CN114936804A - Airport multidimensional resource cooperative scheduling method - Google Patents
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Abstract
The invention relates to the technical field of airport resource allocation, and provides a method for airport multidimensional resource cooperative scheduling. The method comprises the following steps: establishing a mixed integer programming model of airport parking lot resources, and designing a target function and constraint conditions of the mixed integer programming model; a design column generation algorithm is used for solving a linear relaxation problem of the mixed integer programming model, and a plurality of historical parking space scheduling schemes are randomly selected to serve as initial feasible solutions; solving a main problem of limitation to obtain a dual variable; and solving an integer solution by using a diving heuristic algorithm to generate a parking space scheduling scheme, and drawing a parking space scheduling graph by using a Gantt graph to complete the cooperative scheduling of the multidimensional airport resource. According to the invention, through designing the interchange rule, the exchange of airplane activities is realized among the parking positions, the robustness of the scheme is improved, the airport resource scheduling problem is designed from a multi-resource perspective, and a more reasonable and coordinated optimization scheme is obtained.
Description
Technical Field
The invention relates to the technical field of airport resource allocation, in particular to an airport multidimensional resource cooperative scheduling method.
Background
The development of civil aviation is now being developed vigorously due to the benefits of aviation policy and the rapid increase in global travel demand. However, the rapid increase in global airline passenger demand and passenger throughput has resulted in many large airports already approaching saturation in capacity. Therefore, airport operation management faces a great challenge, and managers need to optimize airport resource scheduling urgently. In an airport operation system, the problem of airplane parking space resource allocation is one of the core scheduling jobs of an airport. Each flight that takes off or lands from the airport needs to be assigned a feasible stand to perform ground operations. Therefore, efficient and reliable parking space allocation is of great importance to airports, which not only relates to the operation efficiency of airports, but also affects the degree of satisfaction of passengers for airport services.
Currently, regarding a related method for the problem of airplane parking space allocation, the following three aspects are mainly considered as targets for optimization: passengers, airports, and airlines. Passenger-considered parking space allocation methods are mainly guided by passenger satisfaction, such as minimizing passenger walking distance, airplane turning time and the like. The airport parking space allocation method is mainly based on the airport operation efficiency as guidance, such as maximum bridge approach rate, minimum far airport usage amount and the like. Considering the method for allocating the parking spaces of the airlines, the method is mainly guided by the operation cost, such as minimizing the number of transposition of the airplanes. However, flight delays introduce many uncertainties to airport operations due to uncertain factors such as bad weather, airspace regulations, and the like, which often occur.
Disclosure of Invention
In view of this, the invention provides a method for collaborative scheduling of multidimensional resources of an airport, so as to solve the problem of allocation of parking lot resources in an airport operation system in the prior art.
The invention provides an airport multidimensional resource cooperative scheduling method, which comprises the following steps:
step S1 builds a mixed integer planning model for airport stand resources,
step S11 is based on airport parking space resource database, according to the attributes of the parking space, constructs the parking space setK；
Step S12 is based on the flight schedule, according to the demand attribute, constructs the flight setA；
Step S13 is based on the stand setKAnd the set of flightsAGenerating feasible flight set of each stand, and generating airplane activity set according to three activity states of take-off, arrival and stop of each flight airplaneF；
Step S14 is based on the set of airplane activitiesFAnd parking space setKEstablishing a mixed integer programming model;
step S2, designing an objective function and a constraint condition of the mixed integer programming model;
step S3, a column generation algorithm is designed to solve a linear relaxation problem of the mixed integer programming model, wherein the linear relaxation problem comprises a main constraint problem and a sub-constraint problem;
step S4, randomly selecting a plurality of historical parking space scheduling schemes as initial feasible solutions;
step S5, solving the main problem of limitation to obtain dual variables;
step S6, constructing a subproblem check number formula, constructing each stand aircraft activity network based on the check number formula by each subproblem, designing a shortest path solution to obtain the shortest path of each stand aircraft activity network, if the shortest path check number is less than 0, adding the shortest path as a new variable into the main limiting problem, and returning to the step S5; if the check number of the shortest path of the airplane active network of each stand is not less than 0, the linear relaxation problem solution is completed, and the step S7 is executed;
step S7, solving an integer solution by using a diving heuristic algorithm based on a linear relaxation solution;
and step S8, generating a parking space scheduling scheme based on the obtained integer solution, and drawing a parking space scheduling graph by using a Gantt chart to complete the cooperative scheduling of the airport multidimensional resources.
