CN111563636B - Three-stage meta-heuristic parking space allocation optimization method - Google Patents

Three-stage meta-heuristic parking space allocation optimization method Download PDF

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CN111563636B
CN111563636B CN202010666353.0A CN202010666353A CN111563636B CN 111563636 B CN111563636 B CN 111563636B CN 202010666353 A CN202010666353 A CN 202010666353A CN 111563636 B CN111563636 B CN 111563636B
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赵伟
李瑞瑞
金楚欣
马勇
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Beijing Futong Oriental Technology Co ltd
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Abstract

The invention discloses a three-stage meta-heuristic method for optimizing the distribution of stand-offs, which is implemented according to the following steps: preprocessing the data to obtain a mapping relation between flights and positions; establishing an aircraft stop allocation model according to the mapping relation between the flights and the aircraft stops; and (5) searching by adopting a three-stage meta-heuristic optimal solution to obtain a machine position distribution scheme. The invention solves the problems of overlong time for distributing the parking positions for large-scale flight distribution and unsatisfactory distribution result optimization indexes in the prior art under the multi-constraint condition, can quickly obtain a high-quality parking position distribution scheme under the large-scale and multi-constraint condition of an airport, greatly improves the core indexes such as bridge rate, corridor bridge rate, distribution satisfaction degree and the like compared with the traditional method, and has good adaptability under the continuously changing service scene.

Description

Three-stage meta-heuristic parking space allocation optimization method
Technical Field
The invention belongs to the technical field of aviation, and particularly relates to a three-stage meta-heuristic method for optimizing the distribution of stand-to-aircraft.
Background
With the rapid development of the civil aviation transportation industry in China in recent years, the number of flights is increasing continuously, and it has become a challenge to maintain the orderly and efficient operation of airports. Under the condition that airport parking space resources are limited, scientific allocation of the airport parking space resources becomes one of the keys for improving the guarantee capability and the service level of the airport. In order to optimize the allocation of the stand under the condition of meeting the specific airport constraint, for example, a certain machine type can only stop at a specified stand, how to orderly and efficiently perform large-scale allocation and improve the key optimization index become the key problem of the stand allocation.
In the process of allocating the machine positions, a plurality of constraints and optimization targets need to be considered, wherein the constraints can be divided into hard constraints and soft constraints. Hard constraints are conditions that must be met during the slot assignment process, including: time conflict constraints, model constraints, user-defined mandatory type constraints. Soft constraints are constraints that can be violated in some cases, and are typically user-defined, reflecting additional requirements on the slot allocation scheme.
In the existing airplane space allocation method, problems need to be modeled, and the objective function is usually bridge-dependent rate, corridor bridge rate, allocation satisfaction degree and the like. The constraint conditions are hard constraint and soft constraint, are a multi-objective programming problem, and are generally solved by using methods such as a genetic algorithm, branch and bound, tabu search, simulated annealing and the like. Under a large-scale distribution scene, the method has long solving time, is difficult to meet various complex business requirements, and cannot ensure the efficient operation requirement of the airport in a continuously changing business scene. For example, a flight is delayed in a large area and needs to be reassigned. As another example, an airport may have a plurality of user-defined business rules, such as where an airline aircraft is preferentially parked at a designated location. The prior art cannot obtain a result which satisfies a plurality of constraints and has a perfect optimization target in a short time.
For the problem of the distribution of the parking positions, research methods adopted at home and abroad comprise genetic algorithms, branch and bound, tabu search, simulated annealing and the like. The parking space allocation problem is essentially a CSPs (Constraint safety interfaces Problems), and is a multi-objective planning problem by taking the bridge rate, the corridor bridge rate, the passenger walking distance and the like as objective functions and taking the time conflict Constraint, the model Constraint and other hard constraints as Constraint conditions. The stand allocation problem is also an NP (Non-deterministic Polynomial, NP complete) problem, and in large-scale airplanes and stand allocation problems, the solution time appears exponentially increasing. The existing algorithm has the following defects: (1) when the number of the constraint conditions is increased, the solving time is obviously increased, and the efficiency is lower. (2) When large-scale flights are processed, the result obtaining time is long. When an emergency situation, such as a large-scale flight delay, occurs, the batch distribution cannot be performed quickly.
