CN114936804B - Airport multidimensional resource cooperative scheduling method - Google Patents

Airport multidimensional resource cooperative scheduling method Download PDF

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CN114936804B
CN114936804B CN202210714538.3A CN202210714538A CN114936804B CN 114936804 B CN114936804 B CN 114936804B CN 202210714538 A CN202210714538 A CN 202210714538A CN 114936804 B CN114936804 B CN 114936804B
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杜文博
李嘉琦
朱少川
郑磊
李宇萌
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Abstract

The invention relates to the technical field of airport resource allocation, and provides a multidimensional resource collaborative scheduling method for an airport. The method comprises the following steps: establishing a mixed integer programming model of airport stand resources, and designing an objective function and constraint conditions of the mixed integer programming model; designing a column generation algorithm to solve a linear relaxation problem of a mixed integer programming model, and randomly selecting a plurality of historical stand scheduling schemes to serve as initial feasible solutions; solving the limiting main problem to obtain a dual variable; and solving an integer solution by utilizing a submersible heuristic algorithm to generate a stand scheduling scheme, drawing a stand scheduling diagram by utilizing a Gantt chart, and completing the cooperative scheduling of the multidimensional resources of the airport. According to the invention, through designing interchange rules, the airplane activities are exchanged among the airplane stations, the robustness of the scheme is improved, the airport resource scheduling problem is designed from the perspective of multiple resources, and a more reasonable and coordinated optimization scheme is obtained.

Description

Airport multidimensional resource cooperative scheduling method
Technical Field
The invention relates to the technical field of airport resource allocation, in particular to a multidimensional resource collaborative scheduling method for an airport.
Background
Due to the interest in aviation policy and the rapid increase in global travel demand, the current development of civil aviation is under vigorous development. However, the rapid increase in global aviation passenger demand and passenger throughput has resulted in many large airport capacities having come close to saturation. Thus, airport operation management presents a great challenge, and administrators are in need of optimizing airport resource scheduling. In airport operation systems, the problem of stand resource allocation is one of the core scheduling tasks of an airport. Each flight taking off or landing from the airport needs to be assigned to a viable stand for ground work. Thus, an efficient, reliable allocation of the stand is of vital importance for the airport, which not only relates to the operational efficiency of the airport, but also affects the satisfaction of passengers for airport services.
At present, regarding the related method of the stand allocation problem, the following three aspects are mainly considered for optimization as targets: passengers, airports and airlines. The passenger's stand allocation method is considered to be mainly directed to passenger satisfaction, such as minimizing passenger walking distance, turning time, etc. The airport stand allocation method considering the airport mainly takes the airport operation efficiency as a guide, such as maximizing the bridge leaning rate, minimizing the remote stand use amount, and the like. The method for allocating the stand of the airline is mainly based on the operation cost, such as minimizing the number of transposition of the aircraft. However, flight delays introduce a lot of uncertainty into airport operations due to uncertainty factors such as bad weather, airspace regulations, etc.
Disclosure of Invention
In view of the above, the invention provides a multidimensional resource collaborative scheduling method for an airport, so as to solve the problem of station resource allocation in an airport operation system in the prior art.
The invention provides a multi-dimensional resource collaborative scheduling method for an airport, which comprises the following steps:
step S1 establishes a mixed integer programming model of airport stand resources,
step S11, constructing a stand set according to stand attributes based on an airport stand resource databaseK；
Step S12, constructing a flight set according to the demand attribute based on the flight scheduleA；
Step S13 is based on the set of stand positionsKAnd the flight setAGenerating a feasible flight set of each stand, and generating an aircraft active set according to three active states of take-off, arrival and stay of each flight aircraftF；
Step S14 is based on the aircraft activity setFStand assemblyKEstablishing a mixed integer programming model;
s2, designing an objective function and constraint conditions of a mixed integer programming model;
step S3, designing a column generation algorithm to solve a linear relaxation problem of the mixed integer programming model, wherein the linear relaxation problem comprises a limiting main problem and a sub-problem;
s4, randomly selecting a plurality of historical stand scheduling schemes as initial feasible solutions;
step S5, solving the limiting main problem to obtain a dual variable;
step S6, constructing a child problem inspection number formula, constructing an airplane movable network of each airplane station based on the inspection number formula by each child problem, designing a shortest path solving method to obtain a shortest path of the airplane movable network of each airplane station, adding the shortest path as a new variable into the limiting main problem if the inspection number of the shortest path is smaller than 0, and returning to the step S5; if the inspection number of the shortest path of each stand plane active network is not less than 0, finishing the linear relaxation problem solving, and executing the step S7;
step S7, based on the linear relaxation solution, solving an integer solution by using a diving heuristic algorithm;
and S8, generating a stand scheduling scheme based on the obtained integer solution, drawing a stand scheduling diagram by utilizing the Gantt chart, and completing the cooperative scheduling of the multidimensional resources of the airport.
