CN114358446B - Robust optimization method for airport resource scheduling - Google Patents
Robust optimization method for airport resource scheduling Download PDFInfo
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Abstract
The invention relates to a robust optimization method for airport resource scheduling, belongs to the technical field of airport resource allocation, and solves the problems of poor robustness and low solving efficiency of the conventional airport parking lot scheduling scheme. Constructing an objective function based on the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor, establishing a scheduling optimization model and converting the scheduling optimization model into a linear relaxation model; constructing a corresponding weighted directed graph based on the airplane activity set of each stand; acquiring an initial scheduling scheme set of each stand, solving the solution of the limited main problem, calculating dual variables, circularly acquiring the shortest path with the weight directed graph of each stand and the check number thereof, adding the scheduling scheme corresponding to the shortest path with the check number less than 0 into the scheduling scheme set, and continuously solving until the solutions of the limited main problem are integer solutions; and obtaining an aircraft stop scheduling optimization scheme based on the integer solution and the final scheduling scheme set. The reasonable and efficient distribution of airport resources is realized.
Description
Technical Field
The invention relates to the technical field of airport resource allocation, in particular to a robust optimization method for airport resource scheduling.
Background
With the continuous increase of social economy and the improvement of the requirements of the national people on the quality of life, the civil aviation has the characteristics of convenience and comfort, so that the position of air transportation is continuously improved in a comprehensive transportation system. With the rapid increase of passenger transport demand and passenger throughput, the operation management and safe operation guarantee for airport resources are also receiving more attention. Unreasonable stop-plane scheduling schemes can result in low airport operation efficiency and even flight delay spread. Therefore, efficient and robust parking lot resource scheduling is an important task for guaranteeing efficient operation of the airport.
In the existing airplane parking space scheduling work, the aim of approaching bridge rate is mainly considered, namely, the distributed number of the near airplane spaces is maximized. In a small amount of work considering scheduling robustness, the buffer time of adjacent airplanes in the same flight space is simply maximized, but the flight space conflict caused by the randomness of flight delay cannot be well reflected in the method.
Most of the existing shutdown position scheduling solving algorithms work by using a heuristic or solver to directly solve. However, the heuristic algorithm is difficult to ensure the optimality of the obtained scheduling scheme, and the direct solution of the solver is only suitable for small-scale cases and is difficult to meet the requirements of actual large/medium airports.
Disclosure of Invention
In view of the foregoing analysis, the embodiments of the present invention are directed to providing a robust optimization method for airport resource scheduling, so as to solve the problems of poor robustness and low solution efficiency of the existing airport stand scheduling scheme.
The embodiment of the invention provides a robust optimization method for airport resource scheduling, which comprises the following steps:
constructing an objective function based on the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor, establishing a scheduling optimization model, and converting the model into a linear relaxation model;
constructing a corresponding weighted directed graph according to the check number of the linear relaxation model based on the airplane activity set of each stand;
adopting a branch pricing algorithm taking a column generation algorithm as a core to solve the linear relaxation model, wherein the method comprises the following steps: based on airport parking positions and flight plan information, acquiring a scheduling scheme of each parking position as an initial scheduling scheme set, solving the solution of the limited main problem of a linear relaxation model, calculating dual variables, circularly acquiring the shortest path and the check number of the weighted directed graph of each parking position, and adding the scheduling scheme corresponding to the shortest path with the check number less than 0 into the scheduling scheme set to continuously solve the solution of the limited main problem; performing continuous branch iteration through a column generation algorithm until the solutions of the limited main problem are integer solutions;
and obtaining an aircraft stop scheduling optimization scheme based on the integer solution and the final scheduling scheme set.
Based on the further improvement of the method, the stand comprises a near stand and a far stand;
the stand operation cost is obtained by summing the usage cost of each aircraft activity in the scheduling plan of each stand, wherein:
when the stand is a near stand, the use cost of each airplane activity in the scheduling scheme of the stand is 0;
when the stand is a remote stand, the usage cost of each aircraft activity in the scheduling plan for the stand is a preset non-negative cost.
Based on a further improvement of the above method, the stand robustness cost is derived from the sum of expected stand conflicts for each adjacent aircraft activity in the scheduling plan for each stand.
Based on a further improvement of the above method, the step of calculating the expected position conflict for each adjacent aircraft activity comprises:
preprocessing historical flight data, and acquiring the minimum delay time and the maximum delay time of each airplane activity and the minimum delay time and the maximum delay time of all airplane activities;
taking the minimum delay time and the maximum delay time of all airplane activities as the starting point and the ending point of a statistical range, taking a preset time interval as a frequency band, and counting the airplane activity delay probability in each frequency band in the statistical range to obtain flight delay probability distribution;
and obtaining the delay time range of the activity of the adjacent aircraft when the aircraft stands conflict according to the idle time of the activity of each adjacent aircraft at the same aircraft stand and the delay time of the activity of the previous aircraft, and obtaining the expected aircraft stand conflict of the activity of each adjacent aircraft based on the delay time range and the flight delay probability distribution.
