CN111523188A - Aviation network robustness optimization method - Google Patents

Aviation network robustness optimization method Download PDF

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CN111523188A
CN111523188A CN202010310454.4A CN202010310454A CN111523188A CN 111523188 A CN111523188 A CN 111523188A CN 202010310454 A CN202010310454 A CN 202010310454A CN 111523188 A CN111523188 A CN 111523188A
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刘震
潘亮光
游慧明
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Abstract

The invention discloses an aviation network robustness optimization method, which comprises the following steps: constructing an aviation network according to the flight record data; calculating the importance of nodes in the aviation network and the robustness of the aviation network; constructing a candidate edge according to the importance of the nodes in the aviation network, and acquiring a Gini coefficient increment through the candidate edge and the robustness; and selecting a plurality of edges with the largest increment of the kini coefficient from the candidate edges to complete the optimization of the aeronautical network robustness. The method can optimize the network structure, reduces the influence of the emergency on the air transportation network, firstly constructs the air transportation network according to the flight record data, calculates the importance of the airport city node and the robustness of the network, then selects the local optimization range, and selects the optimized air route needing to be added by using a network optimization method.

Description

Aviation network robustness optimization method
Technical Field
The invention belongs to the technical field of information, and particularly relates to an optimization method for robustness of an aviation network.
Background
With the rapid development of modern society, air transportation has become one of the important industries in global development, and the volume of both goods and passengers is continuously and rapidly increasing, and the size of airlines is continuously expanding. However, this rapid growth also causes problems, such as large area airplane delays, passenger retention, and transportation interruptions, when some emergency causes make certain airports unusable. One of the methods that can solve these conflicts is to evaluate the robustness of the aviation network and then adjust the network by adding some airlines, increasing the network robustness.
Disclosure of Invention
Aiming at the defects in the prior art, the method for optimizing the robustness of the aviation network provided by the invention solves the problem that an airport in the aviation network is unavailable.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: an aviation network robustness optimization method comprises the following steps:
s1, constructing an aviation network according to the flight record data;
s2, calculating the importance of the nodes in the aviation network and the robustness of the aviation network;
s3, constructing candidate edges according to the importance of the nodes in the aviation network, and acquiring a Gini coefficient increment through the candidate edges and the robustness;
and S4, selecting a plurality of edges with the largest increment of the kini coefficient from the candidate edges, and finishing the optimization of the aeronautical network robustness.
Further, the specific method for constructing the aviation network in step S1 is as follows: the airport is taken as a node of the aviation network, the route connected with the airport is taken as an edge of the aviation network, and the operation capacity of the route is taken as the weight of the edge, so that the aviation network G (V, E, W) is obtained, wherein V is { V ═ V { (V }i1, 2., n }, V denotes an airport group, and V denotes a number of airportsiDenotes the ith airport, n denotes the total number of airports in the airline network, E ═ EijI, j ═ 1,2ijRepresentation of an airport viAnd airport vjI ≠ j, W ═ WijI, j ═ 1, 2.., n }, W denotes the set of airline capacities in the aviation network, W denotes the set of airlinesijRepresenting a flight path eijThe operation and performance of the device.
Further, the importance S of the node in the step S2iThe calculation formula is as follows:
Figure BDA0002457581290000021
wherein N (i) denotes the number of airports viAdjacent airports, siIndicating the importance of the ith node.
Further, the robustness gini (S) of the aviation network in the step S2 is:
Figure BDA0002457581290000022
wherein S ═ { S ═ Si1, 2., n }, S denotes a set of importance, S denotes an importance setkDenotes the importance of the kth node in the importance set S, k ═ 1, 2.
Further, the specific method for constructing the candidate edge according to the node in the aviation network in step S3 is as follows:
a1, according to the importance of the nodes in the aviation network, forming a set N by the adjacent nodes of the most important nodes;
a2, selecting nodes with the importance ranking of the top 20% in the set N to form a set H;
a3, selecting the constituent edges of 30% of nodes in the set H as candidate edges, recording the candidate edge set as E ', and removing the candidate edge set as E ' in the aviation network to obtain a real aviation network G ';
further, the specific method for acquiring the kuney coefficient increment through the candidate edge and the robustness in step S3 is as follows:
b1, acquiring a node importance set S of the real aviation network G' according to the importance of the nodes in the aviation networkG'And calculating a node importance set S after the candidate edges (i, j) are added to the real aviation network GG′′；
B2, calculation formula according to robustness gini (S) of aviation network, importance set SG'And importance set SG′', obtaining the robustness of the real aviation network G ' and increasing the robustness of the real aviation network G ' after the candidate edges;
and B3, acquiring the increment of the Gini coefficient according to the robustness of the real aviation network G 'and the robustness of the real aviation network G' after the candidate edges are added.