Further, the set of stand positionsKIn (3) standkComprising the following steps: whether the terminal is near, can place the model, flight type, VIP terminal;
the flight setAFlights in (b)aComprising the following steps: flight number, tail number, model, flight type, departure airport, arrival airport, departure time and arrival time;
the aircraft active setFIn aircraft activitiesfComprising the following steps: tail number, model, stop time, withdrawal time, leading flights and following flights.
Further, the establishing a mixed integer programming model in step S14 includes:
defining a set:
stand assemblyKStand of machinek∈K；
Flight collectionAFlight ofa∈A；
Aircraft activity setFAircraft movementf∈F；
Stand of machinekDistribution plan set of (a)S k Distribution plans∈S k ；
For movement of aircraftfAlternative stand plan set；
Defining parameters:
c ks : stand of machinekDistribution plansIs added to the cost of (a) the (b),
: stand of machinekDistribution plansInherent cost of (2);
: stand of machinekDistribution plansThe tractor use cost;
α f : aircraft activityfThe cost of the de-allocation;
β fk : stand of machinekOn-board aircraft activitiesfExchanging the obtained profit;
defining variables:
δ fs : aircraft activityfDistribution plans1 when the time is equal to or 0 when the time is equal to or less than the time;
v f : aircraft activityfWhen the dragging is needed, the dragging is 1, otherwise, the dragging is 0;
x ks :0-1 variable, at the standkDistribution plans1 when the time is equal to or 0 when the time is equal to or less than the time;
y f :0-1 variable, aircraft movementf1 when de-allocated, otherwise 0;
z fk : integer variable, standkOn-board aircraft activityfThe number of interchangeable stands may be selected.
Further, in the step S2, the objective function is designed based on minimizing the stand use cost, minimizing the tractor use cost, minimizing the flight cancellation cost, and maximizing the stand interchangeability;
to the aircraft activity distributed in the remote location, a penalty cost is givenh 1 Then there is
（1）
For the movement of an aircraft which needs to be towed to another aircraft location by a tractor, one fuel consumption cost is givenh 2 ，
（2）
The objective function expression of the mixed integer programming model is as follows:
further, the constraint conditions in the step S2 include:
wherein Z is + Representing a positive integer.
Further, the dual variables in the step S5 include:p f 、r k andt fk wherein, the method comprises the steps of, wherein,p f as a dual variable of the constraint of formula (4),r k the dual variables that are constraints of equation (5),t fk the dual variables that are constraints of equation (6).
Further, the check number formula in step S6 is as follows:
（10）。
the construction method of each stand plane active network in the step S6 comprises the following steps:
each stand aircraft activity network comprises two types of attributes, namely a node and an edge, wherein the aircraft activity is defined as the node, and flights with non-overlapping duration are connected based on the starting and ending time of the flights, so that two aircraft activities can be placed at the same stand;
newly added two nodes A and B respectively represent a starting point and an ending point, and the two nodes are connected with each aircraft active node;
defining node costs, for start point A and end point B, costs are 0, and the rest of node costs are。
Further, the shortest path solving in step S6 includes:
(1) Generating a directed acyclic graph network according to all nodes contained in the stand;
(2) Performing topological ordering on the directed acyclic graph network;
(3) Initializing the distance to the starting point A to 0, and setting the distances to all other vertexes to infinity;
(4) Traversing the topological node, and continuously updating the node cost based on the dynamic programming principle until the endpoint B.
(5) And selecting the node with the lowest current cost, and backtracking the preamble node to obtain a shortest path.
Further, the step S7 specifically includes:
step S71 sets the maximum value of the non-integer in the linear relaxation solution as the diving boundaryσ；
Step S72 of solving the linear relaxation for greater than the lower diving limitσThe lower bound of the variable of (2) is fixed to be 1;
step S73, re-solving the mixed integer programming model based on the value constraint range updated by the existing variable, and returning to step S71 if a non-integer solution still exists after the solution; otherwise, step S8 is performed.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, the function of stopping the same airplane is considered for different airplane stations, and the exchange of airplane activities among the airplane stations can be realized by designing exchange rules, so that the robustness of the scheme is improved.
