A dynamic landing scheduling method for carrier-based aircraft considering escape and aerial refueling

Abstract

A method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling belongs to the technical field of carrier-based aircraft sortie recovery support. First, considering the special situations that may occur during the landing process, the escape and aerial refueling situations are analyzed; secondly, according to the fleet information, the constraints and objective functions are designed to establish a carrier-based aircraft landing scheduling problem model; then, the carrier-based aircraft landing scheduling problem is solved based on the improved firefly algorithm to obtain the optimal landing plan under different escape probabilities; finally, with the optimal landing plan as the predetermined plan, an online rescheduling mechanism is designed to handle situations such as escape and aerial refueling, so as to realize the dynamic adjustment of the carrier-based aircraft landing plan. The present invention is applicable to the carrier-based aircraft landing scheduling problem considering escape and aerial refueling. After the carrier-based aircraft fleet completes the air mission, a reasonable scheduling plan is provided for the fleet to ensure the efficiency and safety of the fleet recovery, and the scheduling plan is adjusted dynamically in real time when an emergency occurs.

Description

Technical Field

[0001] The invention belongs to the technical field of carrier-based aircraft dispatching and recovery support, and relates to a carrier-based aircraft dynamic landing scheduling method taking into account escape and aerial refueling. Background Art

[0002] Traditional carrier-based aircraft landing scheduling relies on the air traffic control center to perform manual scheduling based on the existing fleet information and past experience, and to arrange and formulate a reasonable scheduling plan. The air traffic control center issues instructions to the aircraft regarding the landing runway, speed, and altitude based on the sea conditions and weather conditions, so that the aircraft is consistent with the assigned runway and maintains a safe distance from the previous aircraft. If the fleet scheduling is only completed by the air traffic control center, it will not only add a lot of burden and pressure to it, but also when the number of recovered fleets is large, it is difficult to obtain an effective scheduling plan in the short term. In recent years, the processing and transformation of carrier-based aircraft scheduling models to solve the optimal landing sequence of carrier-based aircraft fleets has received widespread attention in the field of landing scheduling. However, carrier-based aircraft have only one landing runway and the runway length is much smaller than that of land-based airports, which greatly increases the probability of carrier-based aircraft escaping.

[0003] The existing carrier-based aircraft landing scheduling problem mainly has the following two problems: on the one hand, emergencies such as escape and aerial refueling are rarely considered when the model is established. Even if they are considered, the settings are too simple and lack theoretical basis. For example, the Chinese invention patent "Online Scheduling Method for Carrier-Based Aircraft Dispatch and Recovery Based on Deep Reinforcement Learning" (CN 110781614 A) only mentions the occurrence of emergencies, but does not analyze and process them in detail; on the other hand, most studies, such as the Chinese invention patent "A Coordinated Scheduling Method for Aircraft Dispatch and Recovery on Offshore Platforms" (CN 118094778 A), only give a static scheduling plan, and do not simulate the real dynamic scheduling process. Therefore, it is impossible to dynamically adjust the landing order of carrier-based aircraft, and the optimal scheduling plan obtained by solving it cannot be verified, and the experimental results lack persuasiveness.

[0004] Therefore, it is necessary to develop a reasonable and efficient dynamic scheduling method for the reliable solution of the carrier-based aircraft landing scheduling problem considering escape and aerial refueling. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a carrier-based aircraft dynamic landing scheduling method considering escape and aerial refueling. The present invention introduces escape and aerial refueling processing to model the carrier-based aircraft landing scheduling problem and conducts relevant constraint analysis and objective function design, thereby solving the optimal scheduling solution under the meta-heuristic algorithm, and performing dynamic simulation on the basis of it. In order to ensure the safety and efficiency of carrier-based aircraft recovery landing, firstly, by introducing random variables, the possible escape and aerial refueling situations in the carrier-based aircraft landing process are analyzed and stipulated, and the carrier-based aircraft landing scheduling problem model is established by comprehensively considering indicators such as the remaining fuel amount and the degree of combat damage. An improved algorithm is designed by combining the firefly algorithm with the crossover mutation idea to solve the model. Finally, a dynamic scheduling simulation process is designed to simulate the real fleet landing process such as sequential landing, escape, aerial refueling, etc., and realize online rescheduling, verifying the effectiveness of the solution method.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling, the method comprising: step 1, considering special situations that may occur during landing, analyzing the escape and aerial refueling situations; step 2, designing constraint conditions and objective functions according to fleet information, and establishing a carrier-based aircraft landing scheduling problem model; step 3, designing an improved firefly algorithm based on evolutionary thinking, and solving the optimal landing plan for the carrier-based aircraft landing scheduling problem; step 4, taking the plan in step 3 as the initial plan, and designing an online rescheduling mechanism for special situations to dynamically adjust the landing plan. Specifically comprising the following steps:

[0008] Step 1: Consider the special situations that may occur during the landing process and analyze the escape and aerial refueling situations, specifically:

[0009] Step 1-1: Escape situation analysis;

[0010] During the recovery process, the escape of the preceding aircraft will affect the landing process of the following aircraft. Obviously, this influence is related to the recovery order of the carrier-based aircraft. That is, the later the recovery order is, the more the number of escaped aircraft in the preceding order may be, and the greater the impact will be. The number of escapes of the preceding aircraft of the carrier-based aircraft is set as a random variable , according to the assumption, it follows a binomial distribution, that is , represents the escape probability, so its expectation Calculated as formula (1):

[0011] (1)

[0012] In the formula, Indicates the order of carrier-based aircraft recovery; Indicates the number of carrier-based aircraft that may escape; Represents the number of combinations, then it is in the recycling order Extra recovery time caused by bit escape It can be set as follows:

[0013] (2)

[0014] In the formula, Indicates rounding up; It represents the maximum value of the additional recovery time caused by the escape of a carrier-based aircraft, that is:

[0015] (3)

[0016] In the formula, Indicates the flight time of the carrier-based aircraft's escape route; Indicates the maximum wake interval time.

[0017] Step 1-2: Aerial refueling situation analysis;

[0018] The carrier-based aircraft with insufficient fuel will be refueled in the air. After the refueling of the carrier-based aircraft in the air is completed, if there are other carrier-based aircraft that have not landed, the carrier-based aircraft must return to the top of the Marshall waiting route after refueling, and land after other carrier-based aircraft have completed landing. In order to avoid the situation where the subsequent carrier-based aircraft have to refuel twice or multiple times due to too many escapes of the previous carrier-based aircraft, the present invention assumes that the carrier-based aircraft Refueling amount With random variables related, is the number of carrier-based aircraft to be recovered. The probability of completely safe landing is , then the number of escape aircraft in extreme cases can be determined :

[0019] (4)

[0020] in, represents the number of carrier-based aircraft that escaped and satisfied the inequality; Represents the probability of an event occurring.