Disclosure of Invention
The invention aims to provide a three-stage meta-heuristic method for optimizing the distribution of the stand, which solves the problems that the distribution time of the stand for large-scale flight distribution is too long and the distribution result optimization index is not ideal under the multi-constraint condition in the prior art.
The invention adopts the technical scheme that a three-stage meta-heuristic method for optimizing the allocation of the stand comprises the following steps:
preprocessing the data to obtain a mapping relation between flights and positions;
establishing an aircraft stop allocation model according to the mapping relation between the flights and the aircraft stops;
and (5) searching by adopting a three-stage meta-heuristic optimal solution to obtain a machine position distribution scheme.
Further, the data includes: flight constraint rules and flight position constraint rules;
the constraint rule comprises a weight value representing the importance degree of the constraint rule;
the flight constraint rules include: flight number, model, time of arrival, time of departure, vip grade, route, task type, airline company, terminal building to which it belongs, number of passengers;
the machine position constraint rule comprises the following steps: whether the machine position is close to the aircraft station, the station building to which the machine position belongs, the serial number of the aircraft station and the category of the aircraft station can contain a machine type set;
the machine position categories include: the non-combined machine position, a parent machine position in the combined machine position and a child machine position in the combined machine position;
further, the preprocessing the data to obtain the mapping relationship between the flight and the flight position includes:
obtaining an allocable seat set corresponding to each flight according to the flight constraint rule and the seat constraint rule;
filtering the positions where each flight can not be parked to obtain a distributable position set corresponding to each flight
Figure 961615DEST_PATH_IMAGE001
；
Obtaining the weight value of each flight stopping at the corresponding allocable stop according to the flight constraint rule and the stop constraint rule, and obtaining the allocable stop set corresponding to each flight
Figure 183649DEST_PATH_IMAGE002
Adds each flight correspondenceThe weight value of the assignable flight position is obtained to obtain the mapping relation between each flight and the flight position.
Further, the establishing of the parking space allocation model according to the mapping relationship between the flight and the parking space includes:
establishing an optimization index, wherein the optimization index comprises a bridge approach rate
Figure 783126DEST_PATH_IMAGE003
Corridor bridge ratio
Figure 168715DEST_PATH_IMAGE004
Degree of satisfaction of distribution
Figure 287980DEST_PATH_IMAGE005
；
Setting a hard constraint;
and combining the optimization indexes and the hard constraints to obtain an off-line position distribution model.
Further, the establishing of the optimization index includes:
according to the weight corresponding to each optimization index, carrying out weighted summation on the optimization indexes to obtain an optimization objective function, wherein the optimization objective function is as follows:
Figure 664604DEST_PATH_IMAGE006
（1）；
wherein, alpha, beta and gamma are bridge approach rates respectively
Figure 236531DEST_PATH_IMAGE003
Corridor bridge ratio
Figure 491057DEST_PATH_IMAGE004
Degree of satisfaction of distribution
Figure 730408DEST_PATH_IMAGE005
The weight coefficients α, β, γ corresponding to each optimization index are non-negative numbers, and the sum of the weight coefficients is equal to 1, that is:
Figure 543512DEST_PATH_IMAGE007
（2）；
the bridge bearing rate
Figure 868315DEST_PATH_IMAGE003
According to the proportion of flights near the flight position to all reliable bridge flights distributed in a certain distribution result, the calculation formula is as follows:
Figure 923602DEST_PATH_IMAGE008
（3）；
the bridge ratio of the corridor
Figure 79777DEST_PATH_IMAGE004
According to the proportion of the number of passengers on flights near the flight level to the number of passengers on all reliable bridges distributed in a certain distribution result, the calculation formula is as follows:
Figure 814515DEST_PATH_IMAGE009
（4）；
the distribution satisfaction degree
Figure 610301DEST_PATH_IMAGE005
According to a weight value score in an assignmentikCalculated, the formula is:
Figure 721477DEST_PATH_IMAGE010
（5）；
wherein Maxscore and Minscore are constants, and are calculated by the following formulas respectively under the condition that only one stand can be allocated to one flight:
Figure 92677DEST_PATH_IMAGE011
（10）；
Figure 982005DEST_PATH_IMAGE012
（11）。
flight
Figure 281399DEST_PATH_IMAGE013
F is the set of flights to be allocated and the flight position
Figure 258582DEST_PATH_IMAGE014
G is a machine position set, nfFor the number of flights to be allocated, ngThe number of machine positions;
scoreikthe meaning of (1) is that the flight i stops at the corresponding weight value of the flight k;
sithe number of passengers on flight i;
xikthe meaning of (1) is that if the flight i stops at the station k, otherwise, the flight i is 0;
Figure 832694DEST_PATH_IMAGE015
the mark is a reliable bridge flight mark, if the flight i is a reliable bridge flight, the mark is 1, otherwise, the mark is 0, and the unreliable flight can not be parked at a near airplane position;
Figure 174813DEST_PATH_IMAGE016
the meaning of (1) is that if the machine position k is a near machine position, otherwise, the machine position k is 0.
Further, the hard constraints include:
the uniqueness constraint is as follows: one flight must and can only stop at one flight level;
Figure 945192DEST_PATH_IMAGE017
（6）；
the exclusivity constraint: at most one flight can be parked on the same position at the same time;
Figure 132591DEST_PATH_IMAGE018
（7）；
and (3) combining machine position constraint: at the same time, the parent machine position and the child machine position in the combined machine position can not be used at the same time, but the child machine positions can be used at the same time;
Figure 806280DEST_PATH_IMAGE019
（8）；
safety constraint: a necessary safety time interval is required between two continuous flights distributed to the same position so as to ensure the safe leaving of the previous airplane and the safe entering of the next airplane;
Figure 53722DEST_PATH_IMAGE020
（9）；
wherein G is a set of stand, k is a stand,
Figure 514659DEST_PATH_IMAGE021
f is the set of flights to be allocated, i is the flight,
Figure 771328DEST_PATH_IMAGE013
，ngthe number of the stand positions is;
xikthe meaning of (1) is that if the flight i stops at the station k, otherwise, the flight i is 0;
xjkthe meaning of (1) is that if the flight j stops at the station k, otherwise, the flight j is 0; i is not equal to j;
Nijthe meaning of (1) is that if the time conflict exists between the flight i and the flight j, otherwise, the time conflict is 0;
Cewif the position is a combined machine position, the value is 1, otherwise, the value is 0;
if e is the parent station, w is the child station, xieThe meaning of (1) is that if the flight i stops at the parent station e, otherwise, the flight i is 0;
xjwmeaning is 1 if the flight j stops at the child station w, otherwise 0;
ETAiestimated time of arrival, ETD, for flight iiEstimated departure time, T, for flight ibufferMinimum safe time interval for the same machine position;
ETAjestimated time of arrival, ETD, for flight jjFor flightsProjected time of departure for j.
Further, the three-stage meta-heuristic optimal solution search includes:
and a heuristic stage: under the condition of minimum number of violating hard constraints and maximum optimization objective function, a greedy algorithm is used for allocating flight positions for each flight to obtain an initial solution X0；
Meta-heuristic stage I: obtaining a locally optimal solution using a delayed-tabu search algorithm under conditions that all hard constraints are met and the tabu table length is short, wherein the delayed-tabu search algorithm comprises a delayed acceptance table;
meta-heuristic stage II: using a tabu-simulated annealing algorithm, on the basis of a meta-heuristic I stage, expanding a search range, jumping out a local optimal solution, and searching a result close to global optimal in a larger range, wherein the tabu-simulated annealing algorithm comprises a tabu table;
the tabu table is used for recording historical optimal solutions to guide the direction of algorithm search.