Further, the robustness gini (S) of the real aeronautical network G' in said step B2G') Comprises the following steps:
Figure BDA0002457581290000031
the robustness gini of the candidate edge-behind real aviation network G' is increased in the step B2 (S)G′') is:
Figure BDA0002457581290000032
further, the increment Δ gini of the kini coefficient in the step B3 is:
Figure BDA0002457581290000033
wherein p and q are both constant,
Figure BDA0002457581290000034
q＝s1+s2+...+sn。
further, the step S4 includes the following sub-steps:
s4.1, calculating the increment of each candidate edge Gini coefficient in the candidate edge set E', and recording the increment as
Figure BDA0002457581290000035
And acquiring the operation energy w of each candidate edgexWherein x ═ 1, 2., N denotes the total number of candidate edges in the candidate edge set E';
s4.2, setting the maximum total operation energy of the added candidate edges as C and the maximum added number of the candidate edges as D;
s4.3, according to the transport capacity wxAnd incremental Keyny coefficient
Figure BDA0002457581290000036
Acquiring a Gini coefficient increment state transition equation;
and S4.4, acquiring a plurality of edges which enable the increment of the kini coefficient of the real aeronet G 'in the candidate edge set E' to be maximum according to the maximum total transport capacity of the added candidate edges as C, the maximum added number of the candidate edges as D and the state transfer equation of the kini coefficient increment, and finishing the optimization of the aeronet robustness.
Further, the incremental state transition equation of the kini coefficient in step S4.3 is:
Figure BDA0002457581290000037
wherein dp (x, c, d) represents the maximum increase of the prime coefficient that the total capacity increased in the front x side does not exceed c and the number of the increased pieces does not exceed d, dp (x-1, c, d) represents the maximum increase of the prime coefficient that the total capacity increased in the front x-1 side does not exceed c and the number of the increased pieces does not exceed d, and dp (x-1, c-w)x,d-lx) Indicates that the total capacity increased in the front x-1 edge does not exceed c-wxAnd increasing the number of strips not to exceed d-lxMaximum increase of the coefficient of kini, lxIndicating the number of usable edges of the x-th candidate edge, lx＝1；
The specific method for acquiring the plurality of edges which maximize the increment of the kini coefficient of the real aviation network G 'in the candidate edge set E' in step S4.4 is as follows: calculating the value of dp (N, C, D) according to the state transition equation of the Gini coefficient, and judging whether dp (x, C, D) is equal to dp (x, C, D) in the calculation process
Figure BDA0002457581290000041
If so, selecting the x-th candidate edge to be added into the real aviation network G ', otherwise, not performing operation, and obtaining a plurality of edges which enable the increment of the kiney coefficient of the real aviation network G' to be maximum after calculation is completed.
The invention has the beneficial effects that:
(1) the method for optimizing the robustness of the aviation network is provided by using the Gini coefficient of the network node importance as the network robustness index and using a dynamic programming algorithm to optimize the network robustness index.
(2) The method can optimize the network structure, reduces the influence of the emergency on the air transportation network, firstly constructs the air transportation network according to the flight record data, calculates the importance of the airport city node and the robustness of the network, then selects the local optimization range, and selects the optimized air route needing to be added by using a network optimization method.
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Fig. 1 is a flowchart of an aviation network robustness optimization method proposed by the present invention.
FIG. 2 is a graph comparing the results of a first experiment according to the present invention.
FIG. 3 is a graph comparing the results of a second experiment according to the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1, an aviation network robustness optimization method includes the following steps:
s1, constructing an aviation network according to the flight record data;
s2, calculating the importance of the nodes in the aviation network and the robustness of the aviation network;
s3, constructing candidate edges according to the importance of the nodes in the aviation network, and acquiring a Gini coefficient increment through the candidate edges and the robustness;
and S4, selecting a plurality of edges with the largest increment of the kini coefficient from the candidate edges, and finishing the optimization of the aeronautical network robustness.
