CN113780615A - Tubular route time-varying network design method based on distributed robust optimization - Google Patents

Tubular route time-varying network design method based on distributed robust optimization Download PDF

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CN113780615A
CN113780615A CN202110361963.4A CN202110361963A CN113780615A CN 113780615 A CN113780615 A CN 113780615A CN 202110361963 A CN202110361963 A CN 202110361963A CN 113780615 A CN113780615 A CN 113780615A
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叶博嘉
陈刚
蒋兵
田勇
姚虹翔
李海凉
倪超
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EASTERN CHINA AIR TRAFFIC MANAGEMENT BUREAU CAAC
Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a tubular route time-varying network design method based on distribution robustness optimization, which comprises the steps of firstly, constructing a directed graph system according to tubular route layout associated historical flight operation data; then, the state of each segment of the tubular route in each time period is taken as a decision variable, the service benefits and efficiency of the tubular route are taken as objective functions, and constraint conditions are set to construct a tubular route time-varying network multi-objective combination optimization model; and finally, according to the change of air traffic demands, constructing a distributed uncertain set by adopting a fitting and chi-square test method, and solving by adopting an NSGA-II algorithm through a distributed robust optimization method to obtain the time-varying network of the tubular route. The method can give full play to the characteristics and advantages of the flexibility of the tubular airway, effectively improve the use efficiency of the tubular airway and save the use cost of the tubular airway.

Description

Tubular route time-varying network design method based on distributed robust optimization
Technical Field
The invention relates to a tubular route time-varying network design method based on distributed robust optimization, and belongs to the technical field of tubular route management.
Background
In recent years, with the continuous and high-speed development of the air transportation industry, the situation of civil aviation airspace shortage shows a point-to-face development trend. All countries actively explore new concepts, new ideas and new methods for upgrading and transforming air traffic control systems. Under the background of the increasingly mature new navigation technology, the developed countries in aviation such as Europe and America have led to the introduction of a brand-new tubular route operation concept with the characteristics of high capacity, autonomous separation and flexibility.
In the aspect of the operating efficiency of the tubular airway design, especially in the aspect of dynamic use of fully playing the novel characteristics of the tubular airway design, the related theoretical method has obvious defects and blanks, and the key of the tubular airway concept whether to finally land or not is the tubular airway concept. Because flight operation is greatly influenced by external factors and has strong uncertainty, robust optimization is required to be added when a tubular route time-varying network construction method is researched.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for designing the time-varying network of the tubular route based on the distribution robustness optimization is provided, the characteristics and advantages of the flexibility of the tubular route can be effectively exerted, the utilization rate of the tubular route is improved, and a part of theoretical basis is provided for the final landing implementation of the concept of the tubular route, so that the current flight congestion situation is relieved.
The invention adopts the following technical scheme for solving the technical problems:
a tubular route time-varying network design method based on distribution robust optimization comprises the following steps:
step 1, constructing a directed graph G (N, A) of the tubular airway network according to the layout of the tubular airway network, wherein N represents a set of nodes of the tubular airway network, and A represents a set of segments of the nodes which are interconnected;
step 2, screening out flights in which a take-off airport and an arrival airport are both in the tubular airway network according to flight operation data of a time period to be designed, and constructing a flight path directed graph G of each flightf＝(Nf,Af) Wherein N isfRepresents the set of nodes through which the flight f is flying,
Figure BDA0003005943100000021
Afrepresenting the set of legs that the flight f flies through,
Figure BDA0003005943100000022
step 3, taking the state of each segment in the tubular airway network at each time segment as a decision variable, and constructing a target function and a constraint condition of the tubular airway time-varying network multi-target combination optimization model;
and 4, optimizing the objective function of the tubular route time-varying network multi-objective combined optimization model by a distributed robust optimization method, and solving the optimized objective function by adopting a fast non-dominated multi-objective optimization algorithm NSGA-II to obtain the tubular route time-varying network of the time period to be designed.