Based on the further improvement of the method, based on the delay time range and the flight delay probability distribution, the calculation formula of the expected airplane position conflict of each adjacent airplane activity is obtained as follows:
wherein the content of the first and second substances,t j for the preceding aircraft activity in each adjacent aircraft activityjThe time is delayed,t j’ for the latter aircraft activity in each adjacent aircraft activityj’The delay time, in units of minutes,t j ∈[T MIN ,T MAX ]，T MIN for aircraft activitiesjThe minimum delay time is set to be a minimum,T MAX for aircraft activityjThe maximum time of the delay is set to be,
for aircraft activities𝑗Delay oft j The probability of a minute or so,
for aircraft activities𝑗’Delay oft j’ The probability of a minute or so,b jj’ for each adjacent aircraft in the same standjAndj’the idle time in between.
Based on a further improvement of the above method, the cost of using the towing vehicle is obtained by summing the cost of using the towing vehicle between each adjacent aircraft activity in the scheduling scheme of each stand, wherein:
when the towing operation of the towing vehicle exists between every two adjacent airplane activities, the using cost of the towing vehicle between every two adjacent airplane activities is 1, otherwise, the using cost is 0.
Based on the further improvement of the method, an objective function is constructed based on the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor, and a scheduling optimization model is established, wherein the method comprises the following steps:
taking the sum of the stand operation cost, the stand robustness cost and the tractor use cost as the total scheduling cost, and taking the minimum total scheduling cost as an objective function;
taking as a first constraint that each aircraft activity can be scheduled to a stand;
taking each stand-off position as a second constraint condition, wherein each stand-off position can be only allocated to one scheduling scheme or not allocated to the scheduling scheme;
using the number of the tractors not more than the total number of the tractors at any time as a third constraint condition;
whether the scheduling scheme is used is taken as a decision variable constraint.
Based on the further improvement of the method, based on the airplane activity set of each stand, a corresponding weighted directed graph is constructed according to the check number of the linear relaxation model, and the method comprises the following steps:
acquiring the starting time and the ending time of each airplane activity based on the airplane activity set of each stand;
setting a starting point and an end point of the weighted directed graph, wherein the weights of the starting point and the end point are 0;
all airplane activities are taken as nodes, and the node weight is the cost of using the airplane activities minus the cost of dual variables of the first constraint condition;
all the nodes and the starting point and the end point construct an edge as a direct connection edge, and the weight of the direct connection edge is 0;
traversing the airplane activity set, if the ending time of one airplane activity is less than the starting time of the other airplane activity, constructing an edge between the two airplane activities as an associated edge, wherein the weight of the associated edge is the dual variable of the sum of the expected position conflict and the tractor use cost of the two airplane activities minus a third constraint condition.
Based on the further improvement of the method, the shortest path and the check number of the weighted directed graph of each stand are obtained, and the method comprises the following steps:
carrying out topological sequencing on the airplane active nodes in the weighted directed graph;
initializing a label set of each node to be empty, wherein labels in the label set comprise cost from a starting point to a current node and a number of a previous node;
sequentially traversing each node according to the sequence of topological sorting, calculating the cost from the starting point to the current node of each node, and updating the node label with the minimum cost until the end point;
when all the nodes are traversed, backtracking to the previous node from the end point according to the number of the previous node in the node label set until the starting point, and combining the backtracked nodes to obtain the shortest path;
the cost from the starting point to the current node in the node label set of the node before the end point in the shortest path is used as the cost of the shortest path;
and subtracting the dual variable of the second constraint condition from the shortest path cost to obtain a check number.
Based on the further improvement of the method, the method comprises the following steps of generating an algorithm through a column and continuously branching and iterating until the solutions of the limited main problem are integer solutions:
if the check number is less than 0, adding the corresponding scheduling scheme of the shortest path into the scheduling scheme set, generating a new decision variable, and iteratively solving the solution of the limited main problem; otherwise, whether the solutions of the limited main problems are integers or not is identified, if the solutions are not integers, each non-integer solution is divided into two types of constraints of 0 and 1, the two scheduling optimization models after branching are added respectively, and iterative solution is carried out by using the column generation algorithm again until the solutions of all the limited main problems after branching are integer solutions.
Compared with the prior art, the invention can realize at least one of the following beneficial effects:
1. the method comprises the steps of analyzing possible conflict situations of the stand based on historical flight delay data, and designing an expected stand conflict calculation method according to the delay time range and the aircraft delay probability of each aircraft in the historical flights, so that the robustness cost of stand scheduling is obtained, the stand is enabled to be more consistent with the actual airport operation scene, and the optimized scheduling scheme is more reasonable.
