the queue length threshold that minimizes the total cost of the system in multiple simulations.

[0027] 3. Phase 2: Taking the departing flights during the airport peak hours as the research object, under the premise that the maximum number of taxiway waiting flights is less than the pushback control threshold, the continuous-time Markov chain transfer is introduced in combination with the influence of specific flight models, and the goals are to minimize flight delays and minimize departure costs, where the departure costs include pushback waiting costs, fuel consumption costs, and environmental emission costs.

[0028] 3-1 Objective function:

[0029]

[0030] Formula (6) is the objective function 1. The present invention reduces the flight delay loss as much as possible on the basis of making full use of airport resources. Taking full account of passenger satisfaction, the importance of flight delay is measured by flight load factor, which represents the sum of the takeoff delay value and its importance of each flight. Where, T ir is the optimized departure time of flight i, ET ir is the scheduled departure time of flight i. i represents the ratio of the number of passengers on flight i to its maximum capacity.

[0031] min(C P +C F+C E ) (7)

[0032] Formula (7) is the second objective function. Based on the concept of green civil aviation development, the present invention minimizes the sum of the additional cost of the waiting phase, the fuel consumption cost and the environmental cost caused during the taxiing phase and the taxiing phase. p represents the cost of waiting for the flight to be pushed out of the parking space, C F and C E Represent fuel consumption cost and gas emission cost respectively.

[0033]

[0034] Formula (8) is a supplement to Formula (7), which indicates the waiting cost of all flights at the parking stands. Controlling the push-out rate will cause some flights to stay at the parking stands and delay push-out. This cost is the cost that the airline needs to pay while the departing flights are waiting to be pushed out. It is the unit cost per minute of the gate waiting time for flight model a, in yuan / minute.

[0035]

[0036] Formula (9) is a supplement to Formula (7), which represents the fuel consumption of all flights during the taxiing waiting phase and the taxiing operation phase. and They represent the average fuel consumption rate of the flight of aircraft type a during the taxiway waiting phase and the operation phase, in kg / minute; is the obstacle-free taxiing time of flight i, in minutes.

[0037]

[0038] Formula (10) is a supplement to Formula (7), which represents the cost value of all flights emitting different gases. Where U represents the set of pollutant gases, n engine represents the number of engines of flight i, f u is the emission coefficient of pollutant U, defined as the mass of gaseous pollutants emitted per kilogram of fuel combustion. is the external cost of unit pollutant u, in yuan / kg.

[0039] 3-2 Constraints:

[0040]

[0041] Formula (11) is a dynamic pushout constraint. Based on the established threshold value obtained in the first stage, the flight pushout rate is controlled according to the number of flights waiting on the taxiway after pushout. In the formula, N optis the optimal threshold obtained in the previous stage;

[0042]

[0043] Formula (12) is the safety interval constraint. The two departing flights on the same runway must meet the RECAT-CN wake turbulence interval standard. Among them, F is the set of arriving and departing flights, is a 0-1 variable, which takes the value 1 if both the preceding and following flights take off or land on runway r, otherwise it takes the value 0;

[0044]

[0045] Formula (13) is the runway uniqueness constraint. Each flight must and can only be assigned to one runway. ir is a 0-1 variable, which takes the value 1 if flight i departs from runway r and 0 otherwise;

[0046] R r(A) +R r(D) ≤1 (14)

[0047] Formula (14) is the runway resource constraint. To ensure the safety of arriving and departing flights, it is stipulated that at any time, each runway can only have one flight at most. r(A) and R r(D) denote the number of flights arriving and departing from runway r, respectively.

[0048] ET ir ≤T ir ≤T ir +θ (15)

[0049] Formula (15) is the time window constraint. The delay time of each flight must be controlled within a certain range. The optimized flight take-off time cannot exceed the specified maximum delay time. Among them, θ represents the maximum allowable delay time.

[0050]

[0051] Formula (16) and Formula (17) are scheduling position constraints. Each departing flight must and can only occupy one scheduling position in the takeoff scheduling sequence, and each scheduling position must and can only be assigned to one departing flight. Where Y is the flight sequence position set, τ represents any position in the set, and γ iτ is a 0-1 variable, taking the value 1 if flight i occupies position τ and 0 otherwise;

[0052]

[0053] Formula (18) is the actual operation constraint. All flights cannot take off early. Flights departing from the same runway must meet the takeoff sequence constraint.