Further, the stand setsKParking space inkThe method comprises the following steps: whether the aircraft is close to the airport or not, the type of the aircraft which can be placed, the type of flight and whether the VIP airport or not;
the set of flightsAFlight in (1)aThe method comprises the following steps: flightNumber, tail number, model, flight type, departure airport, arrival airport, departure time, arrival time;
the aircraft activity setFAircraft activity infThe method comprises the following steps: tail number, machine type, stop time, gear withdrawing time, preorder flight and follow-up flight.
Further, the step S14 of building a mixed integer programming model includes:
a set is defined:
parking space setKParking spacek∈K；
Set of flightsAFlight, flighta∈A；
Aircraft activity assemblyFAircraft activityf∈F；
Parking spacekDistribution plan set ofS k Distribution plans∈S k ；
Can be used for airplane activitiesfAlternate stand plan set
；
Defining parameters:
c ks : parking spacekDistribution plansThe cost of (a) of (b),
α f : aircraft activityfA cost of being deallocated;
β fk : parking spacekBoarding activitiesfInterchanging the resulting profits;
defining variables:
δ fs : aircraft activityfDistribution plansIf the value is 1, otherwise, the value is 0;
v f : aircraft activityf1 when dragging is needed, or 0;
x ks : variable 0-1, in standkDistribution plansIf the value is 1, otherwise, the value is 0;
y f : 0-1 variable, airplane activityfWhen the allocation is cancelled, the value is 1, otherwise, the value is 0;
z fk : integer variable, standkAircraft activity onfThe number of stands to be interchanged can 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 interchangeable amount;
giving a penalty cost to the activities of the aircraft allocated to the remote stationsh 1 Then there is
For aircraft activities requiring towing to another location using a towing vehicle, a cost of fuel consumption is givenh 2 ，
The objective function expression of the mixed integer programming model is as follows:
further, the constraint conditions in step S2 include:
wherein Z is + Representing a positive integer.
Further, the dual variables in step S5 include:p f 、r k andt fk wherein, in the process,p f is a dual variable of the constraint of equation (4),r k is a dual variable of the constraint of equation (5),t fk is a dual variable of the constraint of equation (6).
Further, the check number formula in step S6 is as follows:
the method for constructing the activity network of each stand aircraft in the step S6 comprises the following steps:
each stop plane airplane activity network comprises two types of attributes of nodes and edges, airplane activities are defined as the nodes, and flights with non-overlapping duration time are connected on the basis of the starting and ending time of the flights to indicate that the two airplane activities can be placed in the same stop plane;
two new nodes A and B are added to respectively represent a starting point and an end point, and the two nodes are connected with each airplane movable node;
defining node costs, for a starting point A and an end point B, the cost is 0, and the rest of the node costs are
Further, the shortest path solution in step S6 includes:
(1) generating a directed acyclic graph network according to all nodes contained in the stand;
(2) carrying out topological sorting 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 be infinite;
(4) and traversing the topological nodes, and continuously updating the node cost based on the dynamic programming principle until the end point B is reached.
(5) And selecting the node with the lowest current cost, and backtracking the preorder nodes to obtain a shortest path.
Further, the step S7 specifically includes:
step S71, the maximum value of the non-integer in the linear relaxation solution is set as the diving lower boundσ；
Step S72 is to make the linear relaxation larger than the diving lower boundσThe lower bound of the variable of (1) is fixed as 1;
step S73, based on the value constraint range after the existing variable is updated, the mixed integer programming model is solved again, if the non-integer solution still exists after the solution, the step S71 is returned; otherwise, step S8 is executed.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention considers that different parking spaces have the function of parking airplanes of the same model, and the exchange of airplane activities can be realized among the parking spaces by designing the interchange rule, thereby improving the robustness of the scheme.
2. The method brings cost and use constraint of the tractor resources into a model, and designs the airport resource scheduling problem from a multi-resource perspective, thereby obtaining a more reasonable and coordinated optimization scheme.