2. The method is characterized in that a multi-dimensional target optimization-based integer programming model is established by comprehensively considering far/near stand-by positions, tractor use and scheduling scheme robustness, a branch pricing algorithm framework is established to solve the model, and the airplane activity scheduling scheme corresponding to the stand-by positions obtained through a node label shortest path algorithm is used for optimizing the limited main problem for each stand-by position, so that the solving efficiency can be ensured, the effect of stand resource scheduling is better met, and the airport operation efficiency is improved.
3. Not only a near-machine-position scheduling scheme but also a far-machine-position scheduling scheme and the constraint of the traction vehicle resources on the scheduling scheme are considered, so that the optimized scheduling scheme is adaptive to the practical problem, and the applicability of the scheduling scheme is guaranteed.
In the invention, the technical schemes can be combined with each other to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout the drawings;
FIG. 1 is a flowchart of a robust optimization method for airport resource scheduling in an embodiment of the present invention;
FIG. 2 is a schematic illustration of the movement of two aircraft in a normal situation at the same stand in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of the movement of two adjacent aircraft in the event of a conflict at the same stand in accordance with an embodiment of the present invention;
fig. 4 is a flowchart of a method for solving the airplane stop position scheduling optimization scheme in the embodiment of the present invention.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
The invention discloses a robust optimization method for airport resource scheduling, which is based on airport stand and flight plan information acquired from an airport and an airline department, considers the use cost of stands and tractors and the problem of stand conflict caused by airplane delay, and obtains a scheduling optimization scheme of each stand by taking the minimum total scheduling cost of the stands as an optimization target.
It should be noted that, according to the airport stand and flight schedule information, an initial data set is constructed, which includes:
based on the resource information of the airport parking positions, the parking position set is constructed according to the attributes of the parking positionsKThe method comprises the following steps: the number of the stand, the near/far stand, the type of the machine which can be accommodated, whether the stand is moored and whether the stand is international/domestic;
based on flight schedule information, an airplane set is constructed according to flight attributesAWith set of flightsFWherein the aircraft are integratedAThe method comprises the following steps: tail number and type of airplane, set of flightsFThe method comprises the following steps: flight number, execution date, task type, flight nationality, arrival/departure, tail number, takeoff airport, takeoff time, landing airport, landing time, and airplane type;
based on parking space setKAirplane assemblyAWith set of flightsFGenerating each stand according to the flight time information and attribute information of the stop capable of stoppingkAircraft activity set ofJ，k∈KAircraft activity setsJThe method comprises the following steps: type of activity, tail number, startA start time and an end time, wherein the activity types include: the arrival, the stop and the departure of the airplane respectively represent the operation of arriving the airplane, the operation of staying the airplane and the operation of taking off the airplane.
Based on the initial data set, the robust optimization method for airport resource scheduling is shown in fig. 1, and comprises the following steps:
s11: constructing an objective function based on the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor, establishing a scheduling optimization model, and converting the model into a linear relaxation model;
the following details the step S11 into the steps S110 to S113.
S110: constructing the operation cost of the stand;
it should be noted that the operating cost of the stand is mainly determined by the stand types, which include a near stand and a far stand. Because approaching stations can be more involved in boarding and disembarking and cleaning operations, both airports and passengers are more likely to place arriving or departing flights at the approaching stations. Therefore, the bridge approach rate is improved by imposing a certain penalty cost on the remote airport.
Specifically, the stand operation cost is derived from a summation of the usage cost of each aircraft activity in the scheduling plan for each stand, wherein:
when the stand is a near stand, the use cost of each airplane activity in the scheduling scheme of the stand is 0;
when the stand is a remote stand, the usage cost of each aircraft activity in the scheduling plan for the stand is a preset non-negative cost.
As shown in formula (1), standkUpper scheduling schemesThe operation cost of the stand is as follows:
Wherein the content of the first and second substances,a js is a 0-1 parameter, when the scheduling scheme is adoptedsIncluding aircraft activitiesjIf the value is 1, otherwise, the value is 0;assign jk for aircraft activitiesjAt standkThe cost of use ofkWhen the mobile phone is at a remote location,assign jk for a given non-negative cost; when in usekWhen the mobile phone is close to the machine position,assign jk is 0.
It should be noted that the non-negative costs preset for a plurality of remote locations may be the same or different.