[0021] Then you can determine the amount of fuel for:

[0022] (5)

[0023] In the formula, Indicates the fuel consumption caused by one escape; represents the amount of fuel for safe landing, which can be determined as follows:

[0024] (6)

[0025] In the formula, Indicates the minimum landing fuel quantity to ensure that it can reach the aerial refueling position; Indicates the fuel consumption caused by one landing. It can ensure that carrier-based aircraft can still refuel at the tanker after escaping.

[0026] Step 2: According to the fleet information, design constraints and objective functions, and establish a carrier-based aircraft landing scheduling problem model, specifically:

[0027] Step 2-1: Description of constraints;

[0028] Step 2-1-1: Fuel constraints;

[0029] The amount of fuel is the main factor to ensure the endurance of carrier-based aircraft in the air. Indicates carrier-based aircraft The initial fuel quantity, Indicates the amount of fuel for a carrier-based aircraft at the time of landing. Limited by the carrying capacity of the carrier-based aircraft landing gear and arresting cable, to prevent damage to deck resources, the amount of fuel for a carrier-based aircraft at the time of landing should not exceed the maximum landing fuel amount. , combined with the previously set , carrier-based aircraft available The fuel quantity for a safe landing must satisfy the following constraints:

[0030] (7)

[0031] Formula (7) is called the safe fuel quantity constraint, and it is stipulated that the carrier-based aircraft that do not meet the safe fuel quantity constraint will be refueled in the air.

[0032] For ease of processing, the present invention converts the fuel quantity of the carrier aircraft into the available fuel time for subsequent research. For carrier-based aircraft The available fuel time at the initial moment can be calculated as follows:

[0033] (8)

[0034] In the formula, Indicates carrier-based aircraft The fuel consumption rate of a carrier-based aircraft is related to its size. Fuel availability at landing time for:

[0035] (9)

[0036] In the formula, Indicates carrier-based aircraft To simplify the problem, the time when the first carrier-based aircraft passes the Marshall point is is the initial moment, calculate the carrier-based aircraft The landing completion time is:

[0037] (10)

[0038] In the formula, Indicates carrier-based aircraft landing time.

[0039] Accordingly, Also converted to , respectively represent the available fuel time for safe landing, the maximum available fuel time for landing, the minimum available fuel time for landing, the flight time of the escape route and the flight time of the landing route.

[0040] Then equations (6) and (7) can be transformed into the following expressions:

[0041] (11)

[0042] (12)

[0043] In the formula, Indicates a collection of carrier-based aircraft that do not need to be refueled; Indicates a collection of carrier-based aircraft that need to be refueled.

[0044] Since the escape process is introduced, the additional recovery time caused by the escape needs to be considered. Assuming that the carrier-based aircraft The first The following improvements are made to formula (12):

[0045] (13)

[0046] in, Indicates that it is in the recycling order The extra recycling time caused by the escape of bits.

[0047] Step 2-1-2: wake turbulence interval constraint;

[0048] In the process of sequential landing of carrier-based aircraft, in order to avoid the impact of the flight wake of the preceding aircraft on the landing of the succeeding aircraft, it is stipulated that a certain time interval must be met when adjacent aircraft pass the same position on the route to ensure the safety of the recovery process, that is, to meet the following requirements:

[0049] (14)

[0050] In the formula, Indicates carrier-based aircraft The landing completion time; Indicates carrier-based aircraft The landing completion time; Indicates the preceding carrier-based aircraft and subsequent carrier-based aircraft The specific value of the wake interval is related to the models of the two carrier-based aircraft in front and behind. Generally speaking, the larger the model of the leading aircraft, the greater the impact on the flight of the following aircraft, and the longer the wake interval; on the contrary, the smaller the model of the following aircraft, the greater the impact of the wake of the preceding aircraft, and the longer the wake interval.

[0051] Step 2-2: Objective function design;

[0052] Step 2-2-1: Completeness indicator design;

[0053] use Indicates the integrity of carrier-based aircraft, The smaller the value, the lower the integrity of the carrier-based aircraft. As an evaluation indicator in the evaluation function :

[0054] (15)

[0055] in, Indicates carrier-based aircraft The completeness of Indicates carrier-based aircraft completeness.

[0056] The value of The decrease of increases, and the research shows that carrier-based aircraft that are seriously damaged should be arranged to land in advance.

[0057] Step 2-2-2: Design of task priority indicators;

[0058] use Indicates the priority of the subsequent tasks of carrier-based aircraft. The lower the value, the higher the priority of the subsequent task. Similarly, you can define :

[0059] (16)

[0060] in, Indicates carrier-based aircraft Prioritize tasks; Indicates carrier-based aircraft priority of tasks. The value of The decrease of increases, research shows that carrier-based aircraft with higher mission priority should be arranged to land in advance so that they can be put into new missions as soon as possible.

[0061] Step 2-2-3: Fuel index design;

[0062] Based on the analysis of the constraints of the available fuel time in the present invention, it can be seen that after the landing plan is determined, the available fuel time of each carrier-based aircraft at the landing time is It can be determined that, assuming that the carrier-based aircraft The first bit, you can define as follows:

[0063] (17)

[0064] The value of It decreases and increases, indicating that carrier-based aircraft with less fuel should be arranged to land in advance to avoid aerial refueling and waste of resources.

[0065] Step 2-2-4: weighted objective function design;

[0066] The present invention combines the above three evaluation indicators to design an objective function based on weighted landing completion time:

[0067] (18)

[0068] In the formula, They are the weights corresponding to completeness, task priority, and fuel; Indicates carrier-based aircraft The landing completion time; Indicates carrier-based aircraft The completeness index of Indicates carrier-based aircraft Task priority indicators; Indicates carrier-based aircraft Fuel index; Indicates carrier-based aircraft weighted indicator.

[0069] In the actual process, The value of can be determined by the top-level subjective evaluation of the air traffic control center on the current situation. They are all obtained by multiplying two positive numbers and then summing them up. , so from the sorting inequality, we can know that The minimum value is equivalent to Larger Season Smaller, soon to be carrier-based aircraft It ranks at the front of the fleet landing sequence, so the design of the objective function is reasonable.

[0070] Step 2-2-5: Design of refueling penalty items;

[0071] When a carrier-based aircraft cannot meet the safety fuel constraints, it will be refueled in the air to ensure its landing safety. Obviously, such a process can make the carrier-based aircraft that has completed the refueling of The value of the objective function is reduced. However, aerial refueling will cause resource consumption and increase the burden on dispatchers. Generally speaking, aerial refueling is only performed when it is absolutely necessary, and the number of aerial refueling is expected to be as small as possible. Therefore, the present invention introduces a penalty term to reflect the impact of aerial refueling on the objective function, that is, it is modified to:

[0072] (19)

[0073] In the formula, Indicates the number of aerial refuelings performed.

