A robust control method for large-scale flights under uncertain conditions

Abstract

This invention relates to a robust scheduling method for large-scale flights under uncertain conditions, belonging to the field of aircraft scheduling and control technology. The method of this invention is based on robust optimization using a genetic algorithm and stochastic repair based on adaptive search. Specifically, the robust optimization process based on the genetic algorithm follows the genetic algorithm flow, encoding chromosomes with real numbers, considering the worst-case scenario (maximum wake interval) for the wake interval, randomly generating an initial chromosome population, repairing genes using feasible solutions, selecting offspring chromosomes using a binary tournament algorithm, employing a sequence mutation operator based on wake interval differences, and using an elite preservation strategy to generate a new generation of chromosomes. The stochastic repair based on adaptive search uses chromosome robustness assessment based on uncertain parameter sampling, while simultaneously enhancing chromosome robustness. Under the constraints of large-scale flights and complex conditions containing uncertainties, a feasible and robust flight scheduling scheme can be provided in a short time.

Description

Technical Field

[0001] This invention belongs to the field of aircraft scheduling and control technology, specifically relating to a robust control method for large-scale flights under uncertain conditions. Background Technology

[0002] With the booming growth of China's economy and the rapid development of its air transport industry, the number of flights and air traffic volume have increased dramatically, leading to frequent air congestion at major airports. Traditional air traffic flow management methods schedule landing flights under the assumption of deterministic constraints. However, due to the complexity and randomness of the real-world environment, the constraints on landing flights (such as wake turbulence intervals and arrival times) are often uncertain. This uncertainty in landing flight constraints poses a significant challenge to flight scheduling methods. Inappropriate scheduling can cause severe air congestion, seriously affecting flight safety, and the resulting flight delays can lead to substantial economic losses. A robust flight scheduling method applicable to uncertain constraints would play an invaluable role. However, flight scheduling problems with uncertain constraints face challenges such as large solution scale, difficulty in quantifying uncertainty parameters, and the lack of robustness of the optimal solution.

[0003] Most existing flight scheduling methods are based on deterministic constraints, ignoring the uncertainty of these constraints, resulting in unromantic solutions. A few methods that consider the uncertainty of constraints only model the taxiing time of landing flights, leaving gaps in the modeling of arrival times and the uncertainty of wake turbulence intervals. In real-world scenarios, the uncertain approach speeds of landing flights lead to uncertain wake turbulence intervals, making existing flight scheduling algorithms unable to meet the scheduling requirements of such environments. Summary of the Invention

[0004] Based on the above analysis, the embodiments of the present invention aim to provide a robust control method for large-scale flights under uncertain conditions, and particularly to a robust control method for large-scale flight landings under uncertain conditions, in order to solve the problem of poor robustness in existing large-scale flight landing scheduling.

[0005] The present invention provides a robust control method for large-scale flight landings under uncertain conditions, characterized by comprising the following steps:

[0006] Step 1: Construct an uncertainty model for the wake time interval of continuously landing flights;

[0007] Step 2: Construct a source flight landing sequence model based on the uncertainty model of the wake time interval of consecutively landing flights;

[0008] Step 3: Use a genetic algorithm to obtain the source chromosomes and their fitness in the source flight landing order model;

[0009] Step 4: Select offspring chromosomes from the source chromosomes according to the binary tournament principle;

[0010] Step 5: Mutate all offspring chromosomes to obtain mutated offspring chromosomes;

[0011] Step 6: Generate new chromosomes based on the fitness ranking of the mutated offspring chromosomes and the source chromosome;

[0012] Step 7: Initialize and sort the new gene vectors using the adaptive search-based random repair algorithm;

[0013] Step 8: Generate chromosome segment vectors based on the sorted new gene vectors;

[0014] Step 9: Evaluate the robustness value of chromosome segments in the chromosome segment vector;

[0015] Step 10: Repair the new genes on the new chromosome based on the robustness value of each chromosome segment to obtain robust chromosome segments;

[0016] Step 11: Fill in the new chromosome with the robust chromosome fragment to obtain a new robust chromosome fragment;

[0017] Step 12: Use the new robust chromosome fragment to decode into a flight plan for flight scheduling of large-scale flights.

[0018] Optionally, in step 1, the expression for the uncertainty model of the wake time interval of consecutively landing flights is:

[0019]

[0020]

[0021] Where ψ is the wake time interval between the subsequent landing flight F and the preceding landing flight L; D is the total length of the approach path; V0 is the speed of the flight on the approach path; z is a random variable; S FL δV is the wake separation distance between the later landing flight F and the earlier landing flight L. L The uncertainty of the approach speed of the first landing flight L; δV F Let be the uncertainty of the approach speed of flight F;

[0022] The probability density function of the random variable z is:

[0023]

[0024] in,

[0025] Optionally, in step 2, the steps for constructing the source flight landing sequence model based on the wake time interval uncertainty model of consecutively landing flights are as follows:

[0026] The objective function for minimizing the landing order model of the source flights is expressed as:

[0027]

[0028] Among them, A a For the designated landing time of flight a, T a Let N be the estimated landing time of flight a, N be the total number of flights waiting to be dispatched, and Z be the total delay time.