S111: constructing a parking stall robustness cost;
it should be noted that fig. 2 shows two consecutive aircraft activities at the same stand under normal conditions, and no conflict occurs. When a flight is delayed, a conflict may occur between airplane activities, and a specific conflict scenario is shown in fig. 3. When the airplane activity 1 is delayed or the airplane activity 2 arrives in advance, two continuous airplane activities on the original parking space allocation plan are collided, so that the spread in an airport is delayed, and the operation efficiency is influenced. According to the method, the expected airplane position conflict of the activities of two adjacent airplanes in the same airplane parking position is calculated, and the robustness cost of airplane parking position scheduling is built, so that the airplane parking position is more consistent with the actual airport operation scene.
Specifically, the step of calculating the expected airplane space conflict for each adjacent airplane activity comprises:
preprocessing historical flight data, and acquiring minimum delay time and maximum delay time of each airplane activity and minimum delay time and maximum delay time of all airplane activities;
taking the minimum delay time and the maximum delay time of all airplane activities as the starting point and the ending point of a statistical range, taking a preset time interval as a frequency band, and counting the airplane activity delay probability in each frequency band in the statistical range to obtain flight delay probability distribution;
illustratively, the minimum delay time of all airplane activities is 1 minute, and the maximum delay time of all airplane activities is 60 minutes, then the airplane delay probability is counted in the range of [1,60] by using a frequency counting method according to a frequency band of every 5 minutes, and the flight delay probability distribution is obtained.
And thirdly, obtaining the delay time range of the activity of the adjacent aircraft when the aircraft stands conflict according to the idle time of the activity of each adjacent aircraft at the same aircraft stand and the delay time of the activity of the previous aircraft, and obtaining the expected aircraft stand conflict of the activity of each adjacent aircraft based on the delay time range and the flight delay probability distribution.
Adjacent aircraft moving in the same parking positionjAndj’for the purpose of illustration, the first and second components,T MIN for aircraft activitiesjThe minimum delay time is set to be a minimum,T MAX for aircraft activitiesjThe maximum delay time is set to be a maximum,b jj’ for movement adjacent to aircraftjAndj’idle time in between, then when the aircraft is activejDelay time oft j Is [ 2 ]T MIN +b jj’ ,T MAX ]At any time in range, the aircraft is movingj’The delay time of (2)T MIN ,t j -b jj’ ]At any one time, the aircraft stand will collide, and therefore the expected stand collision for each adjacent aircraft activity is calculated as:
Wherein the content of the first and second substances,
for aircraft activities𝑗Delay oft j The probability of a minute or so,
for aircraft activities𝑗’Delay oft j’ The probability of minutes; based on the flight delay probability distribution, according to𝑗And𝑗’corresponding delay time, corresponding delay probability can be obtained.
And (4) summing the expected airplane position conflicts of the activities of each adjacent airplane in the scheduling scheme of each airplane position to obtain the robustness cost of the airplane position, wherein the airplane position is shown as a formula (3)kUpper scheduling schemesCost of robustness ofComprises the following steps:
Wherein the content of the first and second substances,a j’s anda js likewise, for 0-1 parameters, when scheduling schemessIncluding aircraft activitiesj’If the value is 1, otherwise, the value is 0;Jis the airplane activity set.
S112: constructing the use cost of the tractor;
according to the type of airplane activity, only when adjacent activities of the same airplane are parked at different parking spaces, towing operation needs to be carried out by using a towing vehicle. Therefore, the present embodiment measures the cost by counting the towing times of the scheduling plan of each stand, that is, the towing vehicle usage cost is obtained by summing the towing vehicle usage costs between each adjacent aircraft activity in the scheduling plan of each stand, wherein: when the towing operation of the towing vehicle exists between every two adjacent airplane activities, the using cost of the towing vehicle between every two adjacent airplane activities is 1, otherwise, the using cost is 0.
As shown in equation (4), standkUpper scheduling schemesThe tractor has the following use cost:
Wherein the content of the first and second substances,tow jj’ is a 0-1 parameter and represents the activity of each adjacent aircraft at the same parking spacejAnd withj’The cost of tractor use;J A the type of airplane activity is shown as airplane activity at the arrival of the airplane,J P an aircraft activity indicating that the type of aircraft activity is an aircraft-off,f j ≠f j’ the illustration is two different aircraft that are shown,f j ,f j’ belongs to the set of flightsF。
S113: establishing a scheduling optimization model;
constructing an objective function based on the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor, and establishing a scheduling optimization model, wherein the method comprises the following steps:
taking the sum of the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor as the total scheduling cost, taking the minimized total scheduling cost as an objective function, and expressing the minimized total scheduling cost as follows:
Wherein the content of the first and second substances,Kin order to be a set of stand positions,S k for stand of aircraftkEach stand of the feasible scheduling scheme setkUpper scheduling schemesIncluding a set of temporally non-overlapping aircraft activities,
for stand of aircraftkUpper scheduling schemesThe operating cost of the stand of the aircraft,
for stand of aircraftkUpper scheduling schemesThe cost of the stand robustness of the aircraft,
for stand of aircraftkUpper scheduling schemesThe cost of use of the tractor of (a),x ks e {0,1} is a decision variable constraint and represents a machine halt positionkUpper scheduling schemesIf it is used, it is 1, otherwise it is 0.