Further, the meta-heuristic stage I includes:
(a) initialization tabu table M1A delay receiving table N, iteration parameters m and N are 0, the search termination times a, the meta-heuristic I stage termination times b and the initial solution X are set0History optimal solution X*= X0The solution set S is an empty set
Figure 876687DEST_PATH_IMAGE022
；
(b) Obtaining a new solution by adopting a random strategy and adding the new solution into a solution set S, wherein m = m + 1;
(c) judging whether the iteration parameter m is larger than a: if yes, selecting the optimal solution in the solution set S, and updating the historical optimal solution X*Tabu watch M1Delayed acceptance table N; otherwise, returning to the step (b);
(d) judging whether the iteration number n is greater than b: if yes, the algorithm is ended and X is output1=X*Otherwise n = n +1, solution set S =
Figure 42833DEST_PATH_IMAGE022
Reset m =0 and return to step (b).
Further, the meta-heuristic stage II includes:
(a) initialization tabu table M2Setting the iteration parameter m as 0, setting the search termination times c and the initial solution X1Temperature control parameter r, TfTo terminate the temperature, the historical optimum solution X*=X1The solution set S is an empty set
Figure 538536DEST_PATH_IMAGE022
The meta-heuristic type II phase termination condition is temperature T<TfThe initial value of the temperature T is T0；
(b) A random strategy was used to obtain a new solution and add it to S, m = m + 1.
(c) Judging whether the iteration parameter m is larger than c; if yes, selecting the optimal solution in S, and updating X*、M2(ii) a Otherwise, returning to the step (b);
(d) judging whether the meta-heuristic type II stage termination condition is met: if yes, outputting the optimal solution X2=X*，X2In order to satisfy all the hard constraints and optimize the solution that the maximum value of the objective function is closest to the global optimum, the algorithm is ended; otherwise T = T r, solution set S =
Figure 785847DEST_PATH_IMAGE022
Set iteration parameter m =0 and jump to step (b).
The invention has the beneficial effects that: compared with the existing algorithm, the three-stage meta-heuristic parking space allocation optimization method can quickly obtain a high-quality parking space allocation scheme under large-scale and multi-constraint conditions of an airport, greatly improves core indexes such as bridge rate, corridor bridge rate and allocation satisfaction compared with the traditional method, and has good adaptability under continuously changing service scenes.
Drawings
FIG. 1 is a schematic diagram of a three-stage meta-heuristic method for parking space allocation optimization according to the present invention;
fig. 2 is an exploded schematic diagram of a three-stage meta-heuristic method for optimizing the allocation of stand-offs according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a three-stage meta-heuristic method for optimizing distribution of shutdown positions, which is implemented according to the following steps:
step 1, preprocessing data to obtain a mapping relation between flights and seats, and specifically implementing the following steps:
the data comprises flight constraint rules and airplane space constraint rules, and each constraint rule has a weight value representing the importance degree of the constraint rule;
flight constraint rules include: flight number, model, time of arrival, time of departure, vip grade, route, task type, airline company, terminal building to which it belongs, number of passengers;
the machine position constraint rule comprises the following steps: whether the machine position is close to the aircraft station, the station building to which the machine position belongs, the serial number of the aircraft station and the category of the aircraft station can contain a machine type set;
the machine position categories include: a parent machine position, a child machine position and a non-combined machine position in the combined machine positions;
step 1.1, obtaining an allocable seat set corresponding to each flight according to flight constraint rules and seat constraint rules;