[0029] Based on the uncertainty model of the wake time interval for consecutively landing flights, the constraint condition for the wake time interval is established, and the expression is as follows:

[0030] A b ≥A a +S a，b x ab -(L a -T b )x ba ;

[0031] Among them, flight a and flight b are two consecutive flights that landed one after the other. b The designated landing time for flight b; T b x is the estimated landing time for flight b; ab and x ba x indicates the order in which flights a and b land. When flight a lands before flight b, x ab x is 1 ba x is 0 when flight b lands before flight a. ab x is 0 ba =1; S a，b Let S be the wake turbulence interval between flights a and b. a，b L was obtained using a wake time interval uncertainty model for consecutively landing flights; a This refers to the latest landing time for flight A.

[0032] Establish the constraints generated by the flight's time in the air, expressed as follows:

[0033] T a ≤A a ≤L a .

[0034] Optionally, step 3, which uses a genetic algorithm to obtain the source chromosomes in the source flight landing order model, is as follows:

[0035] Step 31: Initialize the parameters of the genetic algorithm and the parameters of the source flight landing order model;

[0036] Initialize the genetic algorithm parameters: Let the number of source chromosomes be M; in the first iteration, iter = 1, where iter is the current iteration number, and iter = 1, 2, ..., Gen, where Gen is the total number of iterations;

[0037] Initialize the parameters of the source flight landing sequence model:

[0038] Let A a max = L a A a min = T a Among them, A a max and A a min represents the maximum and minimum values ​​of the specified landing time for flight a, respectively.

[0039] Let the maximum wake separation between flight a and flight b be

[0040] Step 32: Construct the gene coding vector for each source chromosome in the population;

[0041] The genes of each source chromosome represent the designated landing times for all flights, for the i-th source chromosome. The source gene encoding was obtained, and the source gene encoding vector was... N is the total number of source genes contained in each source chromosome; For the i-th source chromosome The designated landing time of flight n, i.e., the i-th source chromosome. The nth source gene

[0042] Step 33: Randomly initialize all source genes of each source chromosome;

[0043] Step 34: Reassign values ​​to all source genes on each source chromosome;

[0044] Step 35: Obtain the fitness of each source chromosome.

[0045] Optionally, step 33, which involves randomly initializing all source genes on each source chromosome, is as follows:

[0046] Let the first original gene A1 on each source chromosome be... i The initial value is the estimated landing time T1 of its corresponding flight; let the other source genes A of each source chromosome be... m i The initial value is A m i=T m +rand×300,m=2,3,...,N,T m Let be the estimated landing time of flight m, and rand be a random number uniformly distributed between 0 and 1.

[0047] Optionally, the step of reassigning values ​​to all source genes on each source chromosome in step 34 is as follows:

[0048] Sort all source genes of each source chromosome in ascending order according to the initial values ​​in step 33 to obtain the sorted source gene B for each source chromosome. k i k = 1, 2, ..., N, and obtain the source gene A for each source chromosome. n i and sequencing source gene B k i The source mapping relationship, where B k i The k-th source gene in the sequence;

[0049] Let the first sequenced source gene B1 on each source chromosome be... i The updated value is the estimated landing time of its corresponding flight; let the other sequenced source genes B on each source chromosome be... s i The updated value is B s i =B s-1 i +S s-1，s max s = 2, 3, ..., N, where S s-1,s max For the s-th sequencing source gene B s i The corresponding source gene refers to the flight and the (s-1)th sorted source gene B. s-1 i The corresponding source gene represents the maximum wake turbulence time interval of the flight; according to the source mapping relationship, the source gene B of each source chromosome is sorted. k i The updated value is assigned to the source gene on the corresponding source chromosome. The source gene of the source chromosome Obtain new assignment

[0050] Optionally, the step of obtaining the fitness of each source chromosome in step 35 is as follows:

[0051] Determine each source chromosome Does it meet the constraints of the flight wake time interval in step 2 and the constraints generated by the flight's loiter time?

[0052] If the i-th source chromosome If the constraints are met, the fitness of the source chromosome is: Among them, T n This is the estimated landing time for flight number n;

[0053] If the i-th source chromosome The constraints are not met; the fitness of this source chromosome is... Where E represents the maximum penalty.