The specific method for constructing the aviation network in the step S1 is as follows: the airport is taken as a node of the aviation network, the route connected with the airport is taken as an edge of the aviation network, and the operation capacity of the route is taken as the weight of the edge, so that the aviation network G (V, E, W) is obtained, wherein V is { V ═ V { (V }i1, 2., n }, V representing a set of airports，viDenotes the ith airport, n denotes the total number of airports in the airline network, E ═ EijI, j ═ 1,2ijRepresentation of an airport viAnd airport vjI ≠ j, W ═ WijI, j ═ 1, 2.., n }, W denotes the set of airline capacities in the aviation network, W denotes the set of airlinesijRepresenting a flight path eijThe operation and performance of the device.
Importance S of the node in the step S2iThe calculation formula is as follows:
Figure BDA0002457581290000051
wherein N (i) denotes the number of airports viAdjacent airports, siIndicating the importance of the ith node.
The robustness gini (S) of the aviation network in the step S2 is:
Figure BDA0002457581290000052
wherein S ═ { S ═ Si1, 2., n }, S denotes a set of importance, S denotes an importance setkDenotes the importance of the kth node in the importance set S, k ═ 1, 2.
The specific method for constructing the candidate edge according to the node in the aviation network in the step S3 is as follows:
a1, according to the importance of the nodes in the aviation network, forming a set N by the adjacent nodes of the most important nodes;
a2, selecting nodes with the importance ranking of the top 20% in the set N to form a set H;
a3, selecting the constituent edges of 30% of nodes in the set H as candidate edges, recording the candidate edge set as E ', and removing the candidate edge set as E ' in the aviation network to obtain a real aviation network G ';
the specific method for acquiring the increment of the kuney coefficient through the candidate edges and the robustness in the step S3 is as follows:
b1, acquiring the node importance set of the real aviation network G' according to the importance of the nodes in the aviation networkSG'And calculating a node importance set S after the candidate edges (i, j) are added to the real aviation network GG′′；
B2, calculation formula according to robustness gini (S) of aviation network, importance set SG'And importance set SG′', obtaining the robustness of the real aviation network G ' and increasing the robustness of the real aviation network G ' after the candidate edges;
and B3, acquiring the increment of the Gini coefficient according to the robustness of the real aviation network G 'and the robustness of the real aviation network G' after the candidate edges are added.
Robustness gini (S) of the real aeronautical network G' in said step B2G') Comprises the following steps:
Figure BDA0002457581290000061
the robustness gini of the candidate edge-behind real aviation network G' is increased in the step B2 (S)G′') is:
Figure BDA0002457581290000062
the increment Δ gini of the kini coefficient in the step B3 is:
Figure BDA0002457581290000063
wherein p and q are both constant,
Figure BDA0002457581290000064
q＝s1+s2+...+sn。
the step S4 includes the following sub-steps:
s4.1, calculating the increment of each candidate edge Gini coefficient in the candidate edge set E', and recording the increment as
Figure BDA0002457581290000065
And acquiring the operation energy w of each candidate edgexWhere x ═ 1, 2., N denotes the total number of candidate edges in the candidate edge set E ″；
S4.2, setting the maximum total operation energy of the added candidate edges as C and the maximum added number of the candidate edges as D;
s4.3, according to the transport capacity wxAnd incremental Keyny coefficient
Figure BDA0002457581290000071
Acquiring a Gini coefficient increment state transition equation;
and S4.4, acquiring a plurality of edges which enable the increment of the kini coefficient of the real aeronet G 'in the candidate edge set E' to be maximum according to the maximum total transport capacity of the added candidate edges as C, the maximum added number of the candidate edges as D and the state transfer equation of the kini coefficient increment, and finishing the optimization of the aeronet robustness.
The incremental state transition equation of the kini coefficient in the step S4.3 is as follows:
Figure BDA0002457581290000072
wherein dp (x, c, d) represents the maximum increase of the prime coefficient that the total capacity increased in the front x side does not exceed c and the number of the increased pieces does not exceed d, dp (x-1, c, d) represents the maximum increase of the prime coefficient that the total capacity increased in the front x-1 side does not exceed c and the number of the increased pieces does not exceed d, and dp (x-1, c-w)x,d-lx) Indicates that the total capacity increased in the front x-1 edge does not exceed c-wxAnd increasing the number of strips not to exceed d-lxMaximum increase of the coefficient of kini, lxIndicating the number of usable edges of the x-th candidate edge, lx＝1；
The specific method for acquiring the plurality of edges which maximize the increment of the kini coefficient of the real aviation network G 'in the candidate edge set E' in step S4.4 is as follows: calculating the value of dp (N, C, D) according to the state transition equation of the Gini coefficient, and judging whether dp (x, C, D) is equal to dp (x, C, D) in the calculation process
Figure BDA0002457581290000073
If so, selecting the x-th candidate edge to be added into the real aviation network G ', otherwise, not performing operation, and obtaining a plurality of strips which enable the increment of the Gini coefficient of the real aviation network G' to be maximum after calculationAnd (7) edge.