The objective function indicates that a better off-site scheduling scheme is to be found to reduce the overall scheduling cost, i.e., to solve for a feasible solution that makes the objective function smaller.
Second constraint that each aircraft activity can be scheduled to an aircraft stand is expressed as:
It should be noted that, the first constraint condition is taken as an aircraft activity coverage constraint, which ensures that each aircraft activity can be arranged to a near position or a far position, and reduces the loss caused by flight cancellation.
Taking each stand-off position as a second constraint condition, the second constraint condition is expressed as that:
It should be noted that the second constraint condition is used as a uniqueness constraint of the airplane stop scheduling scheme, and in consideration of the idle condition of the flight plan, it is guaranteed that each near airplane stop or far airplane stop can be allocated to only one scheduling scheme or not allocated to the scheduling scheme.
Taking the number of the used tractors at any time not more than the total number of the tractors as a third constraint condition, and expressing as follows:
Wherein the content of the first and second substances,Mrepresents the total number of tractors at the current airport,Tthe time of the opening of the stand is shown,ω jj’t is shown at the time of daytMovement of aircraftjAndj’if the tractor is used, the value is 1 if the tractor is used, otherwise the value is 0. The third constraint condition is used as the constraint of the number of the tractor resources, and the number of the tractors used at any time can be ensured to be less than or equal to the total number of the tractors in the current airport, so that the established scheduling optimization model is really suitable for operation of the airport.
According to the three constraint conditions and the corresponding dual variables, the calculation formula of the decision variable check number is as follows:
Wherein alpha is j Is a dual variable of the first constraint,β k is a dual variable of the second constraint,γ t is a dual variable of the third constraint.
It should be noted that the established scheduling optimization model is an integer programming model based on multi-dimensional optimization, and in order to improve the solving efficiency of the model and obtain a better scheme, the scheduling optimization model is subjected to linear relaxation, and a branch pricing algorithm with a column generation algorithm as a core is adopted for solving.
Performing linear relaxation on the scheduling optimization model, namely, enabling decision variables to be changed from integer variablesx ks E {0,1} change to a continuous variablex ks ∈[0,1],k∈K,s∈S k Thereby obtaining a linear relaxation model.
S12: constructing a corresponding weighted directed graph according to the inspection number of the linear relaxation model based on the airplane activity set of each stand;
by analyzing the composition of equation (9), a pricing subproblem model in the column generation algorithm is constructed.
In particular, equation (9) consists of three parts, a first part relating to a single aircraft activity, a second part relating to the cost of robustness and the cost of towing vehicles for two adjacent aircraft activities of the same stand, and a third part being a fixed cost, corresponding to the dual variable values of the second constraint. To minimize the number of checks, for each standkAnd constructing a specific pricing subproblem model.
The objective function of the pricing subproblem model is a minimized test number, which is used for solving to obtain a new scheduling scheme, and is expressed as:
Constraints for pricing subproblems include:
for each airplane activityjAt each scheduling schemesCan only be selected once orNot selected, represented as:
For each two adjacent aircraft activities on the same standjAndj’there cannot be overlap in time, thus reducing the flight conflict, reducing the robustness cost and the tractor cost, expressed as:
Wherein the content of the first and second substances,
indicating the latter aircraft activity of each adjacent aircraft activityj’The start time of (c) is,
representing the previous aircraft activity in each adjacent aircraft activityjThe end time of (c).
Decision variable constraints for pricing subproblems represent current aircraft activityjWhen the current parking position is arranged, the variable is 1, otherwise, the variable is 0; expressed as:
According to the objective function and constraint conditions of the pricing sub-model, the embodiment expresses the pricing sub-model as the shortest path problem of the weighted directed graph, the aircraft activities in the aircraft activity set are taken as nodes based on the aircraft activity set of each stand, and the weights of the nodes and the edges are defined according to a check number formula, so that the check number of each pricing sub-problem is obtained, and whether a better scheduling scheme exists is identified.