[0074] Step 2-3: Construct a carrier-based aircraft landing scheduling problem model;

[0075] Based on the processing and settings of step 1, step 2-1, and step 2-2, the carrier-based aircraft landing scheduling problem can be summarized as: by reasonably adjusting the landing order of the carrier-based aircraft group, the objective function value shown in formula (19) The smallest combinatorial optimization problem. The decision variables of the combinatorial optimization problem can be expressed by the mixed integer programming model as follows:

[0076] (20)

[0077] Based on formula (20), the mathematical model of the carrier-based aircraft landing scheduling problem can be given as follows:

[0078] (twenty one)

[0079] Subject to:

[0080] (twenty two)

[0081] (twenty three)

[0082] (twenty four)

[0083] (25)

[0084] (26)

[0085] Specifically: Formula (22) represents two constraints; Formula (23) indicates that the refueled carrier-based aircraft should land after the unrefueled carrier-based aircraft; Formula (24) indicates that the carrier-based aircraft undergoing aerial refueling can land only after refueling. Indicates carrier-based aircraft Refueling order: Indicates the time of aerial refueling. Indicates carrier-based aircraft The time to refuel; Formula (25) means that except for the first aircraft, each aircraft has only one preceding aircraft; Formula (26) means that except for the last aircraft, each aircraft has only one succeeding aircraft.

[0086] Step 3: Based on the evolutionary idea, an improved firefly algorithm is designed to solve the optimal landing plan for the carrier-based aircraft landing scheduling problem, specifically:

[0087] Step 3-1: Encoding;

[0088] The present invention uses the landing order of carrier-based aircraft to encode integers. Carrier-based aircraft from , number, then The landing order of the carrier-based aircraft is the coding order.

[0089] Step 3-2: original solution processing;

[0090] When evaluating the original scheduling plan, if there are carrier-based aircraft that need to be refueled in the plan, the carrier-based aircraft that are undergoing aerial refueling must leave the original landing sequence and refuel at the tanker position. This will cause the carrier-based aircraft to frequently move on the Marshall waiting route, resulting in an increase in the recovery time. Therefore, the present invention processes the original plan as follows:

[0091] Step 3-2-1: Add all carrier-based aircraft to the collection , determine the landing completion time of each carrier-based aircraft according to the original scheduling plan , check whether it meets the safety fuel constraint, if it does, it will land in the original order and join the landing set , proceed to step 3-2-2; if not, delete it from the original scheduling plan and add it to the aerial refueling collection , proceed to step 3-2-2;

[0092] Step 3-2-2: Update the collection ,judge Is it an empty set? If it is an empty set, proceed to step 3-2-3; otherwise, proceed to step 3-2-1;

[0093] Step 3-2-3: The available fuel time of carrier-based aircraft To sort, The smaller the size, the higher the order. After sorting, put this order in Landing is performed behind, thus forming a new recovery sequence plan, and proceeding to step 3-2-4;

[0094] Step 3-2-4: Re-determine the landing completion time of each carrier-based aircraft according to the new scheduling plan ,test Whether the carrier-based aircraft in meets the safety fuel constraint, if it does, the carrier-based aircraft will be removed from move in , proceed to step 3-2-5; if not, refuel the aircraft and remove it from move in , proceed to step 3-2-5;

[0095] Step 3-2-5: Judgment Is it an empty set? If it is an empty set, output a new sorting scheme and the process ends; otherwise, proceed to step 3-2-4;

[0096] Step 3-3: Improve the firefly algorithm;

[0097] Step 3-3-1: Firefly distance calculation;

[0098] The code of each firefly is the full permutation of n, so the distance between two fireflies is defined as the number of different elements at the corresponding positions of the code.

[0099] Step 3-3-2: Firefly position update;

[0100] Step 3-3-2-1: Location update method;

[0101] The present invention combines the crossover operation in GA (genetic algorithm) to realize the position update of fireflies. At the same time, according to the original position update formula, a new position update method is designed to obtain the specific steps as follows (assuming that the fireflies Firefly attract):

[0102] Step 3-3-2-1-1: Count fireflies and The distance between ;

[0103] Step 3-3-2-1-2: Identify fireflies and Length of the crossover segment , The calculation formula is:

[0104] (27)

[0105] In the formula, is the current iteration number; represents the light absorption coefficient; It means taking a random integer between two numbers; Firefly and The distance between.

[0106] Step 3-3-2-1-3: When the cross-segment is satisfied Under the premise of determining the fireflies and The intersection position of

[0107] Step 3-3-2-1-4: Place the fireflies Cross-segment move to Firefly Before, then delete the repeated and subsequent elements one by one, and finally form a new firefly .

[0108] Step 3-3-2-2: Setting the number of location updates;

[0109] The present invention controls the upper bound of the number of crossovers per generation according to the standard deviation of the objective function value of each iteration population to avoid meaningless searches in the later stages of iteration. At the same time, in order for the algorithm to effectively update the population and find the optimal solution, it is necessary to specify the lower bound of the number of crossovers per generation, namely:

[0110] (28)

[0111] In the formula, Indicates the number of crossovers between each individual and other individuals in the current iteration; represents the lower bound of the number of crossovers; Indicates the upper bound of the number of crossovers; represents the standard deviation of the current population; Indicates the maximum value of the population standard deviation in each generation during the iteration process; It means taking the maximum value of two numbers.

[0112] Step 3-3-3: Introduce mutation operation;

[0113] Step 3-3-3-1: Variation design;

[0114] In order to avoid the algorithm from falling into the local optimum as much as possible, a mutation operation similar to that in the genetic algorithm is introduced. The mutation methods include flip mutation, exchange mutation and insertion mutation. The specific mutation methods are as follows:

[0115] Step 3-3-3-1-1: Flip variation design;

[0116] A segment of the firefly individual code is flipped and inserted into its original position.

[0117] Step 3-3-3-1-2: exchange variation design;

[0118] Swap the positions of the two codes of a firefly individual.

[0119] Step 3-3-3-1-1: Insert mutation design;

[0120] Insert one code of the dyed firefly individual in front of another code.

[0121] Step 3-3-3-2: Setting the mutation probability;

[0122] The present invention makes the mutation probability increase with However, since mutation is not the main way of population evolution and the probability of mutation in nature is very small, the range of mutation probability is specified as [ p m _min , p m _max ] , and determined as follows:

[0123] (29)

[0124] Step 4: Take the solution in step 3 as the initial solution and design an online rescheduling mechanism for special situations to dynamically adjust the landing solution. Specifically:

[0125] Based on the initial solution obtained in step 3, the present invention simulates the real dynamic scheduling process, which includes the sequential landing, escape and aerial refueling of carrier-based aircraft, and the process of realizing dynamic rescheduling is as follows:

[0126] Step 4-1: refuel the carrier-based aircraft that need to be refueled in the recovery plan obtained in step 3 in order;

[0127] Step 4-2: Add all carrier-based aircraft to the collection in the order of the recovery solutions obtained in step 3 ;

[0128] Step 4-3: Determine whether the carrier-based aircraft in the current landing sequence has escaped. If so, proceed to step 4-4; otherwise, the carrier-based aircraft has successfully landed and the carrier-based aircraft is removed from the assembly. Move into collection , proceed to steps 4-7;

[0129] Step 4-4: Rearrange the landing order of the carrier-based aircraft that failed to land according to the assumptions made during the escape process and update the set , proceed to steps 4-5;

[0130] Step 4-5: Determine whether there are any carrier-based aircraft that do not meet the safety fuel constraint under the new landing sequence. If there are any carrier-based aircraft that do not meet the safety fuel constraint, proceed to step 4-6; otherwise, proceed to step 4-7;

[0131] Step 4-6: Perform aerial refueling on the carrier-based aircraft that do not meet the safety fuel constraint, place them at the end of the fleet for landing, and update the set , proceed to steps 4-7;

[0132] Step 4-7: Determine the set Is it an empty set? If it is an empty set, the recycling process ends; otherwise, repeat step 4-3.