[0054] Optionally, in step 5, the step of mutating all offspring chromosomes to obtain mutated offspring chromosomes is as follows:

[0055] Step 51: Separate each offspring chromosome All source genes are sorted in ascending order according to the specified landing time to obtain the sorted offspring genes. For the p-th offspring chromosome, The sequenced gene is the I-th offspring gene on the p-th offspring chromosome, where p = 1, 2, ..., N, j = 1, 2, ..., N;

[0056] Step 52: Calculate the mutation probability PM of the p-th offspring chromosome. p ;

[0057] Step 53: Randomly generate a real number between 0 and 1. If the real number is less than PM... p Then the p-th offspring chromosome The j-th offspring sequenced genes Mapping back to the j'th flight of the source chromosome Mapping the sorted genes of the (j+1)th progeny on the p-th progeny chromosome back to the (j+1)'th progeny chromosome Transform the specified landing time by swapping it; if the real number is greater than or equal to PM... p The sequenced genes of the j-th offspring on the p-th offspring chromosome are mapped back to the j'-th flight number on the source chromosome. Mapping the sorted genes of the (j+1)th progeny on the p-th progeny chromosome back to the (j+1)'th progeny chromosome The designated landing time remains unchanged;

[0058] Step 54: Increment the gene sorting j of the offspring by 1, and repeat steps 52-54 until j equals N. All offspring chromosomes will undergo mutation to obtain mutated offspring chromosomes.

[0059] Step 55: Reassign genes to the offspring chromosomes of the mutated offspring chromosomes and calculate the fitness of all offspring chromosomes.

[0060] Optionally, in step 52, the mutation probability PM of the p-th offspring chromosome is calculated. p The expression is:

[0061] PM p =1 / (1+e) -dmp )×(L j’,p -T (j+1)’,p -S j’,(j+1)’,p ) / |(L j’,p -T (j+1)’,p -S j’,(j+1)’,p )|;

[0062] Among them, dm p L is the offset factor of the p-th offspring chromosome; e is the natural constant; j' is the flight number of the j-th offspring sequence gene mapped back to the source chromosome from the p-th offspring chromosome, j' = 1, 2, ..., N; L j’,p Map the sequenced genes of the j-th offspring on the p-th offspring chromosome back to the j'-th flight on the source chromosome; T (j+1)’ Map the sequenced genes of the (j+1)th progeny on the p-th progeny chromosome back to the (j+1)'-th progeny on the source chromosome; S j’,(j+1)’,p Map the sorted genes of the jth and (j+1)th offspring on the pth offspring chromosome back to the tail flow interval of the j'th and (j+1)'th flights on the source chromosome.

[0063] Optionally, in step 52, the offset factor dm p The expression is:

[0064] dm p =10 / (1+exp(-2S) (j-1)’,j’,p -2S (j-1)’,(j+1)’,p +S j’,(j+1)’,p -S (j+1)’,j’,p -5;

[0065] Where exp is the exponent of taking e; S (j-1)’,j’,p For the (j-1)th and jth progeny sequencing genes of the p-th progeny chromosome, map them back to the (j-1)'th and j'th flights of the source chromosome; S (j-1)’,(j+1)’,p For the (j-1)th and (j+1)th progeny genes on the p-th progeny chromosome, map them back to the (j-1)'th and (j+1)'th flight times on the source chromosome; S j’,(j+1)’,p S represents the wake interval between the j-th and (j+1)-th descendant genes of the p-th descendant chromosome and their corresponding descendant sequenced genes, mapped back to the source chromosome. (j+1)’,j’Map the (j+1)th and jth descendant sequencing genes of the pth descendant chromosome back to the (j+1)′th and j'th flights of the source chromosome for the tail turbulence interval.

[0066] Compared with the prior art, the present invention has at least the following beneficial effects:

[0067] The method of this invention is based on robust optimization using a genetic algorithm and stochastic repair based on adaptive search. The robust optimization process based on the genetic algorithm follows the genetic algorithm flow, encoding chromosomes with real numbers, considering the worst-case scenario (maximum tail gap) for the tail gap, randomly generating an initial chromosome population, repairing genes using feasible solutions, selecting offspring chromosomes using a binary tournament algorithm, employing a sequence mutation operator based on tail gap differences, and using an elite retention strategy to generate a new generation of chromosomes. The stochastic repair based on adaptive search uses chromosome robustness assessment based on uncertain parameter sampling, while simultaneously enhancing chromosome robustness. Under complex constraints with large flight volumes and uncertainties, a feasible and robust flight scheduling scheme can be provided in a short time. Attached Figure Description

[0068] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0069] Figure 1 This is a flowchart of the robust control method of the present invention;

[0070] Figure 2 This is a flowchart of the genetic algorithm of the present invention;

[0071] Figure 3 This is a flowchart of the stochastic optimization algorithm of the present invention. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] A specific embodiment of the present invention, such as Figure 1-3 A robust control method for large-scale flight landings under uncertain conditions is disclosed, comprising the following steps:

[0074] Step 1: Construct an uncertainty model for the wake time interval of continuously landing flights.

[0075] Step 11: Establish a wake time interval model for consecutively landing flights;

[0076] The expression for the position of the first landing flight is:

[0077] X L =(V L +δV L )t;

[0078] Among them, X L The distance between the first landing flight L and the starting point of the approach path; V L The approach speed of the first landing flight L; δV L For the uncertainty of the approach speed of the first landing flight L, δV L It follows a mean of 0 and a standard deviation of . The random variable is normally distributed; t is the flight time of the first landing flight L in the approach channel. When t = 0, the first landing flight L just enters the approach channel.