Specifically, the steps of constructing the weighted directed graph corresponding to each stand are as follows:
acquiring the starting time and the ending time of each airplane activity based on the airplane activity set of each stand;
setting a starting point and an end point of the weighted directed graph, wherein the weights of the starting point and the end point are 0;
taking all airplane activities as nodes, wherein the node weight is the cost of using the airplane activities minus the cost of dual variables of the first constraint condition, and is expressed as:assign jk -α j ；
fourthly, constructing an edge by all the nodes and the starting point and the end point, wherein the edge is used as a direct connection edge, and the weight of the direct connection edge is 0;
traversing the airplane activity set, if the ending time of one airplane activity is less than the starting time of the other airplane activity, constructing an edge between the two airplane activities as an associated edge, wherein the weight of the associated edge is the dual variable obtained by subtracting a third constraint condition from the sum of the expected airfield conflict and the tractor use cost of the two airplane activities, and the dual variable is represented as:
according to the check number formula (9),β k for stand of aircraftkAnd (4) adding judgment after the shortest path cost calculation is finished. Therefore, the pricing subproblem model is reasonably converted into the weighted directed graph, so that the solving efficiency is ensured, the effect of parking space resource scheduling can be better met, and the operating efficiency of the airport is improved.
S13: adopting a branch pricing algorithm taking a column generation algorithm as a core to solve the linear relaxation model, wherein the method comprises the following steps: based on airport parking positions and flight plan information, acquiring a scheduling scheme of each parking position as an initial scheduling scheme set, solving the solution of the limited main problem of a linear relaxation model, calculating dual variables, circularly acquiring the shortest path and the check number of the weighted directed graph of each parking position, and adding the scheduling scheme corresponding to the shortest path with the check number less than 0 into the scheduling scheme set to continuously solve the solution of the limited main problem; performing continuous branch iteration through a column generation algorithm until the solutions of the limited main problem are integer solutions;
specifically, as shown in fig. 4, the branch pricing algorithm with the column generation algorithm as the core is adopted, and the steps of solving the linear relaxation model are as follows:
s130: acquiring a scheduling scheme of each stand-off position as an initial scheduling scheme set based on the stand-off positions of the airport and flight plan information;
specifically, based on airport stand and flight plan information, a group of airplane activity sequences which are not conflicted in time are quickly obtained by using a depth-first search algorithm aiming at each stand and are used as an initial feasible solution of each stand to be put into a scheduling scheme set.
S131: solving the solution of the limited main problem of the linear relaxation model, and calculating dual variables;
illustratively, a limited main problem is solved by using a mathematical solver Cplex or Gurobi, and dual variables of three constraint conditions are calculated.
S132: circularly acquiring the shortest path and the check number of the weighted directed graph of each shutdown position according to the dual variable;
specifically, for each weighted directed graph, the steps of obtaining the shortest path and its check number are as follows:
carrying out topological sequencing on airplane active nodes in an authorized directed graph;
initializing the label set of each node to be empty, wherein the labels in the label set comprise the cost from the starting point to the current node and the number of the previous node;
traversing each node in sequence according to the sequence of topological sequencing, calculating the cost from the starting point of each node to the current node, and updating the node label with the minimum cost until the end point;
it should be noted that a dynamic programming method may be adopted to ensure that the label set of the node at any time is currently optimal. Exemplarily, the label set of the node 1 is { (2, s) }, the label set of the node 2 is { (3, s) }, and there are associated edges between the node 3 and both the node 1 and the node 2, when the label set of the node 3 is updated, the weight of the node 3 is 1, the weight of the associated edge of the node 1 and the node 3 is 1, and the weight of the associated edge of the node 2 and the node 3 is also 1, then when the previous node of the node 3 is 1, the cost from the starting point to the node 3 = the starting point to the cost of the node 1+ the weight of the associated edge of the node 1 and the node 3+ the weight of the node 3 =2+1+1= 4; when the previous node to node 3 is 2, the cost from the origin to node 3 = the cost from the origin to node 2+ the weight of the associated edge of node 2 with node 3+ the weight of node 3 =3+1+1= 5; and updating with the minimum cost, namely selecting the node 1 as the node before the node 3, wherein the label set of the node 3 can be updated to be { (4,1) }. And the node label set is updated by analogy in sequence until the end point t.
When all nodes are traversed, backtracking to the previous node from the end point according to the number of the previous node in the node label set until the starting point, and combining the backtracked nodes to obtain the shortest path;
fifthly, the cost from the starting point to the current node in the node label set of the node before the end point in the shortest path is used as the cost of the shortest path;
and sixthly, subtracting the dual variable of the second constraint condition from the shortest path cost to obtain a test number.
S133: identifying whether a check number smaller than 0 exists in the check numbers obtained in the previous step, if so, indicating that a scheduling scheme enabling the limited main problem to be more optimal exists, adding the scheduling scheme corresponding to the corresponding shortest path into a scheduling scheme set, generating a new decision variable, and repeating the steps S131-S133 to iteratively solve the solution of the limited main problem; if not, go to step S134;
s134: and identifying whether the solutions of the limited main problems are integers or not, if the solutions are not integers, dividing each non-integer solution into two types of constraints of 0 and 1, respectively adding the two scheduling optimization models after branching, and repeating the steps S131-S134 to carry out iterative solution by using the column generation algorithm again until the solutions of all the limited main problems after branching are integer solutions.