2. The invention brings the cost and the use constraint of the tractor resources into the model, and designs the airport resource scheduling problem from the perspective of multiple resources, thereby obtaining a more reasonable and coordinated optimization scheme.
Drawings
In order to more clearly illustrate the technical solutions of the present invention, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for collaborative scheduling of multidimensional resources at an airport provided by the invention;
FIG. 2 is a schematic diagram of an interchange rule provided by the present invention;
FIG. 3 is a schematic diagram of another interchange rule provided by the present invention;
fig. 4 is a schematic diagram of a sub-problem network provided by the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth such as the particular system architecture, techniques, etc., in order to provide a thorough understanding of the embodiments of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
An airport multidimensional resource collaborative scheduling method according to the present invention will be described in detail with reference to the accompanying drawings.
Fig. 1 is a flow chart of a multi-dimensional resource collaborative scheduling method for an airport.
As shown in fig. 1, the method includes:
step S1 establishes a mixed integer programming model of airport stand resources,
step S11, constructing a stand set according to stand attributes based on an airport stand resource databaseK；
Stand assemblyKIn (3) standkComprising the following steps: whether the terminal is near, can place the model, flight type, VIP terminal;
flight collectionAFlights in (b)aComprising the following steps: flight number, tail number, model, flight type, departure airport, arrival airport, departure time and arrival time;
aircraft activity setFIn aircraft activitiesfComprising the following steps: tail number, model, stop time, withdrawal time, leading flights and following flights.
Step S12, constructing a flight set according to the demand attribute based on the flight scheduleA；
Step S13 based on the set of stand positionsKAnd flight collectionAGenerating a feasible flight set of each stand, and generating an aircraft active set according to three active states of take-off, arrival and stay of each flight aircraftF；
Fig. 2 is a schematic diagram of an interchange rule provided by the present invention, and fig. 3 is a schematic diagram of another interchange rule provided by the present invention.
Step S14 is based on the aircraft activity setFStand assemblyKEstablishing a mixed integer programming model;
the step S14 of establishing a mixed integer programming model includes:
defining a set:
stand assemblyKStand of machinek∈K；
Flight collectionAFlight ofa∈A；
Aircraft activity setFAircraft movementf∈F；
Stand of machinekDistribution plan set of (a)S k Distribution plans∈S k ；
For movement of aircraftfAlternative stand plan set；
Defining parameters:
c ks : stand of machinekDistribution plansIs added to the cost of (a) the (b),
: stand of machinekDistribution plansInherent cost of (2);
: stand of machinekDistribution plansThe tractor use cost;
α f : aircraft activityfThe cost of the de-allocation;
β fk : stand of machinekOn-board aircraft activitiesfExchanging the obtained profit;
defining variables:
δ fs : aircraft activityfDistribution plans1 when the time is equal to or 0 when the time is equal to or less than the time;
v f : aircraft activityfWhen the dragging is needed, the dragging is 1, otherwise, the dragging is 0;
x ks :0-1 variable, at the standkDistribution plans1 when the time is equal to or 0 when the time is equal to or less than the time;
y f :0-1 variable, aircraft movementf1 when de-allocated, otherwise 0;
z fk : integer variable, standkOn-board aircraft activityfThe number of interchangeable stands may be selected.
S2, designing an objective function and constraint conditions of a mixed integer programming model;
in step S2, designing an objective function based on minimizing stand use cost, minimizing tractor use cost, minimizing flight cancellation cost, and maximizing stand interchangeability;
to the aircraft activity distributed in the remote location, a penalty cost is givenh 1 Then there is
（1）
To be towed to another machine position by using a tractorTo give a fuel consumption cost to the aircraft activityh 2 ，
（2）
The objective function expression of the mixed integer programming model is as follows:
the constraint conditions in the step S2 include:
wherein Z is + Representing a positive integer.