[0079] The expression for the position of the later landing flight is:

[0080] X F =(V F +δV F (t-μ);

[0081] Among them, X F V represents the distance between the approach flight F and the starting point of the approach path; F δV is the approach speed of the following landing flight F. F Let δV be the uncertainty of the approach speed of flight F. F It follows a mean of 0 and a standard deviation of . The random variable is normally distributed; μ is the wake time interval between the later landing flight F and the earlier landing flight L.

[0082] The expression for the time it takes for the first landing flight L to land on the runway:

[0083]

[0084] Among them, t L0 The time it takes for the first landing flight L to land on the runway is given, and D is the total length of the approach path.

[0085] Obtain at time t L0 The position of the landing flight F after the time is expressed as:

[0086]

[0087] Furthermore,

[0088] Among them, X F (t L0 ) is at time t L0 At that time, the position of the subsequent landing flight F.

[0089] Optionally,

[0090] The expression for the wake distance interval between the later landing flight F and the earlier landing flight L is:

[0091] DX F (t L0 ) = S FL ;

[0092] Among them, S FL This is the wake separation distance between flight F, which lands later, and flight L, which lands earlier.

[0093] The expression for the wake time interval between the later landing flight F and the earlier landing flight L is:

[0094]

[0095] Optionally, flights can be made to have the same speed on the approach path, which is V0, i.e., V F =V L =V0; The expression for the wake time interval between the later landing flight F and the earlier landing flight L is:

[0096]

[0097] Step 12: Based on the wake time interval between the later landing flight F and the earlier landing flight L obtained in Step 11, establish an uncertainty model for the wake time interval of consecutively landing flights.

[0098] The expression for the uncertainty model of the wake time interval of consecutively landing flights is:

[0099]

[0100]

[0101] Where z is a random variable; V0+δV F It follows a mean of V0 and a variance of . The normal distribution; Follow the mean variance is The normal distribution; It follows a Cauchy distribution.

[0102] The probability density function of the random variable z is:

[0103]

[0104] in,

[0105] Step 2: Construct a source flight landing sequence model based on the uncertainty model of the wake time interval of consecutively landing flights;

[0106] The objective function for minimizing the landing order model of the source flights is expressed as:

[0107]

[0108] Among them, A a For the designated landing time of flight a, T a Let N be the estimated landing time of flight a, N be the total number of flights waiting to be scheduled, and Z be the total delay time.

[0109] It is understandable that the objective function of the source flight landing sequence model is to minimize the total delay time of all flights.

[0110] Based on the uncertainty model of the wake time interval for consecutively landing flights established in step 1, the constraint conditions for the wake time interval of flights are established, and the expression is as follows:

[0111] A b ≥A a +S a，b x ab -(L a -T b )x ba ;

[0112] Among them, flight a and flight b are two consecutive flights that landed one after the other. b The designated landing time for flight b; T b x is the estimated landing time for flight b; ab and x ba x indicates the order in which flights a and b land. When flight a lands before flight b, x ab x is 1 ba x is 0 when flight b lands before flight a. ab x is 0 ba =1; S a，b S is the wake time interval between flights a and b. a，b Use the wake time interval uncertainty model for consecutively landing flights established in step 1; L a This is the latest landing time for flight a.

[0113] Optionally, to ensure the uniqueness of the landing order of flights a and b, flight constraints are established, expressed as follows:

[0114] Establish the constraints generated by the flight's time in the air, expressed as follows:

[0115] T a ≤A a ≤L a .

[0116] Step 3: Use a genetic algorithm to solve for the source chromosomes and their fitness in the source flight landing order model from Step 2;

[0117] Step 31: Initialize the parameters of the genetic algorithm and the parameters of the source flight landing order model;

[0118] Initialize the genetic algorithm parameters: Let the number of source chromosomes be M; in the first iteration, iter = 1, where iter is the current iteration number, and iter = 1, 2, ..., Gen, where Gen is the total number of iterations;

[0119] Initialize the parameters of the source flight landing sequence model:

[0120] Let A a max = L a A a min = T a Among them, A a max and A a min represents the maximum and minimum values ​​of the specified landing time for flight a, respectively.

[0121] Let the maximum wake separation between flight a and flight b be

[0122] Step 32: Construct the gene coding vector for each source chromosome in the population;

[0123] The genes of each source chromosome represent the designated landing times for all flights, for the i-th source chromosome. The source gene encoding was obtained, and the source gene encoding vector was... N is the total number of source genes contained in each source chromosome; For the i-th source chromosome The designated landing time of flight n, i.e., the i-th source chromosome. The nth source gene

[0124] Step 33: Randomly initialize all source genes of each source chromosome;

[0125] Let the first original gene A1 on each source chromosome be... i The initial value is the estimated landing time T1 of its corresponding flight; let the other source genes A of each source chromosome be... m i The initial value is A m i =T m +rand×300,m=2,3,...,N,T mLet be the estimated landing time of flight m, and rand be a random number uniformly distributed between 0 and 1.