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In order to more clearly illustrate the technical solutions of the present invention, the drawings used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart of a multidimensional resource cooperative scheduling method for an airport provided by the present 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 particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the 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.
The airport multidimensional resource cooperative scheduling method according to the present invention will be described in detail below with reference to the accompanying drawings.
Fig. 1 is a flowchart of an airport multidimensional resource cooperative scheduling method provided by the present invention.
As shown in fig. 1, the method includes:
step S1 builds a mixed integer planning model for airport stand resources,
step S11 is based on airport parking space resource database, according to the attributes of the parking space, constructs the parking space setK；
Parking space setKParking space inkThe method comprises the following steps: whether the aircraft is close to the airport or not, the type of the aircraft which can be placed, the type of flight and whether the VIP airport or not;
set of flightsAFlight in (1)aThe method comprises the following steps: flight number, machine tail number, machine type, flight type, takeoff airport, arrival airport, takeoff time and arrival time;
aircraft activity assemblyFAircraft activity infThe method comprises the following steps: the airplane tail number, the airplane type, the stop time, the gear withdrawing time, the preamble flight and the subsequent flight.
Step S12 is based on the flight schedule, according to the demand attribute, constructs the flight setA；
Step S13 is based on the stand setKAnd set of flightsAGenerating feasible flight set of each stand and generating airplane activity set according to three activity states of take-off, arrival and stay of each flight airplaneF；
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 set of airplane activitiesFAnd parking space setKEstablishing a mixed integer programming model;
the step S14 of establishing the mixed integer programming model includes:
defining a set:
parking space setKStop positionk∈K；
Set of flightsAFlight, flighta∈A；
Aircraft activity assemblyFAircraft activityf∈F；
Parking spacekDistribution plan set ofS k Distribution plans∈S k ；
Can be used for airplane activitiesfAlternate stand plan set
；
Defining parameters:
c ks : parking spacekDistribution plansThe cost of (a) of (b),
α f : aircraft activityfA cost of being deallocated;
β fk : parking spacekBoarding activitiesfInterchanging the resulting profits;
defining variables:
δ fs : aircraft activityfDistribution plansIf the value is 1, otherwise, the value is 0;
v f : aircraft activityf1 when dragging is needed, or 0;
x ks : variable 0-1, at standkDistribution plansIf the value is 1, otherwise, the value is 0;
y f : 0-1 variables, airplane activityfWhen the allocation is cancelled, the value is 1, otherwise, the value is 0;
z fk : integer variable, standkAirplane activity onfThe number of stands to be interchanged can be selected.
Step S2, designing an objective function and a constraint condition of the mixed integer programming model;
in step S2, an objective function is designed based on the minimized stand use cost, the minimized tractor use cost, the minimized flight cancellation cost, and the maximized stand interchangeable amount;
giving a penalty cost to the activities of the aircraft allocated to the remote stationsh 1 Then there is
For aircraft activities requiring towing to another location using a towing vehicle, a cost of fuel consumption is givenh 2 ，
The objective function expression of the mixed integer programming model is as follows:
the constraint conditions in step S2 include:
wherein Z is + Represents a positive integer.
Step S3, a column generation algorithm is designed to solve a linear relaxation problem of the mixed integer programming model, wherein the linear relaxation problem comprises a main constraint problem and a sub-constraint problem;
step S4, randomly selecting a plurality of historical parking space scheduling schemes as initial feasible solutions;
step S5, solving a main problem of limitation to obtain a dual variable;
the dual variables in step S5 include:p f 、r k andt fk wherein, in the process,p f is a dual variable of the constraint of equation (4),r k is a dual variable of the constraint of equation (5),t fk is a dual variable of the constraint of equation (6).