[0133] The beneficial effects of the present invention are:

[0134] The present invention sets the additional recovery time and aerial refueling amount involved in the escape and aerial refueling situations by introducing random variables, providing a theoretical basis for the model processing. At the same time, the objective function is designed by integrating evaluation indicators such as carrier-based aircraft integrity, task priority, and fuel quantity, and a carrier-based aircraft landing scheduling model is established in combination with fuel constraints and wake interval constraints. According to the idea of ​​crossover mutation operator, the firefly algorithm is improved to solve the carrier-based aircraft landing scheduling model to obtain the optimal plan for carrier-based aircraft landing. On the basis of the optimal landing plan, an online rescheduling mechanism is designed to dynamically adjust the landing sequence of carrier-based aircraft when emergencies occur, thereby ensuring the landing safety and efficiency of the carrier-based aircraft fleet. BRIEF DESCRIPTION OF THE DRAWINGS

[0135] Figure 1 It is a flow chart of the present invention.

[0136] Figure 2 This is a map of the carrier-based aircraft recovery route.

[0137] Figure 3 This is a schematic diagram of the algorithm coding.

[0138] Figure 4 This is a schematic diagram of the algorithm coding.

[0139] Figure 5 Schematic diagram of firefly position update in the algorithm of the present invention.

[0140] Figure 6 Schematic diagram of the flip mutation operation during the mutation operation.

[0141] Figure 7 Schematic diagram of the exchange mutation operation during the mutation operation process.

[0142] Figure 8 Insert a mutation operation diagram during the mutation operation process.

[0143] Fig. 9 Gantt chart of the initial scheduling plan.

[0144] Fig.10 This is the Gantt chart of the actual scheduling plan. DETAILED DESCRIPTION

[0145] The present invention will be further described below with reference to specific embodiments. Figure 1 It is a flow chart of the present invention.

[0146] Consider the recovery and landing scheduling problem of a carrier-based aircraft group after completing an air mission. The recovery route diagram of the carrier-based aircraft is as follows: Figure 2 As shown. The carrier-based aircraft types are divided into three types: S, M, and L. The types, remaining fuel, integrity, and mission priority information of the carrier-based aircraft group are shown in Table 1, the wake interval time is shown in Table 2, the fuel consumption rate of different models is shown in Table 3, the model-related parameters are shown in Table 4, and the algorithm-related parameters are shown in Table 5. The embodiment shows the optimal landing scheduling solution and the dynamic rescheduling process based on it as the predetermined solution.

[0147] Table 1 Initial status information of each carrier-based aircraft

[0148]

[0149] Table 2 Wake turbulence interval time

[0150]

[0151] Table 3 Fuel consumption rate

[0152]

[0153] Table 4 Parameter settings in the model

[0154]

[0155] Table 5 Parameter settings in the algorithm

[0156]

[0157] A method for dynamic landing scheduling of carrier-based aircraft considering escape and aerial refueling comprises the following steps:

[0158] Step 1: Consider the special situations that may occur during the landing process and analyze the escape and aerial refueling situations, specifically:

[0159] Step 1-1: Escape situation analysis;

[0160] Will be in the recycling order The number of escapes of the preceding aircraft of the carrier-based aircraft is set as a random variable , according to the assumption, it follows a binomial distribution, that is , p b ∈ [ 0 , 0 . 2 ] represents the escape probability, so its expectation can be calculated as follows:

[0161] (1)

[0162] In the formula, Indicates the order of carrier-based aircraft recovery; Indicates the number of carrier-based aircraft that may escape; Represents the number of combinations, then it is in the recycling order Extra recovery time caused by bit escape It can be set as follows:

[0163] (2)

[0164] In the formula, Indicates rounding up; It represents the maximum value of the additional recovery time caused by the escape of a carrier-based aircraft, that is:

[0165] (3)

[0166] In the formula, Indicates the flight time of the carrier-based aircraft's escape route; Indicates the maximum wake interval time.

[0167] Step 1-2: Aerial refueling situation analysis;

[0168] Assuming carrier-based aircraft Refueling amount The amount of refueling and the random variable related, is the number of carrier-based aircraft to be recovered. , then the number of escape aircraft in extreme cases can be determined :

[0169] (4)

[0170] in, represents the number of carrier-based aircraft that escaped and satisfied the inequality; Represents the probability of an event occurring.

[0171] Then the refueling amount can be determined as:

[0172] (5)

[0173] In the formula, Indicates the fuel consumption caused by one escape; represents the amount of fuel for safe landing, which can be determined as follows:

[0174] (6)

[0175] In the formula, Indicates the minimum landing fuel quantity to ensure that it can reach the aerial refueling position; Indicates the fuel consumption caused by one landing. It can ensure that carrier-based aircraft can still refuel at the tanker after escaping.

[0176] Step 2: According to the fleet information, design constraints and objective functions, and establish a carrier-based aircraft landing scheduling problem model, specifically:

[0177] Step 2-1: Description of constraints;

[0178] Step 2-1-1: Fuel constraints;

[0179] The amount of fuel is the main factor to ensure the endurance of carrier-based aircraft in the air. Indicates carrier-based aircraft The initial fuel quantity, Indicates the amount of fuel for a carrier-based aircraft at the time of landing. Limited by the carrying capacity of the carrier-based aircraft landing gear and arresting cable, to prevent damage to deck resources, the amount of fuel for a carrier-based aircraft at the time of landing should not exceed the maximum landing fuel amount. , combined with the previously set , carrier-based aircraft available The fuel quantity for a safe landing must satisfy the following constraints:

[0180] (7)

[0181] Formula (7) is called the safe fuel quantity constraint, and it is stipulated that the carrier-based aircraft that do not meet the safe fuel quantity constraint will be refueled in the air.

[0182] For ease of processing, the present invention converts the fuel quantity of the carrier aircraft into the available fuel time for subsequent research. For carrier-based aircraft The available fuel time at the initial moment can be calculated as follows:

[0183] (8)

[0184] In the formula, Indicates carrier-based aircraft The fuel consumption rate of a carrier-based aircraft is related to its size. Fuel availability at landing time for:

[0185] (9)

[0186] In the formula, Indicates carrier-based aircraft In order to simplify the problem, this paper takes the time when the first carrier-based aircraft passes the Marshall point as is the initial moment, calculate the carrier-based aircraft The landing completion time is:

[0187] (10)

[0188] In the formula, Indicates carrier-based aircraft landing time.