[0126] Step 34: Reassign values ​​to all source genes on each source chromosome;

[0127] Sort all source genes of each source chromosome in ascending order according to the initial values ​​in step 33 to obtain the sorted source gene B for each source chromosome. k i k = 1, 2, ..., N, and obtain the source gene A for each source chromosome. n i and sequencing source gene B k i The source mapping relationship, where B k i The k-th source gene in the sequence;

[0128] Let the first sequenced source gene B1 on each source chromosome be... i The updated value is the estimated landing time of its corresponding flight; let the other sequenced source genes B on each source chromosome be... s i The updated value is B s i =B s-1 i +S s-1，s max s = 2, 3, ..., N, where S s-1，s max For the s-th sequencing source gene B s i The corresponding source gene refers to the flight and the (s-1)th sorted source gene B. s-1 i The corresponding source gene represents the maximum wake turbulence time interval of the flight; according to the source mapping relationship, the source gene B of each source chromosome is sorted. k i The updated value is assigned to the source gene on the corresponding source chromosome. The source gene of the source chromosome Obtain new assignment

[0129] Step 35: Obtain the fitness of each source chromosome.

[0130] Determine each source chromosome Does it meet the constraints of the flight wake time interval in step 2 and the constraints generated by the flight's loiter time?

[0131] If the i-th source chromosome If the constraints are met, the fitness of the source chromosome is: Among them, Tn This is the estimated landing time for flight number n;

[0132] If the i-th source chromosome The constraints are not met; the fitness of this source chromosome is...

[0133] Where E is the maximum penalty, preferably E = 100000.

[0134] Step 4: Select offspring chromosomes according to the binary tournament principle;

[0135] Step 41: Randomly select 2 source chromosomes from M source chromosomes, and use the source chromosome with lower fitness among the 2 randomly selected source chromosomes as the offspring chromosome;

[0136] Step 42: Return the chromosome with higher fitness from the two randomly selected source chromosomes to the population; repeat step 41 until the number of offspring chromosomes is N.

[0137] Step 5: Perform mutations on the chromosomes of all offspring;

[0138] Step 51: Separate each offspring chromosome All source genes are sorted in ascending order according to the specified landing time to obtain the sorted offspring genes. For the p-th offspring chromosome, Let J be the sequenced gene of the j-th offspring on the p-th offspring chromosome, where p = 1, 2, ..., N, j = 1, 2, ..., N;

[0139] Step 52: Calculate the mutation probability PM of the p-th offspring chromosome. p The expression is:

[0140]

[0141] Among them, dm p L is the offset factor of the p-th offspring chromosome; e is the natural constant; j' is the flight number of the j-th offspring sequence gene mapped back to the source chromosome from the p-th offspring chromosome, j' = 1, 2, ..., N; L j’,p Map the sequenced genes of the j-th offspring on the p-th offspring chromosome back to the j'-th flight on the source chromosome; T (j+1)’ Map the sequenced genes of the (j+1)th progeny on the p-th progeny chromosome back to the (j+1)'-th progeny on the source chromosome; S j’,(j+1)’,p Map the sorted genes of the jth and (j+1)th offspring on the pth offspring chromosome back to the tail flow interval of the j'th and (j+1)'th flights on the source chromosome.

[0142] Wherein, the offset factor dm p The expression is:

[0143] dm p =10 / (1+exp(-2S) (j-1)’,j’,p -2S (j-1)’,(j+1)’,p +S j’,(j+1)’,p -S (j+1)’,j’,p -5;

[0144] Where exp is the exponent of taking e; S (j-1)’,j’,p For the (j-1)th and jth progeny sequencing genes of the p-th progeny chromosome, map them back to the (j-1)'th and j'th flights of the source chromosome; S (j-1)’,(j+1)’,p For the (j-1)th and (j+1)th progeny genes on the p-th progeny chromosome, map them back to the (j-1)'th and (j+1)'th flight times on the source chromosome; S j’,(j+1)’,p S represents the wake interval between the j-th and (j+1)-th descendant genes of the p-th descendant chromosome and their corresponding descendant sequenced genes, mapped back to the source chromosome. (j+1)’,j’ Let (j+1)th and jth progeny sequencing genes of the pth progeny chromosome be mapped back to the (j+1)'th and j'th flights of the source chromosome;

[0145] Step 53: Randomly generate a real number between 0 and 1. If the number is less than PM... p Then, the sequenced gene of the j-th offspring on the p-th offspring chromosome is mapped back to the j'-th gene on the source chromosome. Mapping the sorted genes of the (j+1)th progeny on the p-th progeny chromosome back to the (j+1)'th progeny chromosome Transform the value by swapping the specified landing time; if the number is greater than or equal to PM... p The sequenced genes of the j-th offspring on the p-th offspring chromosome are mapped back to the j'-th flight number on the source chromosome. Mapping the sorted genes of the (j+1)th progeny on the p-th progeny chromosome back to the (j+1)'th progeny chromosome The designated landing time remains unchanged.