filtering the positions where each flight can not be parked to obtain a distributable position set corresponding to each flight
Figure 417816DEST_PATH_IMAGE002
(ii) a For example, a type A flight can only be parked in a far-position set, and a type B flight can only be parked in a near-position set;
step 1.2, obtaining the weight value of each flight stopping at the corresponding distributable flight level according to the flight constraint rule and the flight level constraint rule, wherein each flight obtained in the step 1.1 corresponds to the distributable flight level set
Figure 23372DEST_PATH_IMAGE002
In each caseObtaining the mapping relation between each flight and the airplane position; for example, flight p1 is preferentially allocated at flight level m1, and the weight value is 100;
step 2, establishing a parking space distribution model according to the mapping relation obtained in the step 1, and specifically implementing the following steps:
step 2.1, establishing an optimization index, wherein the optimization index comprises a bridge approach rate
Figure 334268DEST_PATH_IMAGE003
Corridor bridge ratio
Figure 932739DEST_PATH_IMAGE004
Degree of satisfaction of distribution
Figure 871746DEST_PATH_IMAGE005
；
According to the weight corresponding to each optimization index, carrying out weighted summation on the optimization indexes to obtain an optimization objective function, wherein the optimization objective function is as follows:
Figure 163050DEST_PATH_IMAGE006
（1）；
in the formula (1), α, β, γ are bridge-approaching ratios, respectively
Figure 695662DEST_PATH_IMAGE003
Corridor bridge ratio
Figure 580048DEST_PATH_IMAGE004
Degree of satisfaction of distribution
Figure 186610DEST_PATH_IMAGE005
The weight coefficients α, β, γ corresponding to each optimization index are non-negative numbers, and the sum of the weight coefficients is equal to 1, that is:
Figure 632504DEST_PATH_IMAGE007
（2）；
bridge bearing rate
Figure 324516DEST_PATH_IMAGE003
According to the proportion of flights near the flight position to all reliable bridge flights distributed in a certain distribution result, the calculation formula is as follows:
Figure 953206DEST_PATH_IMAGE008
（3）；
the bridge ratio of the corridor
Figure 679853DEST_PATH_IMAGE004
According to the proportion of the number of passengers on flights near the flight level to the number of passengers on all reliable bridges distributed in a certain distribution result, the calculation formula is as follows:
Figure 296648DEST_PATH_IMAGE009
（4）；
the distribution satisfaction degree
Figure 538274DEST_PATH_IMAGE005
According to a weight value score in an assignmentikCalculated, the formula is:
Figure 16660DEST_PATH_IMAGE010
（5）；
in the formula (5), flight
Figure 611196DEST_PATH_IMAGE013
F is the set of flights to be allocated and the flight position
Figure 87308DEST_PATH_IMAGE014
G is a machine position set, nfFor the number of flights to be allocated, ngAs number of stations, scoreikThe meaning of (1) is that the flight i stops at the corresponding weight value of the flight k;
wherein Maxscore and Minscore are constants, and are calculated by the following formulas respectively under the condition that only one stand can be allocated to one flight:
Figure 3180DEST_PATH_IMAGE023
（10）
Figure 19677DEST_PATH_IMAGE024
（11）
wherein, a certain distribution result refers to a distribution result obtained by a certain solution search, namely, each flight is distributed with a position;
flight
Figure 206070DEST_PATH_IMAGE013
F is the set of flights to be allocated and the flight position
Figure 915400DEST_PATH_IMAGE014
G is a machine position set, nfFor the number of flights to be allocated, ngThe number of machine positions;
sithe number of passengers on flight i;
xikthe meaning of (1) is that if the flight i stops at the station k, otherwise, the flight i is 0;
Figure 318569DEST_PATH_IMAGE015
the flight identifier is a reliable bridge flight identifier, if the flight is a reliable bridge flight, the flight identifier is 1, otherwise, the flight identifier is 0, and the unreliable flight cannot be parked at a near airport;
Figure 466653DEST_PATH_IMAGE025
the meaning of (1) is that if the machine position k is a near machine position, otherwise, the machine position k is 0.