[0189] Accordingly, Also translates to: , respectively represent the available fuel time for safe landing, the maximum available fuel time for landing, the minimum available fuel time for landing, the flight time of the escape route and the flight time of the landing route.

[0190] Then equations (6) and (7) can be transformed into the following expressions:

[0191] (11)

[0192] (12)

[0193] In the formula, Indicates a collection of carrier-based aircraft that do not need to refuel. Indicates a collection of carrier-based aircraft that need to be refueled.

[0194] Since the escape process is introduced, the additional recovery time caused by the escape needs to be considered. Assuming that the carrier-based aircraft The first The following improvements are made to formula (12):

[0195] (13)

[0196] in, Indicates that it is in the recycling order The extra recycling time caused by the escape of bits.

[0197] Step 2-1-2: Wake turbulence interval constraint;

[0198] In the process of sequential landing of carrier-based aircraft, in order to avoid the impact of the flight wake of the preceding aircraft on the landing of the succeeding aircraft, it is stipulated that a certain time interval must be met when adjacent aircraft pass the same position on the route to ensure the safety of the recovery process, that is, to meet the following requirements:

[0199] (14)

[0200] In the formula, Indicates carrier-based aircraft The landing completion time; Indicates carrier-based aircraft The landing completion time; Indicates the preceding carrier-based aircraft and subsequent carrier-based aircraft The specific value of the wake interval is related to the models of the two carrier-based aircraft in front and behind. Generally speaking, the larger the model of the leading aircraft, the greater the impact on the flight of the following aircraft, and the longer the wake interval; on the contrary, the smaller the model of the following aircraft, the greater the impact of the wake of the preceding aircraft, and the longer the wake interval.

[0201] Step 2-2: Objective function design;

[0202] Step 2-2-1: Completeness indicator design;

[0203] use I ∈ [ 0 , 1 ] Indicates the integrity of carrier-based aircraft. The smaller the value, the lower the integrity of the carrier-based aircraft. As the evaluation index in the evaluation function:

[0204] (15)

[0205] in, Indicates carrier-based aircraft The completeness of Indicates carrier-based aircraft completeness. The value of The decrease of increases, and the research shows that carrier-based aircraft that are seriously damaged should be arranged to land in advance.

[0206] Step 2-2-2: Design of task priority indicators;

[0207] use P ∈ [ 1 , 5 ] Indicates the priority of the subsequent tasks of carrier-based aircraft. The lower the value, the higher the priority of the subsequent task. :

[0208] (16)

[0209] in, Indicates carrier-based aircraft Prioritize tasks; Indicates carrier-based aircraft priority of tasks. The value of The decrease of increases, research shows that carrier-based aircraft with higher mission priority should be arranged to land in advance so that they can be put into new missions as soon as possible.

[0210] Step 2-2-3: Fuel index design;

[0211] Based on the analysis of the constraints of the available fuel time in the present invention, it can be seen that after the landing plan is determined, the available fuel time of each carrier-based aircraft at the landing time is It can be determined that, assuming that the carrier-based aircraft The first bit, you can define as follows:

[0212] (17)

[0213] The value of It decreases and increases, indicating that carrier-based aircraft with less fuel should be arranged to land in advance to avoid aerial refueling and waste of resources.

[0214] Step 2-2-4: weighted objective function design;

[0215] The present invention combines the above three evaluation indicators to design an objective function based on weighted landing completion time:

[0216] (18)

[0217] In the formula, They are the weights corresponding to completeness, task priority, and fuel respectively. Indicates carrier-based aircraft The landing completion time; Indicates carrier-based aircraft The completeness index of Indicates carrier-based aircraft Task priority indicators; Indicates carrier-based aircraft Fuel index; Indicates carrier-based aircraft weighted indicator.

[0218] In practice, their values ​​can be determined by the top-level subjective evaluation of the air traffic control center on the current situation. They are all obtained by multiplying two positive numbers and then summing them up. , so from the sorting inequality, we can know that The minimum value is equivalent to Larger Season Smaller, soon to be carrier-based aircraft It ranks at the front of the fleet landing sequence, so the design of the objective function is reasonable.

[0219] Step 2-2-5: Design of refueling penalty items;

[0220] The penalty term is introduced to reflect the impact of aerial refueling on the objective function, which is modified to:

[0221] (19)

[0222] In the formula, Indicates the number of aerial refuelings performed.

[0223] Step 2-3: Construct a carrier-based aircraft landing scheduling problem model;

[0224] Based on the processing and settings of step 1, step 2-1, and step 2-2, the carrier-based aircraft landing scheduling problem is summarized as adjusting the landing order of the carrier-based aircraft group reasonably so that the objective function value shown in formula (19) The smallest combinatorial optimization problem. The decision variables of the combinatorial optimization problem can be expressed by the mixed integer programming model as follows:

[0225] (20)

[0226] Based on formula (20), the mathematical model of the carrier-based aircraft landing scheduling problem can be given as follows:

[0227] (twenty one)

[0228] Subject to:

[0229] (twenty two)

[0230] (twenty three)

[0231] (twenty four)

[0232] (25)

[0233] (26)

[0234] Specifically: Formula (22) represents two constraints; Formula (23) indicates that the refueled carrier-based aircraft should land after the unrefueled carrier-based aircraft; Formula (24) indicates that the carrier-based aircraft undergoing aerial refueling can land only after refueling. Indicates carrier-based aircraft Refueling order: Indicates the time of aerial refueling. Indicates carrier-based aircraft The time to refuel; Formula (25) means that except for the first aircraft, each aircraft has only one preceding aircraft; Formula (26) means that except for the last aircraft, each aircraft has only one succeeding aircraft.

[0235] Step 3: Based on the evolutionary idea, an improved firefly algorithm is designed to solve the optimal landing plan for the carrier-based aircraft landing scheduling problem, specifically:

[0236] Step 3-1: Encoding;

[0237] The present invention uses the landing order of carrier-based aircraft to encode integers. Carrier-based aircraft from Number, then The landing order of the carrier-based aircraft is the coding order. The coding diagram is as follows: Figure 3 , Figure 4 shown.

[0238] Step 3-2: original solution processing;

[0239] When evaluating the original scheduling plan, if there are carrier-based aircraft that need to be refueled in the plan, the carrier-based aircraft that are undergoing aerial refueling must leave the original landing sequence and refuel at the tanker position. This will cause the carrier-based aircraft to frequently move on the Marshall waiting route, resulting in an increase in the recovery time. Therefore, the present invention processes the original plan as follows:

[0240] Step 3-2-1: Add all carrier-based aircraft to the collection , determine the landing completion time of each carrier-based aircraft according to the original scheduling plan , check whether it meets the safety fuel constraint, if it does, it will land in the original order and join the landing set , proceed to step 3-2-2; if not, delete it from the original scheduling plan and add it to the aerial refueling collection , proceed to step 3-2-2;

[0241] Step 3-2-2: Update the collection ,judge Is it an empty set? If it is an empty set, proceed to step 3-2-3; otherwise, proceed to step 3-2-1;

[0242] Step 3-2-3: The available fuel time of carrier-based aircraft To sort, The smaller the size, the higher the order. After sorting, put this order in Landing is performed behind, thus forming a new recovery sequence plan, and proceeding to step 3-2-4;

[0243] Step 3-2-4: Re-determine the landing completion time of each carrier-based aircraft according to the new scheduling plan ,test Whether the carrier-based aircraft in meets the safety fuel constraint, if it does, the carrier-based aircraft will be removed from move in , proceed to step 3-2-5; if not, refuel the aircraft and remove it from move in , proceed to step 3-2-5;

[0244] Step 3-2-5: Judgment Is it an empty set? If it is an empty set, output a new sorting scheme and the process ends; otherwise, proceed to step 3-2-4;

[0245] Step 3-3: Improve the firefly algorithm;

[0246] Step 3-3-1: Firefly distance calculation;

[0247] The code for each firefly is Therefore, the distance between two fireflies is defined as the number of different elements in the corresponding positions of the code.