[0146] Step 54: Increment the gene sorting j of the offspring by 1, and repeat steps 52-54 until j equals N. All offspring chromosomes have completed the mutation and obtained mutated offspring chromosomes.

[0147] Step 55: Perform step 34 on the mutated offspring chromosomes to reassign gene values ​​to the offspring chromosomes, and then perform step 35 to calculate the fitness of all offspring chromosomes.

[0148] Step 6: Generate new chromosomes based on the fitness ranking of the offspring chromosomes and the source chromosomes;

[0149] Sort the fitness of the offspring chromosomes and the source chromosomes from smallest to largest, and retain the top N chromosomes as iterative chromosomes; increment the current iteration number iter by 1, return to step 4, and iteratively evolve the source chromosomes until iter = Gen to obtain a new chromosome.

[0150] Step 7: Initialize and sort the new gene vectors using the adaptive search-based random repair algorithm;

[0151] Obtain the new chromosome with the lowest fitness from the new chromosomes generated in step 6. s = 1, 2, ..., S, where S is the total number of new chromosomes with the lowest fitness; the new genes on the new chromosomes are encoded to obtain the new gene encoding vector as D = (D1, ..., D2). n ), n=1,2,…,N; Sort the new genes in ascending order according to their specified landing time to obtain the sorted new gene vector h=(h1,h2,…,h n ), n=1,2,…,N, where h n Let h be the index of the nth-ranked source gene within the source chromosome in the original vector. For example, when h... n When equal to 1, That is, D1 ranks nth.

[0152] Step 8: Generate chromosome fragment vectors based on the sorted new gene vectors obtained in Step 7;

[0153] Let there be variable k, k = n. When k equals 1, what is the robust optimal vector? The first chromosome segment vector When k is greater than 1, the vector of the kth chromosome segment temp k-1 (1, 2) is the vector of the (k-1)th robust chromosome segment; h is the indicator vector for the s-th new chromosome; k This is the index of the k-th ranked source gene in the original vector.

[0154] Step 9: Evaluate the robustness of the chromosome segment;

[0155] Sample r random variables z, and calculate the h-th probability density function of each of the r random variables z. k-1 Flight number h and kThe wake interval of flight number 1; calculate the fitness of chromosome segments for each wake interval under the condition of r random variables z according to step 35; calculate the average fitness of all chromosome segments, which is the robustness value ψ of the chromosome segment.

[0156] Step 10: Apply robustness values ​​for each chromosome segment to the new chromosome. The new gene was repaired to obtain a robust chromosome fragment;

[0157] The adjustment factor is calculated based on the robustness value of the chromosome segment, and the expression is:

[0158]

[0159] Where θ is the adjustment factor and rand is a random number uniformly distributed between 0 and 1.

[0160] The vector temp of the kth chromosome segment k Recalculate the k-th robust chromosome segment The expression is:

[0161]

[0162] in, This is the k-th robust chromosome segment; It is the hth generation generated by sampling k-1 Flight number h and k Wake turbulence interval of flight number [number] It is the hth k-1 Flight number h and k The maximum wake turbulence interval for flight number [number].

[0163] Evaluate the robustness value of the newly generated chromosome fragment. If the robustness value is lower than the historical robustness value, replace the original chromosome fragment with the newly generated chromosome fragment and replace the historical robustness value with the robustness value. Then repeat step 10 until the number of loops reaches the preset number of loops to obtain a robust chromosome fragment.

[0164] Step 11: Fill in the new chromosome with the robust chromosome fragment to obtain the new robust chromosome fragment, expressed as:

[0165]

[0166] in, For new robust chromosome segments; temp k (1,2) represents the vectors of k robust chromosome segments;

[0167] Then k is incremented by 1, and the process returns to step 8. The next vector component of the robust optimal vector is then randomly optimized until all robust optimal vectors are optimized, resulting in a robust optimal chromosome of dimension n. This robust optimal chromosome is the robust optimal solution of the source model in step 2.

[0168] Understandably, the robust optimal solution of the source model in step 2 is the solution that minimizes the total flight delay time when landing time is scheduled under the condition of uncertain flight wake intervals.

[0169] Step 12: Use the new robust chromosome fragment to decode into a flight plan for flight scheduling of large-scale flights.