As a preferred embodiment of the present invention, the specific content of step 3 is as follows:
3.1 using each of the tube-type airway networksState of leg in each time segment
Figure BDA0003005943100000023
As a decision variable, the decision variable is,
Figure BDA0003005943100000024
is a variable from 0 to 1, 1 represents activation, 0 represents closing, m, N represents nodes at two ends of the flight segment, m, N belongs to NfAnd t represents a time slice,
Figure BDA0003005943100000025
Figure BDA0003005943100000026
a set representing time segments;
3.2 constructing an objective function o of mutual constraints1(. mu.) and o2(μ)，o1(mu) flight number, o, which can be served by the cast airway network2(mu) represents the average occupancy rate of the pipe type airway network;
Figure BDA0003005943100000027
Figure BDA0003005943100000028
the objective function of the tubular route time-varying network multi-objective combination optimization model is as follows: maxμ<o1(μ),o2(μ)>；
Wherein the content of the first and second substances,
Figure BDA0003005943100000029
representing the amount of flights that already exist within the leg (m, n) at the beginning of the t-th time segment,
Figure BDA00030059431000000210
representing the amount of flights entering leg (m, n) at the t-th time segment, p representing flights flying off from a cast-in-flight due to deactivation of a certain time segmentThe penalty factor of (2);
3.3, constructing a constraint condition of the tubular route time-varying network multi-target combination optimization model as follows:
Figure BDA00030059431000000211
Figure BDA00030059431000000212
Figure BDA00030059431000000213
Figure BDA00030059431000000214
Figure BDA00030059431000000215
wherein the content of the first and second substances,
Figure BDA00030059431000000216
representing the amount of flights flying off leg (m, n) at the t-th time segment.
As a preferred embodiment of the present invention, the specific content of step 4 is as follows:
4.1, setting up
Figure BDA0003005943100000031
A random vector of air traffic demand changes for the t-th time segment leg (m, n), thereby adjusting the objective function to:
Figure BDA0003005943100000032
Figure BDA0003005943100000033
the objective function after the optimization of the tubular route time-varying network multi-objective combination optimization model is as follows:
Figure BDA0003005943100000034
wherein the content of the first and second substances,
Figure BDA0003005943100000035
representing the variation of air traffic demand of the t-th time segment (m, n),
Figure BDA0003005943100000036
represents the expected value under the candidate distribution D, Ω (q) represents the distributed uncertainty set,
Figure BDA0003005943100000037
representing the amount of flights that already exist within the leg (m, n) at the beginning of the t-th time segment,
Figure BDA0003005943100000038
represents the amount of flights entering leg (m, n) at the t-th time segment, p represents the penalty factor for flights flying off from the pipe-type airway due to deactivation of a certain time segment,
Figure BDA0003005943100000039
showing the state of each segment in the tube-type airway network in each time segment,
Figure BDA00030059431000000310
Figure BDA00030059431000000311
a set representing time segments;
4.2, setting q to obey a discrete distribution
Figure BDA00030059431000000312
And distribution of each time slice
Figure BDA00030059431000000313
Is independent of, given
Figure BDA00030059431000000314
Is a univariate probability density function P0,iGiving a null hypothesis
Figure BDA00030059431000000315
Chi-square test is carried out on the null hypothesis to obtain discrete distribution
Figure BDA00030059431000000316
Corresponding confidence degrees, comparing all the confidence degrees, and taking the discrete distribution corresponding to the highest confidence degree as a candidate distribution D;
and 4.3, solving the optimized objective function by adopting a fast non-dominated multi-objective optimization algorithm NSGA-II to obtain the tubular route time-varying network of the time period to be designed.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the tubular route time-varying network design method based on distributed robust optimization can effectively exert the characteristics and advantages of tubular route flexibility, improve the utilization rate of the tubular route, effectively improve the stability and applicability of the tubular route time-varying network through robust optimization, provide a part of theoretical basis for the final landing implementation of the concept of the tubular route, and effectively relieve the current serious flight delay problem.
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FIG. 1 is a flow chart of a method for designing a tubular route time-varying network based on distribution robust optimization according to the present invention.
FIG. 2 is a diagram illustrating an exemplary layout of a tube-type airway network according to an embodiment of the present invention.
Fig. 3 is a distributed uncertainty set for different time segments of a flight segment according to an embodiment of the present invention.