Illustratively, a solution to a restricted master problemx 1 When =0.3, two types of constraints are generated,x 1 =0 andx 1 =1, two models after branching are added separately.
S14: and obtaining an aircraft stop scheduling optimization scheme based on the integer solution and the final scheduling scheme set.
It should be noted that, if the integer solution of the shutdown position is 1, the shutdown position corresponds to a scheduling scheme; if the integer solution of the stand is 0, the stand is not used in the scheduling scheme. And taking out the scheduling scheme with the integer solution of 1 from the final scheduling scheme set to obtain the stop position scheduling optimization scheme.
Preferably, based on the scheduling optimization scheme, a gantt chart control of Qt (a C + + graphical user interface application framework across platforms) is used to generate a scheduling gantt chart, with time as the abscissa and a scheduling scheme of specified aircraft stops as the ordinate, and with blocks representing the duration of the stop of the aircraft activity and indicating the aircraft tail number.
Compared with the prior art, the robust optimization method for airport resource scheduling provided by the embodiment analyzes the possible conflict situation of the stand based on the historical flight delay data, and according to the delay time range and the aircraft delay probability of each aircraft in the historical flights, the computer stands conflict, so that the robust cost of the stand scheduling is established, the stand is more consistent with the actual airport operation scene, and the optimized scheduling scheme is more reasonable; the method comprises the steps of comprehensively considering robustness of far/near stand, tractor use and scheduling schemes, establishing an integer programming model based on multi-dimensional target optimization, and establishing a branch pricing algorithm framework to solve the model, wherein for each stand, an airplane activity scheduling scheme corresponding to the stand obtained through a node label shortest path algorithm is used for optimizing a limited main problem, so that the solving efficiency can be ensured, the effect of stand resource scheduling is better met, and the airport operation efficiency is improved; not only a near-machine-position scheduling scheme but also a far-machine-position scheduling scheme and the constraint of the traction vehicle resources on the scheduling scheme are considered, so that the optimized scheduling scheme is adaptive to the practical problem, and the applicability of the scheduling scheme is guaranteed.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (8)
1. A robust optimization method for airport resource scheduling is characterized by comprising the following steps:
constructing an objective function based on the operation cost of the stand, the robustness cost of the stand and the use cost of the tractor, establishing a scheduling optimization model, and converting the model into a linear relaxation model;
the stand robustness cost is obtained by summing expected stand conflicts of each adjacent aircraft activity in a scheduling scheme of each stand;
the step of calculating the expected airplane space conflict of each adjacent airplane activity comprises the following steps:
preprocessing historical flight data, and acquiring the minimum delay time and the maximum delay time of each airplane activity and the minimum delay time and the maximum delay time of all airplane activities;
taking the minimum delay time and the maximum delay time of all airplane activities as the starting point and the ending point of a statistical range, taking a preset time interval as a frequency band, and counting the airplane activity delay probability in each frequency band in the statistical range to obtain flight delay probability distribution;
obtaining the delay time range of the activity of the adjacent aircraft when the aircraft stands conflict according to the idle time of the activity of each adjacent aircraft at the same aircraft stand and the delay time of the activity of the previous aircraft, and obtaining the expected aircraft stand conflict of the activity of each adjacent aircraft based on the delay time range and the flight delay probability distribution;
the scheduling optimization model takes the sum of the stand operation cost, stand robustness cost and tractor use cost as a total scheduling cost, and takes the minimized total scheduling cost as an objective function;
constructing a corresponding weighted directed graph according to the check number of the linear relaxation model based on the airplane activity set of each stand; the set of aircraft activities includes: an activity type, a tail number, a start time, and an end time, wherein the activity type includes: aircraft arrive, berth and depart;
adopting a branch pricing algorithm taking a column generation algorithm as a core to solve the linear relaxation model, wherein the method comprises the following steps: based on airport parking positions and flight plan information, obtaining a scheduling scheme of each parking position as an initial scheduling scheme set, solving the solution of the limited main problem of the linear relaxation model, calculating dual variables, circularly obtaining the shortest path and the check number of the weighted directed graph of each parking position, and adding the scheduling scheme corresponding to the shortest path with the check number smaller than 0 into the scheduling scheme set to continuously solve the solution of the limited main problem; performing continuous branch iteration through a column generation algorithm until the solutions of the limited main problem are integer solutions;
and obtaining an aircraft stop scheduling optimization scheme based on the integer solution and the final scheduling scheme set.