Step S3, designing a column generation algorithm to solve a linear relaxation problem of the mixed integer programming model, wherein the linear relaxation problem comprises a limiting main problem and a sub-problem;
s4, randomly selecting a plurality of historical stand scheduling schemes as initial feasible solutions;
s5, solving a limiting main problem to obtain a dual variable;
the dual variables in step S5 include:p f 、r k andt fk wherein, the method comprises the steps of, wherein,p f as a dual variable of the constraint of formula (4),r k the dual variables that are constraints of equation (5),t fk the dual variables that are constraints of equation (6).
Step S6, constructing a child problem inspection number formula, constructing an airplane movable network of each airplane station based on the inspection number formula by each child problem, designing a shortest path solving method to obtain a shortest path of the airplane movable network of each airplane station, adding the shortest path as a new variable into the limiting main problem if the inspection number of the shortest path is smaller than 0, and returning to the step S5; if the inspection number of the shortest path of each stand plane active network is not less than 0, finishing the linear relaxation problem solving, and executing the step S7;
the formula of the check number in step S6 is as follows:
（10）。
the construction method of each stand plane active network in the step S6 comprises the following steps:
each stand aircraft activity network comprises two types of attributes, namely a node and an edge, wherein the aircraft activity is defined as the node, and flights with non-overlapping duration are connected based on the starting and ending time of the flights, so that two aircraft activities can be placed at the same stand;
fig. 4 is a schematic diagram of a sub-problem network provided by the present invention.
Newly added two nodes A and B respectively represent a starting point and an ending point, and the two nodes are connected with each aircraft active node;
defining node costs, for start point A and end point B, costs are 0, and the rest of node costs are。
The shortest path solution in step S6 includes:
(1) Generating a directed acyclic graph network according to all nodes contained in the stand;
(2) Performing topological ordering on the directed acyclic graph network;
(3) Initializing the distance to the starting point A to 0, and setting the distances to all other vertexes to infinity;
(4) Traversing the topological node, and continuously updating the node cost based on the dynamic programming principle until the endpoint B.
(5) And selecting the node with the lowest current cost, and backtracking the preamble node to obtain a shortest path.
S7, solving an integer solution by using a diving heuristic algorithm based on a linear relaxation solution;
the step S7 specifically comprises the following steps:
step S71 sets the maximum value of the non-integer in the linear relaxation solution as the diving boundaryσ；
Step S72 of solving the linear relaxation for greater than the lower diving limitσThe lower bound of the variable of (2) is fixed to be 1;
step S73, re-solving the mixed integer programming model based on the value constraint range updated by the existing variable, and returning to step S71 if a non-integer solution still exists after the solution; otherwise, step S8 is performed.
And S8, generating a stand scheduling scheme based on the obtained integer solution, drawing a stand scheduling diagram by utilizing the Gantt chart, and completing the cooperative scheduling of the multidimensional resources of the airport.
Any combination of the above optional solutions may be adopted to form an optional embodiment of the present application, which is not described herein in detail.
The following are examples of the apparatus of the present invention that may be used to perform the method embodiments of the present invention. For details not disclosed in the embodiments of the apparatus of the present invention, please refer to the embodiments of the method of the present invention.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic, and should not limit the implementation process of the embodiment of the present invention.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and are intended to be included in the scope of the present invention.

Claims (2)

1. The multi-dimensional resource collaborative scheduling method for the airport is characterized by comprising the following steps of:
step S1 establishes a mixed integer programming model of airport stand resources,
step S11, constructing a stand set according to stand attributes based on an airport stand resource databaseK；
Step S12, constructing a flight set according to the demand attribute based on the flight scheduleA；
Step S13 is based on the set of stand positionsKAnd the flight setAGenerating a feasible flight set of each stand, and generating an aircraft active set according to three active states of take-off, arrival and stay of each flight aircraftF；
Step S14 is based on the aircraft activity setFStand assemblyKEstablishing a mixed integer programming model;
s2, designing an objective function and constraint conditions of a mixed integer programming model;
step S3, designing a column generation algorithm to solve a linear relaxation problem of the mixed integer programming model, wherein the linear relaxation problem comprises a limiting main problem and a sub-problem;
s4, randomly selecting a plurality of historical stand scheduling schemes as initial feasible solutions;