FIG. 4 is a tubular route time-varying network according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in fig. 1, the invention provides a method for designing a tubular route time-varying network based on distribution robust optimization, which comprises the following specific steps:
the method comprises the following steps: and constructing a tube type route network directed graph G (N, A) according to the tube type route layout, wherein N represents a set of tube type route nodes, and A represents a set of route segments with interconnected nodes.
Step two: constructing a flight path directed graph G of the flight f according to the flight planf＝(Nf,Af) Wherein, in the step (A),
Figure BDA0003005943100000041
represents the set of nodes through which the flight f is flying,
Figure BDA0003005943100000042
representing the set of legs that the flight f flies through.
Step three: determining decision variables, constructing an objective function and a constraint condition which are mutually restricted, and providing a multi-objective combined optimization model of the tubular route time-varying network.
Step four: and constructing a distributed uncertain set, and solving by adopting an NSGA-II algorithm through a distributed robust optimization method to obtain the time-varying network of the tubular route.
The following description will specifically explain an embodiment.
The method comprises the following steps: taking the pipe-type route layout as shown in fig. 2 as an example, the flights in the graph all represent large circular tracks between nodes, and a pipe-type route network directed graph G is constructed as (N, a), where N represents a set of pipe-type route nodes, and a represents a set of interconnected flights of nodes, and totally comprises 17 nodes and 40 flights, where the zbcaa nodes comprise zbcaa and ZBTJ airports, the ZSSS nodes comprise ZSSS, ZSPD and ZSHC airports, the ZGGG nodes comprise ZGGG and ZGSZ airports, the ZJHK airports comprise ZJHK and ZJSY airports, and the rest nodes all represent single airports.
Step two: adopting flight operation data around 3 months in summer and autumn of 2017, screening out flights in which a take-off airport and an arrival airport are both in the tubular airway network, using the flights as the available tubular airways, and constructing a flight path directed graph G of the flight ff＝(Nf,Af) Wherein, in the step (A),
Figure BDA0003005943100000043
represents the set of nodes through which the flight f is flying,
Figure BDA0003005943100000044
representing the set of legs that the flight f flies through.
Step three: (3.1) firstly, constructing a multi-objective combination optimization model of the tubular route time-varying network under the following assumption: (1) the tubular routes are of sufficient capacity (which can be achieved by horizontally expanding the number of channels), all flights can autonomously maintain separation within the tubular routes, and flight conflicts caused by intersections in the network of tubular routes are not considered. (2) Considering that the time when the daily flight number is the lowest is about 4:00 a.m., in order to divide the flight into two different operation days as little as possible, an operation cycle is set to be 4:00 a.m. to 4:00 a.m. next day. (3) In order to ensure the flexibility of use of each flight segment and improve the use benefit, in one operation cycle, all flight segments can be activated and closed for multiple times according to flight requirements, and 1 hour is taken as the minimum activation time period. (4) Flight requirements of all flight sections are correlated, but no mutual influence exists in operation. (5) When the tubular airway is not activated, flights which have entered the tubular airway need to exit the tubular airway immediately, enter the traditional control sector and airway, and the number of flights in the tubular airway is reset; flights may continue to enter the tubular airways while they continue to be activated.
Decision variables for constructing tubular route time-varying network multi-target combination optimization model
Figure BDA0003005943100000051
The state of each segment of the tubular airway in each time interval is set as a variable 0-1 (1 represents activation, 0 represents closing), wherein m, N belongs to NfThe reference to the flight node, indicates,
Figure BDA0003005943100000052
the time slice is represented by a time slice,
Figure BDA0003005943100000053
representing a collection of time segments.