[0248] Step 3-3-2: Firefly position update;

[0249] Step 3-3-2-1: Location update method;

[0250] The present invention combines the crossover operation in GA (genetic algorithm) to realize the position update of fireflies. At the same time, according to the original position update formula, a new position update method is designed to obtain the specific steps as follows (assuming that the fireflies Firefly attract):

[0251] Step 3-3-2-1-1: Count fireflies and The distance between ;

[0252] Step 3-3-2-1-2: Identify fireflies and Length of the crossover segment , The calculation formula is:

[0253] (27)

[0254] In the formula, is the current iteration number; represents the light absorption coefficient; It means taking a random integer between two numbers; Firefly and The distance between

[0255] Step 3-3-2-1-3: When the cross-segment is satisfied Under the premise of determining the fireflies and The intersection position of

[0256] Step 3-3-2-1-4: Place the fireflies Cross-segment move to Firefly Before, then delete the repeated and subsequent elements one by one, and finally form a new firefly , the specific crossover operation is as follows Figure 5 shown.

[0257] Step 3-3-2-2: Setting the number of location updates;

[0258] The present invention controls the upper bound of the number of crossovers per generation according to the standard deviation of the objective function value of each iteration population to avoid meaningless searches in the later stages of iteration. At the same time, in order for the algorithm to effectively update the population and find the optimal solution, it is necessary to specify the lower bound of the number of crossovers per generation, namely:

[0259] (28)

[0260] In the formula, Indicates the number of crossovers between each individual and other individuals in the current iteration. represents the lower bound of the number of crossovers, represents the upper bound of the number of crossovers, represents the standard deviation of the current population, It represents the maximum value of the population standard deviation in each generation during the iteration process. It means taking the maximum value of two numbers.

[0261] Step 3-3-3: Introduce mutation operation;

[0262] Step 3-3-3-1: Variation design;

[0263] In order to avoid the algorithm from falling into the local optimum as much as possible, a mutation operation similar to that in the genetic algorithm is introduced. The mutation methods include flip mutation, exchange mutation and insertion mutation. The specific mutation methods are as follows:

[0264] Step 3-3-3-1-1: Flip variation design;

[0265] Flip a segment of the firefly individual code and insert it into the original position. The specific flip mutation operation is as follows: Figure 6 shown.

[0266] Step 3-3-3-1-2: exchange variation design;

[0267] Exchange the positions of the two codes of the firefly individual. The specific exchange mutation operation is as follows: Figure 7 shown.

[0268] Step 3-3-3-1-1: Insert mutation design;

[0269] Insert one code of the firefly individual in front of another code. The specific insertion mutation operation is as follows: Figure 8 shown.

[0270] Step 3-3-3-2: Setting the mutation probability;

[0271] This project makes the mutation probability increase with However, since mutation is not the main way of population evolution and the probability of mutation in nature is very small, the range of mutation probability is specified as [ p m _min , p m _max ] = [ 0 . 1 , 0 . 5 ] , and determined as follows:

[0272] (29)

[0273] For this embodiment, the initial solution Gantt chart obtained in step 3 is as follows: Fig. 9 As shown, five carrier-based aircraft need to be refueled in the air.

[0274] Step 4: Take the plan in step 3 as the initial plan, and design an online rescheduling mechanism for special situations to dynamically adjust the landing plan;

[0275] Based on the initial solution obtained in step 3, the real dynamic scheduling process is simulated, including the sequential landing, escape and aerial refueling of carrier-based aircraft. The process of dynamic rescheduling is as follows:

[0276] Step 4-1: refuel the carrier-based aircraft that need to be refueled in the recovery plan obtained in step 3 in order;

[0277] Step 4-2: Add all carrier-based aircraft to the collection in the order of the recovery solutions obtained in step 3 ;

[0278] Step 4-3: Determine whether the carrier-based aircraft in the current landing sequence has escaped. If so, proceed to step 4-4; otherwise, the carrier-based aircraft has successfully landed and the carrier-based aircraft is removed from the assembly. Move into collection , proceed to steps 4-7;

[0279] Step 4-4: Rearrange the landing order of the carrier-based aircraft that failed to land according to the assumptions made during the escape process and update the set , proceed to steps 4-5;

[0280] Step 4-5: Determine whether there are any carrier-based aircraft that do not meet the safety fuel constraint under the new landing sequence. If there are any carrier-based aircraft that do not meet the safety fuel constraint, proceed to step 4-6; otherwise, proceed to step 4-7;

[0281] Step 4-6: Perform aerial refueling on the carrier-based aircraft that do not meet the safety fuel constraint, place them at the end of the fleet for landing, and update the set , proceed to steps 4-7;

[0282] Step 4-7: Determine the set Is it an empty set? If it is an empty set, the recycling process ends; otherwise, repeat step 4-3.

[0283] The simulation is carried out based on the initial plan obtained in step 3. The Gantt chart of the actual execution scheduling plan is as follows: Fig.10 As shown. In the initial stage, the carrier-based aircraft group lands sequentially according to the initial scheduling plan. When a carrier-based aircraft escapes during landing, such as the No. 21 carrier-based aircraft, it needs to immediately enter the escape route to wait for landing, and wait for the No. 20 and No. 7 carrier-based aircraft that have entered the landing route to complete landing, and then make a second landing from point E on the escape route. When a carrier-based aircraft escapes multiple times, such as the No. 13 and No. 5 carrier-based aircraft, this will greatly increase the recovery time, and then cause the No. 16 carrier-based aircraft that can land safely in the initial scheduling plan to need to refuel in the air. The online rescheduling mechanism handles special situations during the landing process and dynamically adjusts the landing order of the carrier-based aircraft group.