[0054] 4. According to the model principle and formula described in step 3, an innovative whale algorithm based on continuous-time Markov chain optimization is proposed, that is, the improved CMTC embedded whale algorithm is used to adjust the queue length of the current taxiway in real time based on a fixed queue threshold and a variable service rate, so as to adapt to the changes in the airport surface status. The specific implementation is as follows:

[0055] The first step is population initialization. Assign a population of size K X = {X1, X2, X3, ... X K}, the population X consists of multiple individuals, each of which represents a flight scheduling plan, including flight sequence and runway assignment.

[0056] The second step is fitness evaluation. The optimization target is dimensionless. i , the CMTC algorithm is run inside the scheme to correct the position of individual whales and update their status. By executing the CMTC algorithm to further optimize the individual status, if the number of runways is 2, then the output rate of the taxiway waiting queue is

[0057] The third step is to locally develop the optimal solution. Each individual whale performs a search in its neighborhood and points to the current global optimal solution, and then updates the positions of all solutions in the group relative to the position of the global optimal solution.

[0058] The fourth step is to jump out of the local optimal solution and find the global optimal value. The update position of the mandatory candidate solution points to the randomly selected solution. Assume that any random solution is the optimal candidate solution or close to the optimal solution, and perform a global search to obtain a better flight sorting solution.

[0059] In the second step, the fitness calculation requires dimensionless treatment of the two objectives, aiming to reflect the maximum possible values ​​of the different objectives. The objective is expressed as the minimum sum of the normalized delay level and the cost.

[0060]

[0061] Among them, f(X i ) ranges from [0,2]. In the present invention, the delay level and the departure cost have the same weight.

[0062] In the third step, the whale algorithm based on continuous-time Markov chain optimization needs to continuously update the position to perform iterative optimization. Define and Represent the candidate solution and the current local optimal solution in iteration t respectively. The optimization equation is as follows:

[0063]

[0064] Formula (20) indicates that when |A| < 1, it tends to conduct intensive search for the whale's next position near the current optimal solution, and decides the hunting strategy based on the random number p∈[0,1], assuming that the probability of the whale updating its position according to the contraction path and the spiral path is 0.5 respectively. and is the coefficient vector: Used to control how close or far away a searching whale moves from a selected target. It simulates the behavior of whales around prey by controlling the balance of exploration and exploitation of solutions; using the coefficient Determine the path and orientation of the whale around its prey, introduce randomness in the update of the solution position, and Set to twice its random value to enhance the global search ability of the algorithm. b is a random constant between -1 and 1. They are expressed as:

[0065]

[0066] Formula (21) to Formula (24) are supplements to Formula (20). is a random number in the interval [0,1], a represents the number of iterations t divided by the maximum number of iterations t max A linear decreasing value from 2 to 0; represents the distance between the i-th individual and the current global optimal solution from iteration t.

[0067] In the fourth step, define For any random solution in iteration t, the optimization process is as follows:

[0068]

[0069] Formula (25) indicates that when |A|≥1, a random search is performed on whale individuals far away from the current optimal solution to explore more areas of the search space. The definition of the distance value at this time is different from the third step and is expressed as follows:

[0070]

[0071] The multi-runway departure sorting optimization method based on dynamic pushback rate control proposed in the present invention shows unique advantages compared with the current traditional sorting method, including:

[0072] 1) The multi-runway airport is abstracted as a queuing system, and a continuous-time Markov chain is introduced to describe the state transition process of departing flights entering the taxiway queue. Combined with the runway assignment scheme of the flight, the service rate in each state is dynamically adjusted, thereby effectively reflecting the dynamic characteristics of the taxiway queuing system over time.

[0073] 2) The introduction of control strategies effectively reduces the taxiing waiting time of departing flights on the ground, thereby achieving better cost-effectiveness and environmental benefits, which is in line with the current trend of green aviation development.

[0074] 3) The optimization of the order of departing flights has played a significant role in reducing the level of delays. Compared with the case without optimization, the taxiing waiting time of flights has been reduced by 55.58%, and the total departure time has been reduced by 5.86%, which has effectively alleviated the congestion at the airport and improved the punctuality rate of departing flights. This proves the synergistic benefits of the joint optimization strategy in reducing delays and optimizing flight scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a schematic diagram of the overall process of the present invention.