(3.2) constructing a multi-objective function o of the tubular route time-varying network multi-objective combination optimization model1(. mu.) and o2(μ)，o1(mu) represents the number of flights (unit: number of racks) that can be served by the cast airway network, o2And (mu) represents the average occupancy rate (unit: number of frames/hour) of the tubular type airway, and the two objective functions have a mutual constraint relationship, and the specific expression is as follows:
Figure BDA0003005943100000054
Figure BDA0003005943100000055
therefore, the final objective function of the tube-type air route time-varying network multi-objective combination optimization model is determined as follows: maxμ<o1(μ),o2(μ)>；
Wherein the content of the first and second substances,
Figure BDA0003005943100000056
representing the amount of flights that already exist within the tubular airway (m, n) at the beginning of the t-th period,
Figure BDA0003005943100000057
represents the amount of flights entering a tubular airway (m, n) during time t, and ρ represents a penalty factor for flights flying away from the tubular airway due to deactivation for a certain period of time.
(3.3) constructing constraint conditions of the tube-type air route time-varying network multi-objective combination optimization model:
constraint 1:
Figure BDA0003005943100000058
constraint 2:
Figure BDA0003005943100000059
constraint 3:
Figure BDA00030059431000000510
constraint 4:
Figure BDA00030059431000000511
constraint 5:
Figure BDA00030059431000000512
wherein the content of the first and second substances,
Figure BDA0003005943100000061
represents the number of flights departing from the cast route (m, n) during time t. The constraint condition 1 limits the number relation of existing flights, entering flights and leaving flights, the constraint conditions 2, 3 and 4 limit the number of the existing flights, the entering flights and the leaving flights to be more than or equal to 0, and the constraint condition 5 limits the decision variable to be 0-1 variable.
Step four: and (4.1) according to historical data of different operation days, the uncertainty requirements of each flight segment in different time periods can be calculated. Is provided with
Figure BDA0003005943100000062
A vector of air traffic demand changes for the tube-type airway (m, n) at the t-th time period, thereby adjusting the objective function to:
Figure BDA0003005943100000063
Figure BDA0003005943100000064
thus, the final objective function is adjusted to
Figure BDA0003005943100000065
Making it robust.
Wherein the content of the first and second substances,
Figure BDA0003005943100000066
representing the air traffic demand variation of the pipe-type air route (m, n) at the t-th time period,
Figure BDA0003005943100000067
represents the expected value under the candidate distribution D, and Ω (q) represents the distributed uncertainty set.
(4.2) assume that q obeys an unknown discrete distribution
Figure BDA0003005943100000068
And marginal distribution per time period
Figure BDA0003005943100000069
Are independent. Given a discrete univariate distribution P0,iIncluding single point distribution, Bernoulli distribution, binomial distribution, Poisson distribution, geometric distribution, hypergeometric distribution, Pascal distribution, and negative binomial distribution, giving a null hypothesis
Figure BDA00030059431000000610
And performing chi-square test, and marking the discrete distribution with the highest confidence coefficient as a candidate distribution D. Taking zba-zss flight segment as an example, a distributed uncertainty set (with a confidence of 80%) of air traffic demand changes at different time periods is calculated, as shown in fig. 3.
(4.3) writing an NSGA-II algorithm by using a python language to solve the model, wherein specific parameters are set as follows: the population scale is 500, the number of terminated generations is 1500, the crossover probability is 0.8, the mutation probability is 0.02, the elite strategy reserves 8 optimal chromosomes for each generation, and linear recombination crossover and random factor mutation rules are adopted in genetic operation. And obtaining the tubular route time-varying network after solving, as shown in fig. 4.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (3)

1. A tubular route time-varying network design method based on distribution robust optimization is characterized by comprising the following steps:
step 1, constructing a directed graph G (N, A) of the tubular airway network according to the layout of the tubular airway network, wherein N represents a set of nodes of the tubular airway network, and A represents a set of segments of the nodes which are interconnected;
step 2, screening out flights in which a take-off airport and an arrival airport are both in the tubular airway network according to flight operation data of a time period to be designed, and constructing a flight path directed graph G of each flightf＝(Nf,Af) Wherein N isfRepresents the set of nodes through which the flight f is flying,
Figure FDA0003005943090000011
Afrepresenting the set of legs that the flight f flies through,
Figure FDA0003005943090000012
step 3, taking the state of each segment in the tubular airway network at each time segment as a decision variable, and constructing a target function and a constraint condition of the tubular airway time-varying network multi-target combination optimization model;
and 4, optimizing the objective function of the tubular route time-varying network multi-objective combined optimization model by a distributed robust optimization method, and solving the optimized objective function by adopting a fast non-dominated multi-objective optimization algorithm NSGA-II to obtain the tubular route time-varying network of the time period to be designed.