[0170] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust control method for large-scale flight landings under uncertain conditions, characterized in that, Includes the following steps: Step 1: Construct an uncertainty model for the wake time interval of continuously landing flights; Step 2: Construct a source flight landing sequence model based on the uncertainty model of the wake time interval of consecutively landing flights; Step 3: Use a genetic algorithm to obtain the source chromosomes and their fitness in the source flight landing order model; Step 4: Select offspring chromosomes from the source chromosomes according to the binary tournament principle; Step 5: Mutate all offspring chromosomes to obtain mutated offspring chromosomes; Step 6: Generate new chromosomes based on the fitness ranking of the mutated offspring chromosomes and the source chromosome; Step 7: Initialize and sort the new gene vectors using the adaptive search-based random repair algorithm; Step 8: Generate chromosome segment vectors based on the sorted new gene vectors; Step 9: Evaluate the robustness value of chromosome segments in the chromosome segment vector; Step 10: Repair the new genes on the new chromosome based on the robustness value of each chromosome segment to obtain robust chromosome segments; Step 11: Fill in the new chromosome with the robust chromosome fragment to obtain a new robust chromosome fragment; Step 12: Decode the new robust chromosome fragment into a flight plan for large-scale flight scheduling; In step 1, the expression for the uncertainty model of the wake time interval of consecutively landing flights is: ； ； in, For flights that land later F Compared to the flights that landed earlier L The wake interval; D This is the total length of the approach channel; The speed of the flight on the approach path; z It is a random variable; For flights that land later F Compared to the flights that landed earlier L The wake separation distance; For the first flight to land L Uncertainty regarding the approach velocity; Let be the uncertainty of the approach speed of flight F; random variable z The probability density function is: ； in, , , , ; In step 2, the steps for constructing the source flight landing sequence model based on the uncertainty model of the wake time interval of consecutively landing flights are as follows: The objective function for minimizing the landing order model of the source flights is expressed as: f ( Z )=Min ; in, For flights The designated landing time, For flights The estimated landing time, The total number of flights waiting to be scheduled; Z Total delay time; Based on the uncertainty model of the wake time interval for consecutively landing flights, the constraint condition for the wake time interval is established, and the expression is as follows: ； Among them, flights a and flights b These are two consecutive flights that landed in quick succession. A b For flights b The designated landing time; T b For flights b The estimated landing time; x ab and x ba For flights a and flights b The order of landing is indicated when flights... On the flight During the previous landing, x ab =1, x ba The value is 0 when the flight b On the flight a During the previous landing, x ab =0, x ba =1; For flights a and flights b Wake time interval, wake time interval Obtained using a wake time interval uncertainty model for consecutively landing flights; For flights Latest landing time; Establish the constraints generated by the flight's time in the air, expressed as follows: 。 2. The robust control method according to claim 1, characterized in that, Step 3 involves obtaining the source chromosomes in the source flight landing order model using a genetic algorithm: Step 31: Initialize the parameters of the genetic algorithm and the parameters of the source flight landing order model; Initialize genetic algorithm parameters: Let the number of source chromosomes be... M In the first iteration, iter=1, where iter is the current iteration number, and iter=1,2,…,Gen, where Gen is the total number of iterations. Initialize the parameters of the source flight landing sequence model: make A a max = L a , A a min= T a ; in, A a max and A a min represents the number of flights a The maximum value of the specified landing time and the flight a The minimum specified landing time; Order the flight a and flights b The maximum wake interval is =max( ); Step 32: Construct the gene coding vector for each source chromosome in the population; The genes of each source chromosome represent the designated landing times for all flights, for the first... i source chromosome The source gene encoding was obtained, and the source gene encoding vector was... A i = , i= 1,2,…, M , n= 1,2,…, N , N This represents the total number of source genes contained in each source chromosome. For the first i source chromosome The n The designated landing time for flight number [number], i.e., [number] i source chromosome The n Individual genes ; Step 33: Randomly initialize all source genes of each source chromosome; Step 34: Reassign values ​​to all source genes on each source chromosome; Step 35: Obtain the fitness of each source chromosome.

3. The robust control method according to claim 2, characterized in that, Step 33 involves randomly initializing all source genes on each source chromosome as follows: Let the first original gene of each source chromosome A 1 i The initial value is the estimated landing time of its corresponding flight. T 1; Let the other source genes on each source chromosome be... A m i The initial value is A m i = , m =2,3,…, N , T m For the first m The estimated landing time of flight number [number] rand These are random numbers that are uniformly distributed between 0 and 1.

4. The robust control method according to claim 2 or 3, characterized in that, The step 34, which involves reassigning values ​​to all source genes on each source chromosome, is as follows: Sort all source genes of each source chromosome in ascending order according to the initial values ​​in step 33 to obtain the sorted source genes of each source chromosome. Bki , k =1,2,…, N And obtain the source genes of each source chromosome. Ani and sequencing source genes Bki The source mapping relationship, where, Bki For the first k The source gene for the sequence number; Let the first sequence of source genes on each source chromosome be... B 1 i The updated value is the estimated landing time of its corresponding flight; let the other sequenced source genes of each source chromosome be... Bsi The updated value is Bsi = Bs-1i + S s-1，s max , s =2,3,…, N ,in, S s-1，s max For the first s Sequencing source genes Bsi The corresponding source gene refers to the flight and the first s -1 source gene for sequencing Bs-1i The corresponding source gene represents the maximum wake turbulence time interval of the flight; according to the source mapping relationship, the source genes of each source chromosome are sorted. Bki The updated value is assigned to the source gene on the corresponding source chromosome. The source gene of the source chromosome Obtain new assignment .