[0284] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling, characterized in that: The carrier-based aircraft dynamic landing scheduling method is as follows: Step 1: Consider the special situations that may occur during the landing process and analyze the escape and aerial refueling situations; Step 2: According to the fleet information, design constraints and objective functions, and establish a carrier-based aircraft landing scheduling problem model; specifically: Step 2-1: Description of constraints; Step 2-1-1: Fuel constraints; Step 2-1-2: wake turbulence interval constraint; Step 2-2: Objective function design; Step 2-2-1: Completeness indicator design; I is used to represent the integrity of carrier-based aircraft, and As an evaluation indicator in the evaluation function Among them, I i Indicates the integrity of carrier-based aircraft i; I j represents the integrity of carrier-based aircraft j; The value of I i The carrier-based aircraft that are seriously damaged should be arranged to land in advance; Step 2-2-2: Design of task priority indicators; P is used to represent the priority of the subsequent tasks of the carrier-based aircraft. The lower the value of P, the higher the priority of the subsequent tasks. Similarly, we can define Among them, P i represents the mission priority of carrier-based aircraft i; P j represents the mission priority of carrier-based aircraft j; The value of P i The decrease of increases, carrier-based aircraft with higher mission priority should be arranged to land in advance; Step 2-2-3: Fuel index design; After the landing plan is determined, the available fuel time FT of each carrier-based aircraft at the landing time can be determined. i,l , assuming that the carrier aircraft i is in the kth position of the recovery sequence, then define as follows: The value of FT i,l The decrease of ART indicates that the carrier-based aircraft with less fuel should be arranged to land in advance. k Indicates the extra recovery time caused by the escape at the kth position in the recovery order; FT safe Indicates the time available for fuel to land safely; Step 2-2-4: weighted objective function design; An objective function based on weighted landing completion time is proposed: Where μ1, μ2, and μ3 are the weights corresponding to completeness, task priority, and fuel respectively; LCT i represents the landing completion time of carrier-based aircraft i; represents the integrity index of carrier-based aircraft i; represents the mission priority index of carrier-based aircraft i; represents the fuel index of carrier-based aircraft i; J i represents the weighted index of carrier-based aircraft i; Step 2-2-5: Design of refueling penalty items; The impact of aerial refueling on the objective function is reflected by introducing a penalty term, that is, formula (18) is adjusted to: Where n rf Indicates the number of aerial refuelings; Step 2-3: Construct a carrier-based aircraft landing scheduling problem model; Based on the processing and settings of step 1, step 2-1, and step 2-2, the carrier-based aircraft landing scheduling problem is summarized as a combinatorial optimization problem that minimizes the objective function value J shown in formula (19) by reasonably adjusting the landing order of the carrier-based aircraft group. The decision variables of the combinatorial optimization problem are expressed by a mixed integer programming model as follows: Based on formula (20), the mathematical model of the carrier-based aircraft landing scheduling problem is given as follows: Subject to: Constraints (13)-(14) (22) x ij =0,i∈Ω1;j∈Ω0 (23) LCT i ≥s i ·T F +RFT i ,i∈Ω1 (24) Formula (22) represents two constraints; Formula (23) indicates that the refueled carrier-based aircraft should land after the unrefueled carrier-based aircraft; Formula (24) indicates that the carrier-based aircraft undergoing aerial refueling can land only after refueling. In the formula, s i represents the refueling order of carrier-based aircraft i, T F Indicates the air refueling time, RFT i represents the time when carrier-based aircraft i goes to refuel; Formula (25) indicates that except for the first aircraft, each aircraft has only one preceding aircraft; Formula (26) indicates that except for the last aircraft, each aircraft has only one succeeding aircraft; Step 3, design an improved firefly algorithm based on evolutionary thinking to solve the optimal landing plan for the carrier-based aircraft landing scheduling problem; Step 4: Using the optimal landing plan determined in step 3 as the initial plan, design an online rescheduling mechanism for special situations and dynamically adjust the landing plan. The constraints of step 2-1 are specifically: Step 2-1-1: Fuel constraints; Adopt F i represents the fuel quantity of carrier aircraft i at the initial moment, F i,l Indicates the fuel quantity of the carrier-based aircraft at the time of landing; the fuel quantity of the carrier-based aircraft at the time of landing should not exceed the maximum landing fuel quantity F max , combined with the set F safe , the fuel quantity of carrier-based aircraft i for safe landing must satisfy the constraint: F safe ≤F i,l ≤F max (7) Formula (7) is called the safe fuel quantity constraint, and it is stipulated that the carrier-based aircraft that do not meet the safe fuel quantity constraint will be refueled in the air; Convert the fuel quantity of the carrier aircraft into the available fuel time, record FT i is the available fuel time of carrier aircraft i at the initial moment, which can be calculated as follows: In the formula, fcr i represents the fuel consumption rate of carrier-based aircraft i; then the available fuel time FT of carrier-based aircraft i at the time of landing i,l for: FT i,l =FT i -LCT i (9) Where, LCT i represents the landing completion time of carrier-based aircraft i. To simplify the problem, the time T0 when the first carrier-based aircraft passes through the Marshall point is taken as the initial time, and the landing completion time of carrier-based aircraft i is calculated, that is, LCT i =LT i -T0 (10) In the formula, LT i represents the landing time of carrier-based aircraft i; Accordingly, F safe ,F max ,F min ,F b ,F l Also converted to FT safe ,FT max ,FT min ,T b ,T l , respectively represent the available fuel time for safe landing, the maximum available fuel time for landing, the minimum available fuel time for landing, the flight time of the escape route and the flight time of the landing route; Then equations (6) and (7) are transformed into the following expressions: FT safe =FT min +T b +T l (11) In the formula, Ω0 represents the set of carrier-based aircraft that do not need to be refueled; Ω1 represents the set of carrier-based aircraft that need to be refueled; Considering the extra recovery time caused by escape, assuming that carrier aircraft i is located at the kth position in the recovery sequence, equation (12) is improved as follows: Among them, ART k Indicates the extra recycling time caused by the escape at the kth position in the recycling order; Step 2-1-2: wake turbulence interval constraint; During the process of sequential landing of carrier-based aircraft, it is stipulated that a certain time interval must be met when adjacent aircraft pass the same position on the route to ensure the safety of the recovery process, that is, to meet the following requirements: LCT i -LCT j ≥WIT ij (14) Where, LCT i Indicates the landing completion time of carrier-based aircraft i; LCT j WIT represents the landing completion time of carrier-based aircraft j; ij represents the wake interval between the preceding carrier-based aircraft i and the succeeding carrier-based aircraft j.