2. The robust optimization method of airport resource scheduling of claim 1, wherein said stand comprises a near stand and a far stand;
the stand operation cost is obtained by summing usage costs of each aircraft activity in a scheduling plan for each stand, wherein:
when the stand is a near stand, the use cost of each airplane activity in the scheduling scheme of the stand is 0;
when the stand is a remote stand, the usage cost of each aircraft activity in the scheduling plan for the stand is a preset non-negative cost.
3. The robust optimization method for airport resource scheduling of claim 1, wherein the calculation formula for obtaining the expected flight level conflict for each adjacent airplane activity based on the delay time range and the flight delay probability distribution is as follows:
wherein, the first and the second end of the pipe are connected with each other,t j for the preceding aircraft activity in each adjacent aircraft activityjThe time is delayed,t j’ for the latter aircraft activity in each adjacent aircraft activityj’The delay time, in units of minutes,t j ∈[T MIN ,T MAX ]，T MIN for aircraft activitiesjThe minimum delay time is set to be a minimum,T MAX for aircraft activitiesjThe maximum delay time is set to be a maximum,
for aircraft activity𝑗Delay oft j The probability of a minute or so,
for aircraft activity𝑗’Delay oft j’ The probability of a minute or so,b jj’ for each adjacent aircraft in the same standjAndj’the idle time in between.
4. The robust optimization method for airport resource scheduling of claim 1, wherein the cost of tractor usage is derived from the sum of the cost of tractor usage between each adjacent aircraft activity in the scheduling scheme for each stand, wherein:
when the towing operation of the towing vehicle exists between every two adjacent airplane activities, the using cost of the towing vehicle between every two adjacent airplane activities is 1, otherwise, the using cost is 0.
5. The robust optimization method for airport resource scheduling of claim 1, wherein said constructing an objective function based on stand operation cost, stand robustness cost and tractor usage cost, and establishing a scheduling optimization model comprises:
taking as a first constraint that each aircraft activity can be scheduled to a stand;
taking each stand-off position as a second constraint condition, wherein each stand-off position can be only allocated to one scheduling scheme or not allocated to the scheduling scheme;
using the number of the tractors not more than the total number of the tractors at any time as a third constraint condition;
whether the scheduling scheme is used is taken as a decision variable constraint.
6. The robust optimization method for airport resource scheduling of claim 5, wherein said constructing a corresponding weighted directed graph based on the activity set of the aircraft at each stand according to the number of checks of the linear relaxation model comprises:
acquiring the starting time and the ending time of each airplane activity based on the airplane activity set of each stand;
setting a starting point and an end point of a weighted directed graph, wherein the weights of the starting point and the end point are 0;
all airplane activities serve as nodes, and the node weight is the cost of using the airplane activities minus the cost of dual variables of the first constraint condition;
all nodes and a starting point and an end point construct an edge as a direct connection edge, and the weight of the direct connection edge is 0;
and traversing the aircraft activity set, if the ending time of one aircraft activity is less than the starting time of the other aircraft activity, constructing an edge between the two aircraft activities as an associated edge, wherein the weight of the associated edge is the dual variable of the sum of the expected position conflict and the tractor use cost of the two aircraft activities minus a third constraint condition.
7. The method of claim 6, wherein the obtaining the shortest path of the weighted directed graph and its check number for each stand comprises:
carrying out topological sequencing on the airplane active nodes in the weighted directed graph;
initializing a label set of each node to be empty, wherein labels in the label set comprise cost from a starting point to a current node and a number of a previous node;
sequentially traversing each node according to the topological sorting sequence, calculating the cost from the starting point to the current node of each node, and updating the node label with the minimum cost until the end point;
when all the nodes are traversed, backtracking to the previous node from the end point according to the number of the previous node in the node label set until the starting point, and combining the backtracked nodes to obtain the shortest path;
the cost from the starting point to the current node in the node label set of the node before the end point in the shortest path is used as the cost of the shortest path;
and subtracting the dual variable of the second constraint condition from the shortest path cost to obtain a check number.
8. The method of robust optimization of airport resource scheduling of claim 1 or 7, wherein said iterating through a column generation algorithm and through successive branches until the solutions of the constrained main problem are all integer solutions, comprises:
the check number of the shortest path of the weighted directed graph of each stand is used as the check number of a pricing subproblem in a column generation algorithm, if the check number is less than 0, the scheduling scheme corresponding to the corresponding shortest path is added into the scheduling scheme set, a new decision variable is generated, and the solution of the limited main problem is solved in an iterative manner; otherwise, whether the solutions of the limited main problems are integers or not is identified, if the solutions are not integers, each non-integer solution is divided into two types of constraints of 0 and 1, the two scheduling optimization models after branching are added respectively, and iterative solution is carried out by using the column generation algorithm again until the solutions of all the limited main problems after branching are integer solutions.
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