In this example, the american aviation published flight record dataset used includes a total of 779 airports and 6103 airlines.
As shown in fig. 2, DP represents an experimental result of the method used in the present invention, Greedy represents an experimental result of a Greedy algorithm, an edge with the largest increment of the kini is selected each time, in fig. 2, (a), (b), and (C), the maximum increment total operation energy of the candidate edges C is set to 150, 200, and 250, respectively, and the maximum increment number D of the candidate edges is set to 30; in fig. 2, (D) the maximum increase number D of the candidate edges is set to 30, and the maximum increase total operation capacity C of the candidate edges is set to 150,160.., 250, and multiple experiments are performed, and the maximum robustness of each experiment is recorded; it can be seen that the robustness increased by the optimization of the method of the invention under different parameters is finally greater than the robustness increased by the greedy method, i.e. the method of the invention is superior to the greedy method. The method selects the optimal route from the whole situation, and does not preferentially select some routes with larger operation capacity, so that compared with the greedy method, the robustness cannot be continuously increased because of the limitation of the operation capacity, and the amplification of the finally selected route is obviously larger than that of the greedy method.
As shown in fig. 3, (a), (b) and (C) in fig. 3 set the maximum increase number D of the candidate edges to 10, 30 and 50, respectively, and set the maximum increase total operation capacity C of the candidate edges to 200; in fig. 3, (D) the maximum increase total operation capacity C of the candidate edge is set to 200, and the maximum increase number D of the candidate edge is set to 10, 15.., 60, and multiple experiments are performed, and the maximum robustness of each experiment is recorded; it can be seen that the maximum number of the added lines D on different candidate edges is greater than the robustness increased by the greedy method, and when the number of the allowed increased lines is greater, the method is not obviously limited by the number of the lines, and the effect is obviously superior to that of the greedy method.
The invention has the beneficial effects that:
(1) the method for optimizing the robustness of the aviation network is provided by using the Gini coefficient of the network node importance as the network robustness index and using a dynamic programming algorithm to optimize the network robustness index.
(2) The method can optimize the network structure, reduces the influence of the emergency on the air transportation network, firstly constructs the air transportation network according to the flight record data, calculates the importance of the airport city node and the robustness of the network, then selects the local optimization range, and selects the optimized air route needing to be added by using a network optimization method.

Claims (10)

1. An aviation network robustness optimization method is characterized by comprising the following steps:
s1, constructing an aviation network according to the flight record data;
s2, calculating the importance of the nodes in the aviation network and the robustness of the aviation network;
s3, constructing candidate edges according to the importance of the nodes in the aviation network, and acquiring a Gini coefficient increment through the candidate edges and the robustness;
and S4, selecting a plurality of edges with the largest increment of the kini coefficient from the candidate edges, and finishing the optimization of the aeronautical network robustness.
2. The aviation network robustness optimization method of claim 1, wherein the specific method for constructing the aviation network in the step S1 is as follows: the airport is taken as a node of the aviation network, the route connected with the airport is taken as an edge of the aviation network, and the operation capacity of the route is taken as the weight of the edge, so that the aviation network G (V, E, W) is obtained, wherein V is { V ═ V { (V }i1, 2., n }, V denotes an airport group, and V denotes a number of airportsiDenotes the ith airport, n denotes the total number of airports in the airline network, E ═ EijI, j ═ 1,2ijRepresentation of an airport viAnd airport vjI ≠ j, W ═ WijI, j ═ 1, 2.., n }, W denotes the set of airline capacities in the aviation network, W denotes the set of airlinesijRepresenting a flight path eijThe operation and performance of the device.
3. The aeronautical network robustness optimization method of claim 2, wherein the importance S of the node in step S2iThe calculation formula is as follows:
Figure FDA0002457581280000011
wherein N (i) denotes the number of airports viAdjacent airports, siIndicating the importance of the ith node.