[0076] Figure 2 is the change curve of the phase 1 cost based on the queue threshold N

[0077] Figure 3 is the iterative process of the cost function in stage 2

[0078] Figure 4 It is the peak overall strategy execution effect.

[0079] Figure 5 It is a bar chart of departure costs. DETAILED DESCRIPTION

[0080] The technical solution of the present invention will be described in detail below in conjunction with specific embodiments, but the present invention is not limited thereto.

[0081] Example:

[0082] Taking the actual departure data of a large domestic hub airport on November 1, 2013 as an example, the data set mainly includes flight number, aircraft model, planned take-off time, actual take-off time, planned push-out time, and actual push-out time. The departure data of runway 36L / 18R and runway 36R / 18L are selected for case analysis. In order to ensure the continuity of flight push-out on that day, stage one uses all-day data; stage two optimizes the sorting and assignment scheme of 147 departing flights during the peak period of 9:00-10:00 under the condition of implementing the all-day push-out control strategy. In addition, in response to relevant policies on the development of my country's civil aviation, the present invention adopts the RECAT-CN wake turbulence interval test operation standard formulated by the Civil Aviation Administration of China in 2019 based on domestic and foreign operating experience and domestic civil aviation operation characteristics. At the same time, the present invention relates to the path problem from the boarding gate to the end of the runway. This embodiment adopts the barrier-free taxiing time from the parking stand to the runway.

[0083] The present invention extends the research on linear dynamic push-out control strategy to multi-runway scenarios. In order to improve the adaptability of the model, the first stage does not distinguish between flight models, so the service intensity is set to the mean value of the wake turbulence safety interval under a certain aircraft model ratio. Figure 2 The trend of the cost value of the pushback control stage changing with the taxiway queue threshold N value is shown. Obviously, when N is less than 5, it is not shown because the cost is too large. The optimal solution is obtained when N = 9 for the dual runway case and when N = 13 for the single runway case. It shows that when the cost of stage 1 is optimal, the optimal threshold N for the dual runway case is smaller than that for the single runway case, that is, the pushback control strategy is implemented more strictly; and under different thresholds, the cost of the dual runway case is obviously lower than that of the single runway.

[0084] For the whale algorithm based on CMTC optimization proposed in this paper, the population size is set to 50 and the number of iterations is set to 100 in stage 2. The iteration process is as follows: Figure 3 Some flight plans after optimized scheduling are shown in Table 1.

[0085] Table 1 Optimized scheduling schedule (part)

[0086]

[0087] Among them, the delay reduction rate index is defined as the ratio of the difference between the unoptimized and optimized simulated take-off times to the unoptimized take-off time, thereby obtaining the optimization status of each flight. The optimized flight scheduling is subject to the influence of incoming flights, showing that runway 36R is chosen much more than runway 36L, reflecting the functionality of runway 36R as the main take-off runway; at the same time, due to the introduction of the distance factor from the parking stand to the runway, this method has achieved multi-aircraft stand grouping to a certain extent, such as flight 90 / 101, flight 99 / 105, etc., further making up for the lack of parallelism in the original push-out theory. At the same time, it can be found that not all flights can reduce delays after optimization, but for most flights, the dynamic scheduling method proposed in the present invention effectively reduces a large number of delays, especially in the excerpt, the average delay reduction rate of flights is 22.96%, and the delay reduction rate of the 15th flight is as high as 73.06%. In order to explore the impact of the collaborative scheduling method proposed in the present invention on the operation of the entire airport, four scenarios under the optimized flight sequence are analyzed respectively, namely, no sorting optimization without push-out control strategy, sorting optimization without push-out control strategy, no sorting optimization under push-out control strategy, and sorting optimization under push-out control strategy, as shown in Table 2.

[0088] Table 2 Results analysis

[0089]

[0090] By comparing the results, the implementation of the pushback strategy is mainly to convert the taxiway queue time of the flight into the parking stand waiting time, so it remains at a stable value; relatively speaking, the total waiting time after scheduling optimization has been reduced. Comparing Scenario 1 and Scenario 2, it can be seen that the flight sorting optimization method without the introduction of pushback control can effectively reduce flight delays. However, due to the lack of control over the situation on the ground, the high taxiway waiting time still generates relatively high costs. Comparing Scenario 1 and Scenario 3, it reflects the ability of the linear dynamic pushback control method optimized in this paper to reduce taxi waiting time, significantly reduce the departure operation cost, and enable the airport to have better environmental benefits. However, it is not effective in reducing flight delays. Scenario 4 is a coupled optimization based on Scenario 2 and Scenario 3, which is also the ultimate goal of this paper. Obviously, considering the flight delay based on passenger load priority, the departure cost and flight delay are further reduced, and the average flight delay is reduced by 4.58 minutes compared with the non-optimized case.