Step S6, constructing a subproblem check number formula, constructing each stand aircraft activity network based on the check number formula by each subproblem, designing a shortest path solution to obtain the shortest path of each stand aircraft activity network, if the shortest path check number is less than 0, adding the shortest path as a new variable into the main limiting problem, and returning to the step S5; if the check number of the shortest path of the airplane active network of each stand is not less than 0, the linear relaxation problem solution is completed, and the step S7 is executed;
the check number formula in step S6 is as follows:
the method for constructing the activity network of each stand aircraft in the step S6 comprises the following steps:
each stand-off airplane activity network comprises two attributes of a node and an edge, airplane activities are defined as the nodes, flights with non-overlapping duration are connected on the edge based on the starting and ending time of the flights, and the fact that the two airplane activities can be placed in the same stand-off is shown;
FIG. 4 is a schematic diagram of a sub-problem network provided by the present invention.
Two new nodes A and B are added to respectively represent a starting point and an end point, and the two nodes are connected with each airplane movable node;
defining node costs, for a starting point A and an end point B, the cost is 0, and the rest of the 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) carrying out topological sorting 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 be infinite;
(4) and traversing the topological nodes, and continuously updating the node cost based on a dynamic programming principle until the end point B is reached.
(5) And selecting the node with the lowest current cost, and backtracking the preorder nodes to obtain a shortest path.
S7, solving an integer solution by using a diving heuristic algorithm based on a linear relaxation solution;
step S7 specifically includes:
step S71, the maximum value of the non-integer in the linear relaxation solution is set as the diving lower boundσ；
Step S72 is to make the linear relaxation larger than the diving lower boundσThe lower bound of the variable of (1) is fixed as 1;
step S73, re-solving the mixed integer programming model based on the updated value constraint range of the existing variable, and returning to the step S71 if a non-integer solution remains after solving; otherwise, step S8 is executed.
And step S8, generating a parking space scheduling scheme based on the obtained integer solution, and drawing a parking space scheduling graph by using a Gantt chart to complete the cooperative scheduling of the airport multidimensional resources.
All the above optional technical solutions may be combined arbitrarily to form optional embodiments of the present application, and are not described herein again.
The following are embodiments of the apparatus of the present invention that may be used to perform embodiments of the method of the present invention. For details which are not disclosed in the embodiments of the apparatus of the present invention, reference is made to the embodiments of the method of the present invention.
It should be understood that, the sequence numbers of the steps in the foregoing embodiments do not imply an execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.
The above examples are only intended to illustrate the technical solution of the present invention, and not to limit it; although the present 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 solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present invention, and are intended to be included within the scope of the present invention.
Claims (10)
1. An airport multidimensional resource cooperative scheduling method is characterized by comprising the following steps:
step S1 builds a mixed integer planning model for airport stand resources,
step S11 is based on the airport stand resource database, according to the attributes of the stand, constructs the stand setK；
Step S12 is based on the flight schedule, according to the demand attribute, constructs the flight setA；
Step S13 is based on the stand setKAnd the set of flightsAGenerating a set of feasible flights for each stand, and followingThree activity states of take-off, arrival and stay of each flight airplane are generated to generate airplane activity setsF；
Step S14 is based on the set of airplane activitiesFAnd stand setKEstablishing a mixed integer programming model;
step S2, designing an objective function and a constraint condition of the mixed integer programming model;
step S3, a column generation algorithm is designed to solve a linear relaxation problem of the mixed integer programming model, wherein the linear relaxation problem comprises a main constraint problem and a sub-constraint problem;
step S4, randomly selecting a plurality of historical parking space scheduling schemes as initial feasible solutions;
step S5, solving the main problem of limitation to obtain dual variables;
step S6, constructing a subproblem check number formula, constructing each stand aircraft activity network based on the check number formula by each subproblem, designing a shortest path solution to obtain the shortest path of each stand aircraft activity network, if the shortest path check number is less than 0, adding the shortest path as a new variable into the main limiting problem, and returning to the step S5; if the check number of the shortest path of the airplane active network of each stand is not less than 0, the linear relaxation problem solution is completed, and the step S7 is executed;
step S7, solving an integer solution by using a diving heuristic algorithm based on the linear relaxation solution;
and step S8, generating a parking space scheduling scheme based on the obtained integer solution, and drawing a parking space scheduling graph by using a Gantt chart to complete the cooperative scheduling of the airport multidimensional resources.