4. The aviation network robustness optimization method according to claim 3, wherein the robustness gini (S) of the aviation network in the step S2 is as follows:
Figure FDA0002457581280000012
wherein S ═ { S ═ Si1, 2., n }, S denotes a set of importance, S denotes an importance setkDenotes the importance of the kth node in the importance set S, k ═ 1, 2.
5. The aviation network robustness optimization method according to claim 4, wherein the specific method for constructing the candidate edges according to the nodes in the aviation network in the step S3 is as follows:
a1, according to the importance of the nodes in the aviation network, forming a set N by the adjacent nodes of the most important nodes;
a2, selecting nodes with the importance ranking of the top 20% in the set N to form a set H;
a3, selecting the constituent edges of 30% of nodes in the set H as candidate edges, recording the candidate edge set as E ', and removing the candidate edge set as E ' in the aviation network to obtain a real aviation network G '.
6. The aviation network robustness optimization method according to claim 5, wherein the specific method for obtaining the increment of the kini coefficient through the candidate edges and the robustness in the step S3 is as follows:
b1, acquiring a node importance set S of the real aviation network G' according to the importance of the nodes in the aviation networkG'And calculating the addition candidate edges (i, j) of the real aviation network GNode importance set S ofG’’；
B2, calculation formula according to robustness gini (S) of aviation network, importance set SG'And importance set SG’', obtaining the robustness of the real aviation network G ' and increasing the robustness of the real aviation network G ' after the candidate edges;
and B3, acquiring the increment of the Gini coefficient according to the robustness of the real aviation network G 'and the robustness of the real aviation network G' after the candidate edges are added.
7. The aeronautical network robustness optimization method according to claim 6, wherein the robustness gini (S) of the real aeronautical network G' in step B2G') Comprises the following steps:
Figure FDA0002457581280000021
the robustness gini of the candidate edge-behind real aviation network G' is increased in the step B2 (S)G’') is:
Figure FDA0002457581280000022
8. the aeronautical network robustness optimization method of claim 6, wherein the kuni coefficient increment Δ gini in step B3 is:
Figure FDA0002457581280000031
wherein p and q are both constant,
Figure FDA0002457581280000032
q＝s1+s2+...+sn。
9. the airline robustness optimization method according to claim 6, wherein the step S4 includes the sub-steps of:
s4.1, calculating the increment of each candidate edge Gini coefficient in the candidate edge set E', and recording the increment as
Figure FDA0002457581280000033
And acquiring the operation energy w of each candidate edgexWherein x ═ 1, 2., N denotes the total number of candidate edges in the candidate edge set E';
s4.2, setting the maximum total operation energy of the added candidate edges as C and the maximum added number of the candidate edges as D;
s4.3, according to the transport capacity wxAnd incremental Keyny coefficient
Figure FDA0002457581280000034
Acquiring a Gini coefficient increment state transition equation;
and S4.4, acquiring a plurality of edges which enable the increment of the kini coefficient of the real aeronet G 'in the candidate edge set E' to be maximum according to the maximum total transport capacity of the added candidate edges as C, the maximum added number of the candidate edges as D and the state transfer equation of the kini coefficient increment, and finishing the optimization of the aeronet robustness.
10. The aeronautical network robustness optimization method of claim 9, wherein the incremental state transition equations of the kini coefficients in step S4.3 are:
Figure FDA0002457581280000035
wherein dp (x, c, d) represents the maximum increase of the prime coefficient that the total capacity increased in the front x side does not exceed c and the number of the increased pieces does not exceed d, dp (x-1, c, d) represents the maximum increase of the prime coefficient that the total capacity increased in the front x-1 side does not exceed c and the number of the increased pieces does not exceed d, and dp (x-1, c-w)x,d-lx) Indicates that the total capacity increased in the front x-1 edge does not exceed c-wxAnd increasing the number of strips not to exceed d-lxMaximum increase of the coefficient of kini, lxIndicating the number of usable edges of the x-th candidate edge, lx＝1；
Said step S4.4, the specific method for acquiring the plurality of edges in the candidate edge set E 'which maximizes the increment of the kini coefficient of the real aeronautical network G' includes: calculating the value of dp (N, C, D) according to the state transition equation of the Gini coefficient, and judging whether dp (x, C, D) is equal to dp (x, C, D) in the calculation process
Figure FDA0002457581280000041
If so, selecting the x-th candidate edge to be added into the real aviation network G ', otherwise, not performing operation, and obtaining a plurality of edges which enable the increment of the kiney coefficient of the real aviation network G' to be maximum after calculation is completed.
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