[0091] in, Figure 4 is the departure time of flights during peak hours, reflecting the flight pushback characteristics of the present invention. During continuous peak periods, the conversion effect of taxiway queue time is more significant, which is manifested in the continuous dominance of waiting at the parking position, thereby reducing the taxiing volume on the ground. The present invention sets the maximum gate occupancy time to 30 minutes. If it exceeds, the flight must be pushed back. For example, for flights 183 to 188, when consecutive flights continue to wait at the boarding gate for the maximum detention time, the corresponding taxiway queue time shows a trend of first increasing and then decreasing, which illustrates the effectiveness of the pushback control strategy during peak periods.

[0092] In terms of cost, Figure 5 The bar chart shows the push-out phase cost, fuel consumption cost, and environmental cost. Obviously, under the push-out control, the fuel consumption caused by the taxiing process is greatly reduced compared with that without push-out control, and Case 3 and 4 are reduced by about 26.61% and 30.14% compared with Case 1. Among them, the optimization effect is most significant when push-out control is combined with sequencing optimization, and the overall departure cost is reduced by 19.92% compared with the non-optimization case, which further verifies the synergistic effect of push-out control strategy and sequencing optimization method in improving airport operation efficiency.

[0093] The whale algorithm based on continuous-time Markov chain optimization is used to solve the complex multi-runway flight sequencing proposed in the present invention. The detailed solution process includes:

[0094] STEP 1: Set the initial population, set the key parameters of the whale algorithm, such as population size, number of iterations, dynamic position, etc., and generate an initial solution population, where each whale individual represents a potential sorting assignment solution.

[0095] STEP2: Execute the particle fitness evaluation. According to the objective function and constraints of the model and based on the operation results of the CMTC algorithm, calculate the individual fitness value of the whale, that is, the flight delay value and the flight departure cost.

[0096] STEP 3: Based on the evaluation results, adjust the whale's state, use the whale's local optimal position to guide its movement, and randomly judge and select the whale's predation strategy.

[0097] STEP4: To avoid premature convergence, implement a global exploration strategy to maintain the exploration of the solution space and the diversity of the population.

[0098] STEP5: Determine whether the iteration has reached the termination condition, otherwise return to STEP2 to continue iterating.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A collaborative two-stage multi-runway departure flight sequencing method, characterized in that: The steps include: The arrival and departure flight information is obtained and preprocessed. Taking the taxiway waiting cost and parking space occupancy penalty as the optimization objectives, a multi-runway dynamic launch control model is constructed to solve the optimal threshold of the optimal taxiway queue. Taking into account the flight delay cost and environmental impact, a collaborative launch sorting assignment model with the goal of minimizing flight delay and minimum operating cost is constructed. The continuous-time Markov chain interactive whale algorithm is introduced to realize the flight launch order and runway resource allocation.

2. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 1, characterized in that: The objective function of the multi-track dynamic push-out control model is: Formula (1) is the objective function, which represents the phase 1 cost of all flights. It mainly includes two parts: the fuel consumption cost of the flight waiting on the taxiway and the penalty value of parking space occupancy; where F D is the departure flight assembly, R is the runway assembly, represents the fuel cost per minute, in RMB / minute; for flight i that chooses runway r, W ir and G i They represent taxiway waiting time and gate waiting time respectively, in minutes.

3. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 2, characterized in that: The constraints of the multi-track dynamic pushback control model include: Formula (2) is the push-out rate constraint, where n is the current queue length on the taxiway, i.e., the number of flights on the ground; N is the taxiway queue threshold, which is an unknown variable. The purpose of this stage is to find the optimal N value; Formula (3) is the push interval constraint, where T i pushback represents the pushback request time, Δt represents the minimum safety interval between consecutive flights, and based on the model applicability, it is set that the two consecutive pushback flights in this stage must meet the average wake safety interval; G i ≤G max (4) Formula (4) is the parking space occupancy constraint. According to the operating rules of a large airport, a flight is considered "on time" if it is pushed out of the boarding gate within 30 minutes of the estimated departure time. Therefore, G max Set to 30 minutes; 0≤n≤N min ≤N≤N max (5) Formula (5) is the taxiway queue length constraint. The maximum taxiway queue length cannot be greater than the control threshold. The upper and lower limits of the N value are set to 30 and 1 respectively.

4. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 3, characterized in that: The method for obtaining the optimal threshold of the taxiway queue based on the fixed service rate of the multi-runway dynamic push-out control model comprises the following steps: The first step is to import the initialization data and run the model through MATLAB software; sort all flights according to their pushback application time, generate a pushback request sequence, and ensure that the flight sequence is processed according to the principle of time priority. And initialize the key parameters in the iterative algorithm, such as the initial value of the queue length, the mean value of the wake safety interval, and the taxiway capacity; In the second step, a taxiway capacity cycle is initiated, where the capacity depends on the airport configuration; In the third step, for each flight to be pushed out, a judgment is made based on the current taxiway queue length n; when the taxiway queue length is less than the taxiway capacity described in the second step, a linear dynamic push-out method is used to control flight i; when the push-out time interval is greater than or equal to μ(n) and meets the input requirements, (i+1) flights are allowed to enter the taxiway waiting queue. During the evaluation process, if the calculated G i Value exceeds G max , then the third step is interrupted and the second step is continued. This N value is marked as infeasible; Step 4: For each flight launch request, the simulation calculates the cost index under flight launch control and the cumulative cost C under the entire threshold. TN , and return to step 2; Step 5: When the maximum taxiway capacity is reached in step 2, all C TN The values ​​are compared and the optimal taxiway queue length is marked as the optimal threshold, along with its corresponding taxiway waiting time and other parameter values.

5. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 4, characterized in that: On the basis of launch rate control, we further introduce aircraft type and distance factors, and consider the scheduling stakeholders. We establish optimization goals from flight delays and departure costs. The objective function of the collaborative launch scheduling assignment model is divided into two parts: 1) Minimize flight delays C1 Formula (6) is the first objective function. The present invention reduces the flight delay loss as much as possible on the basis of making full use of airport resources; fully considers passenger satisfaction, measures the importance of flight delays by flight load factor, and represents the sum of the takeoff delay value and its importance of each flight; where, T ir is the optimized departure time of flight i, ET ir is the scheduled departure time of flight i, α i represents the ratio of the number of passengers on flight i to its maximum capacity; 2) Minimize departure cost C2 min(C P +C F +C E )(7) Formula (7) is the second objective function. Based on the concept of green civil aviation development, the present invention minimizes the sum of the additional cost of the waiting phase, the fuel consumption cost and the environmental cost caused during the taxiing phase and the taxiing phase; where C p represents the cost of waiting for the flight to be pushed out of the parking space, C F and C E represent fuel consumption cost and gas emission cost respectively; Formula (8) is a supplement to Formula (7), which represents the waiting cost of all flights at the parking stands. Controlling the push-out rate will cause some flights to stay at the parking stands and delay push-out. This cost is the fee that the airline needs to pay while the departing flights are waiting to be pushed out. is the unit cost per minute of gate waiting time for flight model a, in yuan / minute; Formula (9) is a supplement to Formula (7), which represents the fuel consumption of all flights during the taxiing waiting phase and the taxiing operation phase; and They represent the average fuel consumption rate of the flight of aircraft type a during the taxiway waiting phase and the operation phase, in kg / minute; is the obstacle-free taxiing time of flight i, in minutes; Formula (10) is a supplement to Formula (7), which represents the cost value of all flights emitting different gases; where U represents the set of pollutant gases, n engine represents the number of engines of flight i, f u is the emission coefficient of pollutant U, defined as the mass of gaseous pollutants emitted per kilogram of fuel combustion, is the external cost of unit pollutant u, in yuan / kg.

6. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 5, characterized in that: The constraints of the collaboratively launched sorting assignment model include: Formula (11) is a dynamic pushout constraint. Based on the established threshold value obtained in the first stage, the flight pushout rate is controlled according to the number of flights waiting on the taxiway after pushout. In the formula, N opt is the optimal threshold obtained in the previous stage; Formula (12) is the safety interval constraint. The two departing flights on the same runway must meet the RECAT-CN wake turbulence interval standard. Among them, F is the set of arriving and departing flights, is a 0-1 variable, which takes the value 1 if both the preceding and following flights take off or land on runway r, otherwise it takes the value 0; Formula (13) is the runway uniqueness constraint. Each flight must and can only be assigned to one runway. ir is a 0-1 variable, which takes the value 1 if flight i departs from runway r and 0 otherwise; R r(A) +R r(D) ≤1 (14) Formula (14) is the runway resource constraint. To ensure the safety of arriving and departing flights, it is stipulated that at any time, each runway can only have one flight at most. r(A) and R r(D) They represent the number of flights arriving and departing from runway r respectively; AND ir ≤T ir ≤T ir +θ (15) Formula (15) is the time window constraint. The delay time of each flight must be controlled within a certain range. The optimized flight take-off time cannot exceed the specified maximum delay time. Among them, θ represents the maximum allowable delay time. Formula (16) and Formula (17) are scheduling position constraints. Each departing flight must and can only occupy one scheduling position in the takeoff scheduling sequence, and each scheduling position must and can only be assigned to one departing flight. Where Y is the flight sequence position set, τ represents any position in the set, and γ iτ is a 0-1 variable, taking the value 1 if flight i occupies position τ and 0 otherwise; Formula (18) is the actual operation constraint. All flights cannot take off early, and the departure flights from the same runway must meet the takeoff sequence constraint.

7. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 6, characterized in that: The method for obtaining the optimal sorting assignment scheme for departing flights based on the variable service rate and the fixed taxiway queue threshold comprises the following steps: Step 1: Import the initialization data, including flight model and configuration information, flight number, aircraft type, take-off and landing starting point pairs, planned and actual take-off time, application push-out time and obstacle-free taxiing time. Run the model through MATLAB software, combined with the whale algorithm based on continuous-time Markov chain optimization, to initialize the initial parameters such as population size. Step 2: Fitness evaluation; The optimization target is dimensionless, and the CMTC algorithm is run within the scheme to correct the position of individual whales and update the status; Step 3: Locally develop the optimal solution; each individual whale performs a search in its neighborhood and points to the current global optimal solution, and then updates the positions of all solutions in the group relative to the position of the global optimal solution; Step ④: Jump out of the local optimal solution and look for the global optimal value, forcing the update position of the candidate solution to point to the randomly selected solution; assume that any random solution is the optimal candidate solution or close to the optimal solution, and perform a global search to obtain a better flight sorting solution.

8. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 7, characterized in that: In the first step, the population X={X 1, X 2, X 3，… X K }, the population X is composed of multiple individuals, each of which represents a flight scheduling solution, including flight order and runway assignment; the solution of each individual is called a position vector, which represents a position of the algorithm in the search space; for any flight scheduling solution X i ={(f1,r1),(f2,r2),…,(f n ,r n )}, the initial order of flights follows the FCFS principle.

9. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 7, characterized in that: In the second step, the two objectives are dimensionless, aiming to reflect the maximum possible value of different objectives. The target is set as the minimum sum of the normalized delay level and cost: Among them, f(X i ) ranges from [0,2]. In the present invention, the delay level and the departure cost have the same weight.

10. The collaboratively launched two-stage multi-runway departure flight sequencing method according to claim 7, characterized in that: In step ③, local development requires continuous updating of the position to perform iterative optimization. and Represent the candidate solution and the current local optimal solution in iteration t respectively. The optimization equation is as follows: Formula (20) indicates that when |A| < 1, it tends to conduct intensive search for the whale's next position near the current optimal solution, and decides the hunting strategy based on the random number p∈[0,1], assuming that the probability of the whale updating its position according to the contraction path and the spiral path is 0.5 respectively; where, and is the coefficient vector: used to control how close or far away a searching whale moves from a chosen target, controlling the balance of exploration and exploitation of solutions to simulate the behavior of whales around prey; Used to determine the path and direction of the whale around its prey, b is a random constant between -1 and 1; Formula (21) to Formula (24) are supplements to Formula (20); is a random number in the interval [0,1], a represents the number of iterations t divided by the maximum number of iterations t max A linear decreasing value from 2 to 0, represents the distance between the i-th individual and the current global optimal solution from iteration t; In step ④, define For any random solution in iteration t, the optimization process is as follows: Formula (25) indicates that when |A|≥1, a random search is performed on whale individuals far away from the current optimal solution to explore more areas of the search space. At this time, the definition of the distance value is different from that in step ③ and is expressed as follows:

Images