2. The airport multidimensional resource collaborative scheduling method of claim 1,
the set of standKParking space inkThe method comprises the following steps: whether the aircraft is close to the airport or not, the type of the aircraft which can be placed, the type of flight and whether the VIP airport or not;
the set of flightsAFlight in (1)aThe method comprises the following steps: flight number, machine tail number, machine type, flight type, takeoff airport, arrival airport, takeoff time and arrival time;
the aircraft activity setFAircraft activity infThe method comprises the following steps: the airplane tail number, the airplane type, the stop time, the gear withdrawing time, the preamble flight and the subsequent flight.
3. The airport multidimensional resource collaborative scheduling method of claim 2, wherein the step S14 of establishing the mixed integer programming model comprises:
defining a set:
parking space setKParking spacek∈K；
Set of flightsAFlight, flighta∈A；
Aircraft activity assemblyFAircraft activityf∈F；
Parking spacekDistribution plan set ofS k Distribution plans∈S k ；
Can be used for airplane activitiesfAlternate stand plan set
；
Defining parameters:
c ks : parking spacekDistribution plansThe cost of (a) of (b),
α f : aircraft activityfA cost of being deallocated;
β fk : parking spacekBoarding activitiesfInterchanging the resulting profits;
defining variables:
δ fs : aircraft activityfDistribution plansIf the value is 1, otherwise, the value is 0;
v f : aircraft activityf1 when dragging is needed, or 0;
x ks : variable 0-1, at standkDistribution plansIf the value is 1, otherwise, the value is 0;
y f : 0-1 variable, airplane activityfWhen the allocation is cancelled, the value is 1, otherwise, the value is 0;
z fk : integer variable, standkAirplane activity onfThe number of stands to be interchanged can be selected.
4. The airport multidimensional resource co-scheduling method of claim 3, wherein in step S2, the objective function is designed based on minimizing stand use cost, minimizing tractor use cost, minimizing flight cancellation cost, and maximizing stand interchangeable quantity;
giving a penalty cost to the activities of the aircraft allocated to the remote locationh 1 Then there is
For aircraft activities that require towing to another location using a towing vehicle, a cost of fuel consumption is givenh 2 ，
The objective function expression of the mixed integer programming model is as follows:
5. the airport multidimensional resource co-scheduling method of claim 3, wherein the constraints of step S2 include:
wherein Z is + Representing a positive integer.
6. The airport multidimensional resource co-scheduling method of claim 3, wherein the dual variables in step S5 comprise:p f 、r k andt fk wherein, in the step (A),p f is a dual variable of the constraint of equation (4),r k is a dual variable of the constraint of equation (5),t fk is a dual variable of the constraint of equation (6).
7. The airport multidimensional resource co-scheduling method of claim 3, wherein the check number formula in step S6 is as follows:
8. the airport multidimensional resource collaborative scheduling method of claim 6, wherein the construction method of each stand aircraft activity network in the step S6 is as follows:
each stand-off airplane activity network comprises two attributes of a node and an edge, airplane activities are defined as the nodes, flights with non-overlapping duration are connected on the edge based on the starting and ending time of the flights, and the fact that the two airplane activities can be placed in the same stand-off is shown;
two new nodes A and B are added to respectively represent a starting point and an end point, and the two nodes are connected with each airplane movable node;
defining node costs, for a starting point A and an end point B, the cost is 0, and the rest of the node costs are
9. The airport multidimensional resource co-scheduling method of claim 8, wherein the shortest path solution in step S6 comprises:
(1) generating a directed acyclic graph network according to all nodes contained in the stand;
(2) carrying out topological sorting 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 be infinite;
(4) traversing the topological nodes, and continuously updating the node cost based on a dynamic programming principle until a terminal point B is reached;
(5) and selecting the node with the lowest current cost, and backtracking the preorder nodes of the node to obtain a shortest path.
10. The airport multidimensional resource collaborative scheduling method of claim 1, wherein the step S7 specifically comprises:
step S71, the maximum value of the non-integer in the linear relaxation solution is set as the diving lower boundσ；
Step S72 is to make the linear relaxation larger than the diving lower boundσThe lower bound of the variable of (1) is fixed as 1;
step S73, based on the value constraint range after the existing variable is updated, the mixed integer programming model is solved again, if the non-integer solution still exists after the solution, the step S71 is returned; otherwise, step S8 is executed.
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