5. The robust control method according to claim 4, characterized in that, The steps in step 35 to obtain the fitness of each source chromosome are as follows: Determine each source chromosome Does it meet the constraints of the flight wake time interval in step 2 and the constraints generated by the flight's loiter time? If the i source chromosome If the constraints are met, the fitness of the source chromosome is: ,in, T n For the first n The estimated landing time of flight number [number]; If the i source chromosome The constraints are not met; the fitness of this source chromosome is... ,in, E This constitutes an extremely large punishment.

6. The robust control method according to claim 1, characterized in that, Step 5 involves mutating all offspring chromosomes to obtain mutated offspring chromosomes. Step 51: Separate each offspring chromosome All source genes are sorted in ascending order according to the specified landing time to obtain the sorted offspring genes. Cjp , For the first p sliver generation chromosome, Cjp For the first p The first chromosome of the offspring j Sequencing genes in each offspring. p =1,2,…, N , j =1,2,…, N ; Step 52, calculate the first... p Chromosomal mutation probability in offspring PM p ; Step 53: Randomly generate a real number between 0 and 1. If the real number is less than 1... PM p Then the first p progeny chromosome The j Genetic sequencing of offspring Cjp Mapping back to the source chromosome j Flight No. and the p The first chromosome of the offspring j +1 offspring sorted genes mapped back to the source chromosome ( ) j +1) ’ Flight No. Transform the specified landing time by swapping it; if the real number is greater than or equal to... PM p , No. p The first chromosome of the offspring j The sequenced genes of each offspring are mapped back to the source chromosome. j Flight No. and the p The first chromosome of the offspring j +1 offspring sorted genes are mapped back to the source chromosome at the ( )th ( j +1) ’ Flight No. The designated landing time remains unchanged; Step 54: Offspring Sequencing and Gene Sequencing j Increase by 1, and repeat steps 52-54 until... j equal N All offspring chromosomes undergo mutation to obtain mutated offspring chromosomes; Step 55: Reassign genes to the offspring chromosomes of the mutated offspring chromosomes and calculate the fitness of all offspring chromosomes.

7. The robust control method according to claim 6, characterized in that, In step 52, calculate the first p Chromosomal mutation probability in offspring PM p The expression is: PM p =1 / (1+ e -dm p )×( L j’,p - T (j+1)’,p - S j’,(j+1)’,p ) / |( L j’,p - T (j+1)’,p - S j’,(j+1)’,p )|； in, dm p For the first p The shift factor of offspring chromosomes; e It is a natural constant; j 'For the first p The first chromosome of the offspring j The sequenced genes of each offspring are mapped back to the source chromosome. j Flight number ' j =1,2,…, N ; L j’,p For the first p The first chromosome of the offspring j The sequenced genes of each offspring are mapped back to the source chromosome. j The latest landing time for flight number '; T (j+1)’ For the first p The first chromosome of the offspring j +1 offspring sorted genes are mapped back to the source chromosome at the ( )th ( j +1) ’ The estimated landing time of flight number [number]; S j’,(j+1)’,p For the first p The first chromosome of the offspring j The and the first j +1 offspring sequencing genes mapped back to the source chromosome's first... j Flight No. ' and ( j +1) ’ The wake interval of flight number 1.

8. The robust control method according to claim 7, characterized in that, Offset factor in step 52 dm p The expression is: dm p =10 / (1+ exp (-2 S (j-1)’,j’,p -2 S (j-1)’,(j+1)’,p + S j’,(j+1)’,p - S (j+1)’,j’, p )-5； in, exp To take the exponent of e; S (j-1)’,j’,p For the first p The first chromosome of the offspring j -1 and the first j Each offspring's sequenced genes are mapped back to the source chromosome at the ( )th ( ) j Flight -1) and the j The wake turbulence interval of flight number '; S (j-1)’,(j+1)’,p For the first p The first chromosome of the offspring j -1 and the first j +1 offspring sorted genes are mapped back to the source chromosome at the ( )th ( j Flight -1)' and ( j +1) ’ The wake turbulence interval of flight number 1; S j’,(j+1)’,p For the first p The first chromosome of the offspring j The and the first j +1 offspring sequencing genes mapped back to the source chromosome's first... j Flight No. ' and ( j +1) ’ The wake turbulence interval of flight number 1; S (j+1)’,j’ For the first p The first chromosome of the offspring j +1 and the first j Each offspring's sequenced genes are mapped back to the source chromosome at the ( )th ( ) j +1) ’ Flight No. 1 and No. 2 j The wake interval of flight number '.

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