2. The tube-type airway time-varying network design method based on distribution robust optimization according to claim 1, wherein the specific content of the step 3 is as follows:
3.1 Using the status of each leg in the tube-type airway network at each time slice
Figure FDA0003005943090000013
As a decision variable, the decision variable is,
Figure FDA0003005943090000014
is a variable from 0 to 1, 1 represents activation, 0 represents closing, m, N represents nodes at two ends of the flight segment, m, N belongs to NfAnd t represents a time slice,
Figure FDA0003005943090000015
Figure FDA0003005943090000016
a set representing time segments;
3.2 constructing an objective function o of mutual constraints1(. mu.) and o2(μ)，o1(mu) flight number, o, which can be served by the cast airway network2(mu) represents the average occupancy rate of the pipe type airway network;
Figure FDA0003005943090000017
Figure FDA0003005943090000018
the objective function of the tubular route time-varying network multi-objective combination optimization model is as follows: maxμ<o1(μ),o2(μ)>；
Wherein the content of the first and second substances,
Figure FDA0003005943090000019
representing the amount of flights that already exist within the leg (m, n) at the beginning of the t-th time segment,
Figure FDA00030059430900000110
representing the amount of flights entering a leg (m, n) at the t-th time segment, p representing a penalty factor for flights flying off from a tube-type airway due to deactivation of a certain time segment;
3.3, constructing a constraint condition of the tubular route time-varying network multi-target combination optimization model as follows:
Figure FDA0003005943090000021
Figure FDA0003005943090000022
Figure FDA0003005943090000023
Figure FDA0003005943090000024
Figure FDA0003005943090000025
wherein the content of the first and second substances,
Figure FDA0003005943090000026
representing the amount of flights flying off leg (m, n) at the t-th time segment.
3. The tube-type airway time-varying network design method based on distribution robust optimization according to claim 1, wherein the specific content of the step 4 is as follows:
4.1, setting up
Figure FDA0003005943090000027
A random vector of air traffic demand changes for the t-th time segment leg (m, n), thereby adjusting the objective function to:
Figure FDA0003005943090000028
Figure FDA0003005943090000029
the objective function after the optimization of the tubular route time-varying network multi-objective combination optimization model is as follows:
Figure FDA00030059430900000210
wherein the content of the first and second substances,
Figure FDA00030059430900000211
representing the variation of air traffic demand of the t-th time segment (m, n),
Figure FDA00030059430900000212
represents the expected value under the candidate distribution D, Ω (q) represents the distributed uncertainty set,
Figure FDA00030059430900000213
representing the amount of flights that already exist within the leg (m, n) at the beginning of the t-th time segment,
Figure FDA00030059430900000214
represents the amount of flights entering leg (m, n) at the t-th time segment, p represents the penalty factor for flights flying off from the pipe-type airway due to deactivation of a certain time segment,
Figure FDA00030059430900000215
showing the state of each segment in the tube-type airway network in each time segment,
Figure FDA00030059430900000216
Figure FDA00030059430900000217
a set representing time segments;
4.2, setting q to obey a discrete distribution
Figure FDA00030059430900000218
And distribution of each time slice
Figure FDA00030059430900000219
Is independent of, given
Figure FDA00030059430900000220
Is a univariate probability density function P0,iGiving a null hypothesis
Figure FDA00030059430900000221
Chi-square test is carried out on the null hypothesis to obtain discrete distribution
Figure FDA00030059430900000222
Corresponding confidence degrees, comparing all the confidence degrees, and taking the discrete distribution corresponding to the highest confidence degree as a candidate distribution D;
and 4.3, solving the optimized objective function by adopting a fast non-dominated multi-objective optimization algorithm NSGA-II to obtain the tubular route time-varying network of the time period to be designed.
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CN107025806A (en) * 2017-05-11 2017-08-08 中国电子科技集团公司第二十八研究所 A kind of single phase interim flight path robust Optimal methods
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