2. The method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling according to claim 1, characterized in that: The specific steps include: Step 1: Consider the special situations that may occur during the landing process and analyze the escape and aerial refueling situations, specifically: Step 1-1: Escape situation analysis; The number of escapes of the preceding aircraft of the carrier-based aircraft in the kth position of the recovery order is set as a random variable X k , which follows a binomial distribution, that is, X k ~B(k-1,p b ), p b represents the escape probability, whose expectation is E(X k ); the extra recovery time caused by the escape at the kth position in the recovery order is ART k Set as follows: In the formula, Indicates rounding up; ART max It represents the maximum value of the additional recovery time caused by the escape of a carrier-based aircraft, that is: ART max =T b +WIT max (3) Where, T b Indicates the flight time of the carrier-based aircraft escape route; WIT max Indicates the maximum wake interval time; Step 1-2: Aerial refueling situation analysis; Assume that the refueling amount RF of carrier-based aircraft i is i With random variable X n The probability of completely safe landing is defined as p. s , then the number of escape planes n in extreme cases can be determined w : Where l represents the number of carrier-based aircraft that escape and satisfy the inequality; P(·) represents the probability of the event occurring; Determine the refueling amount RF i for: RF i =n b ·F b +F safe (5) In the formula, F b Indicates the fuel consumption caused by one escape; F safe Indicates the amount of fuel for safe landing; Step 2: According to the fleet information, design constraints and objective functions, and establish a carrier-based aircraft landing scheduling problem model; Step 3: Based on the evolutionary idea, an improved firefly algorithm is designed to solve the optimal landing plan for the carrier-based aircraft landing scheduling problem. Specifically: Step 3-1: Encoding; The landing order of the carrier-based aircraft is used for integer coding, and n carrier-based aircraft are numbered from 1 to n. Then the landing order of the n carrier-based aircraft is the coding order; Step 3-2: original solution processing; Step 3-2-1: Add all carrier-based aircraft to the set Ω ul , determine the landing completion time LCT of each carrier-based aircraft according to the original scheduling plan, and check whether it meets the safety fuel constraint. If it does, it will land in the original order and join the landing set Ω l , proceed to step 3-2-2; if not, delete it from the original scheduling plan and add it to the aerial refueling set Ω rf , proceed to step 3-2-2; Step 3-2-2: Update the set Ω ul =Ω ul -Ω l -Ω rf , judge Ω ul Is it an empty set? If it is an empty set, proceed to step 3-2-3; otherwise, proceed to step 3-2-1; Step 3-2-3: Ω rf The carrier-based aircraft in the sequence are sorted by the available fuel time FT. The smaller the FT, the higher the order. After sorting, the sequence is placed in Ω l Landing is performed behind, thus forming a new recovery sequence plan, and proceeding to step 3-2-4; Step 3-2-4: Re-determine the landing completion time LFT of each carrier-based aircraft according to the new scheduling plan, and check Ω rf Does the carrier-based aircraft in meet the safety fuel constraint? If it does, the carrier-based aircraft will be removed from Ω rf Move in Ω l , proceed to step 3-2-5; if not, refuel the aircraft and move the aircraft from Ω rf Move in Ω l , proceed to step 3-2-5; Step 3-2-5: Determine Ω rf Is it an empty set? If it is an empty set, output a new sorting scheme and the process ends; otherwise, proceed to step 3-2-4; Step 3-3: Improve the firefly algorithm; Step 3-3-1: Firefly distance calculation; The code of each firefly is the full permutation of n, and the distance between two fireflies is defined as the number of different elements at the corresponding positions of the code; Step 3-3-2: Firefly position update; Step 3-3-2-1: Location update method; Combine the crossover operation in the genetic algorithm GA to realize the position update of fireflies, and design a new position update method based on the original position update formula; Step 3-3-2-2: Setting the number of location updates; The upper bound of the number of crossovers per generation is controlled according to the standard deviation of the objective function value of each iteration population. At the same time, in order to effectively update the population and find the optimal solution, the lower bound of the number of crossovers per generation needs to be specified, that is: Where n c Indicates the number of crossovers between each individual and other individuals in the current iteration; n c_min represents the lower bound of the number of crossovers; n c_max Indicates the upper bound of the number of crossovers; std indicates the standard deviation of the current population; std max Indicates the maximum value of the population standard deviation of each generation during the iteration process; max() means taking the maximum value of two numbers; Step 3-3-3: Introduce mutation operation; Step 3-3-3-1: Variation design; Step 3-3-3-2: Setting the mutation probability; Make the mutation probability change with the change of std, and specify the range of mutation probability [p m_min ,p m_max ] and determined as follows: Step 4: Take the plan determined in step 3 as the initial plan, design an online rescheduling mechanism for special situations, and dynamically adjust the landing plan. The process of implementing dynamic rescheduling is as follows: Step 4-1: refuel the carrier-based aircraft that need to be refueled in the recovery plan obtained in step 3 in order; Step 4-2: Add all carrier-based aircraft to the set Ω in the order of the recovery solutions obtained in step 3. ul ; Step 4-3: Determine whether the carrier-based aircraft in the current landing sequence escapes. If so, proceed to step 4-4; otherwise, the carrier-based aircraft successfully lands and the carrier-based aircraft is removed from the set Ω. ul Move into set Ω l , proceed to steps 4-7; Step 4-4: Rearrange the landing order of the carrier-based aircraft that failed to land according to the assumptions during the escape process, and update the set Ω ul , proceed to step 4-5; Step 4-5: Determine whether there is a carrier-based aircraft that does not meet the safety fuel constraint under the new landing sequence. If there is a carrier-based aircraft that does not meet the safety fuel constraint, proceed to step 4-6; otherwise, proceed to step 4-7; Step 4-6: Perform aerial refueling on the carrier-based aircraft that do not meet the safety fuel constraint, and place it at the end of the fleet for landing, updating the set Ω ul , proceed to steps 4-7; Step 4-7: Determine the set Ω ul Is it an empty set? If it is an empty set, the recycling process ends; otherwise, repeat step 4-3.

3. The method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling according to claim 2, characterized in that: In step 1: The E(X k ) is calculated as formula (1): In the formula, k represents the recovery order of carrier-based aircraft; j represents the number of possible escaped carrier-based aircraft; Indicates the number of combinations; The amount of fuel for safe landing F safe Calculated as formula (6): F safe =F min +F b +F l (6) In the formula, F min Indicates the minimum landing fuel quantity to ensure that it can reach the aerial refueling position; F l Indicates the fuel consumption caused by one landing; F safe It can ensure that carrier-based aircraft can still refuel at the tanker after escaping.

4. The method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling according to claim 2, characterized in that: The step 3-3-2-1 is specifically as follows, assuming that firefly i is attracted by firefly j: Step 3-3-2-1-1: Calculate the distance r between fireflies i and j ij ; Step 3-3-2-1-2: Determine the length a of the intersection segment between fireflies i and j. The calculation formula for a is: a=random(1,r ij ·γ gen ) (27) In the formula, gen is the current iteration number; γ represents the light absorption coefficient; random() represents a random integer between two numbers; r ij represents the distance between fireflies i and j; Step 3-3-2-1-3: Under the premise that the intersection segment is a, determine the intersection position of fireflies i and j; Step 3-3-2-1-4: Move the cross-segment of firefly j to the front of firefly i, and then delete the repeated elements that are located behind in turn, and finally form a new firefly i.

5. The method for dynamic carrier-based aircraft landing scheduling considering escape and aerial refueling according to claim 2, characterized in that: In the step 3-3-3-1, the mutation modes include flip mutation, exchange mutation and insertion mutation. The specific mutation modes are as follows: Step 3-3-3-1-1: Flip variation design; A segment of the firefly individual code is flipped and inserted into its original position; Step 3-3-3-1-2: exchange variation design; Swap the positions of the two codes of a firefly individual; Step 3-3-3-1-1: Insert mutation design; Insert one code of the dyed firefly individual in front of another code.

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