step S5, solving the limiting main problem to obtain a dual variable;
step S6, constructing a child problem inspection number formula, constructing an airplane movable network of each airplane station based on the inspection number formula by each child problem, designing a shortest path solving method to obtain a shortest path of the airplane movable network of each airplane station, adding the shortest path as a new variable into the limiting main problem if the inspection number of the shortest path is smaller than 0, and returning to the step S5; if the inspection number of the shortest path of each stand plane active network is not less than 0, finishing the linear relaxation problem solving, and executing the step S7;
step S7, based on the linear relaxation solution, solving an integer solution by using a diving heuristic algorithm;
s8, generating a stand scheduling scheme based on the obtained integer solution, drawing a stand scheduling diagram by utilizing the Gantt chart, and completing cooperative scheduling of multidimensional resources of the airport;
the stand assemblyKIn (3) standkComprising the following steps: whether the terminal is near, can place the model, flight type, VIP terminal;
the flight setAFlights in (b)aComprising the following steps: flight number, tail number, model, flight type, departure airport, arrival airport, departure time and arrival time;
the aircraft active setFIn aircraft activitiesfComprising the following steps: tail number, model, stop time, withdrawal time, leading flights and following flights;
the step S14 of establishing a mixed integer programming model includes:
defining a set:
stand assemblyKStand of machinek∈K；
Flight collectionAFlight ofa∈A；
Aircraft activity setFAircraft movementf∈F；
Stand of machinekDistribution plan set of (a)S k Distribution plans∈S k ；
For movement of aircraftfAlternative stand plan set；
Defining parameters:
c ks : stand of machinekDistribution plansIs added to the cost of (a) the (b),
: stand of machinekDistribution plansInherent cost of (2);
: stand of machinekDistribution plansThe tractor use cost;
α f : aircraft activityfThe cost of the de-allocation;
β fk : stand of machinekOn-board aircraft activitiesfExchanging the obtained profit;
defining variables:
δ fs : aircraft activityfDistribution plans1 when the time is equal to or 0 when the time is equal to or less than the time;
v f : aircraft activityfWhen the dragging is needed, the dragging is 1, otherwise, the dragging is 0;
x ks :0-1 variable, at the standkDistribution plans1 when the time is equal to or 0 when the time is equal to or less than the time;
y f :0-1 variable, aircraft movementf1 when de-allocated, otherwise 0;
z fk : integer numberVariable, standkOn-board aircraft activityfThe number of interchangeable stands can be selected;
in the step S2, the objective function is designed based on minimizing the stand use cost, minimizing the tractor use cost, minimizing the flight cancellation cost and maximizing the stand interchangeable quantity;
to the aircraft activity distributed in the remote location, a penalty cost is givenThen there is
（1）
To the aircraft activity which needs to be towed to another aircraft location using a tractor, a fuel consumption cost is given，
（2）
The objective function expression of the mixed integer programming model is as follows:
（3）；
the constraint conditions in the step S2 include:
wherein Z is + Represents a positive integer;
the dual variables in the step S5 include: 、/>and->Wherein->Dual variable for constraint of formula (4), +.>Dual variable for constraint of formula (5), +.>A dual variable that is a constraint of equation (6);
the formula of the check number in step S6 is as follows:
（10）；
the construction method of the movable network of each stand plane in the step S6 comprises the following steps:
each stand aircraft activity network comprises two types of attributes, namely a node and an edge, wherein the aircraft activity is defined as the node, and flights with non-overlapping duration are connected based on the starting and ending time of the flights, so that two aircraft activities can be placed at the same stand;
newly adding two nodes C and B which respectively represent a starting point and an ending point, wherein the two nodes are connected with each aircraft active node;
defining node costs, for node C and node B, costs are 0, and the remaining node costs are；
The shortest path solving method in step S6 includes:
(1) Generating a directed acyclic graph network according to all nodes contained in the stand;
(2) Performing topological ordering on the directed acyclic graph network;
(3) Initializing the distance to the node C to 0, and setting the distances to all other nodes to infinity;
(4) Traversing the topological node, and continuously updating the node cost based on a dynamic planning principle until the node B;
(5) And selecting the node with the lowest current cost, and backtracking the preamble node to obtain a shortest path.
2. The method for collaborative scheduling of airport resources according to claim 1, wherein step S7 specifically comprises:
step S71 sets the maximum value of the non-integer in the linear relaxation solution as the diving boundaryσ；
Step S72 of solving the linear relaxation for greater than the lower diving limitσThe lower bound of the variable of (2) is fixed to be 1;
step S73, re-solving the mixed integer programming model based on the value constraint range updated by the existing variable, and returning to step S71 if a non-integer solution still exists after the solution; otherwise, step S8 is performed.
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