Step 2.2, setting hard constraints, including:
(1) the uniqueness constraint is as follows: one flight must and can only stop at one flight level;
Figure 756820DEST_PATH_IMAGE017
（6）；
(2) the exclusivity constraint: at most one flight can be parked on the same position at the same time;
Figure 384854DEST_PATH_IMAGE018
（7）；
(3) and (3) combining machine position constraint: at the same time, the parent machine position and the child machine position in the combined machine position can not be used at the same time, but the child machine positions can be used at the same time;
Figure 26051DEST_PATH_IMAGE019
（8）；
(4) safety constraint: a necessary safety time interval is required between two continuous flights distributed to the same position so as to ensure the safe leaving of the previous airplane and the safe entering of the next airplane;
Figure 633619DEST_PATH_IMAGE020
（9）；
wherein G is a set of stand, k is a stand,
Figure 247134DEST_PATH_IMAGE014
f is the set of flights to be allocated, i is the flight,
Figure 48999DEST_PATH_IMAGE013
，ngthe number of the stand positions is;
xikthe meaning of (1) is that if the flight i stops at the station k, otherwise, the flight i is 0;
xjkthe meaning of (1) is that if the flight j stops at the station k, otherwise, the flight j is 0; i is not equal to j;
Nijthe meaning of (1) is that if the time conflict exists between the flight i and the flight j, otherwise, the time conflict is 0;
Cewif the position is a combined machine position, the value is 1, otherwise, the value is 0;
if e is the parent station, w is the child station, xieMeaning if flight i stops at the parente, is 1, otherwise is 0;
xjwmeaning is 1 if the flight j stops at the child station w, otherwise 0;
ETAiestimated time of arrival, ETD, for flight iiEstimated departure time, T, for flight ibufferMinimum safe time interval for the same machine position;
ETAjestimated time of arrival, ETD, for flight jjThe expected departure time for flight j.
Step 2.3, combining the optimized objective function obtained in the step 2.1 and the hard constraint set in the step 2.2 to obtain a stand allocation model;
step 3, searching a three-stage meta-heuristic optimal solution to obtain a machine position distribution scheme, and specifically implementing the following steps:
step 3.1, heuristic stage: under the condition of minimum number of violating hard constraints and maximum optimization objective function, a greedy algorithm is used for allocating flight positions for each flight to obtain an initial solution X0；
Step 3.2, meta-heuristic stage I: under the condition that all hard constraints are met and the length of a tabu table is short, a local optimal solution is obtained by using a delay-tabu search algorithm, wherein the delay-tabu search algorithm comprises a delay acceptance table, and specifically comprises the following steps:
step 3.2.1, initialize tabu table M1A delay receiving table N, iteration parameters m and N are 0, the search termination times a, the meta-heuristic I stage termination times b and the initial solution X are set0History optimal solution X*= X0The solution set S is an empty set
Figure 911913DEST_PATH_IMAGE022
；
Step 3.2.2, obtaining a new solution by adopting a random strategy and adding the new solution into a solution set S, wherein m = m + 1;
step 3.2.3, judging whether the iteration parameter m is larger than a: if yes, selecting the optimal solution in the solution set S, and updating the historical optimal solution X*Tabu watch M1Delayed acceptance table N; otherwise, returning to the step 3.2.2;
step 3.2.4, judging whether the iteration number n is greater than b: if yes, the algorithm is ended and X is output1=X*Otherwise n = n +1, solution set S =
Figure 323172DEST_PATH_IMAGE022
Go back to step 3.2.2 and reset m = 0;
the meta-heuristic I stage can correct an initial solution which is obtained by using a greedy algorithm in the heuristic stage and violates a hard constraint;
in the conventional TS (Tabu Search ) algorithm, a relatively short Tabu table is generally used to improve the global Search capability, but in this way, the global Search capability is obtained at the expense of the local Search capability, in order to improve the global Search capability of the algorithm, a delay acceptance is used to improve the conventional Tabu Search algorithm, a delay acceptance table is added to the TS algorithm to improve the Search capability of the TS algorithm, the input of the current stage is the local optimal solution obtained in the heuristic stage, and the output is the local optimal solution searched in the current stage and the corresponding objective function value thereof;
step 3.3, meta-heuristic II stage: using a tabu-simulated annealing algorithm, on the basis of a meta-heuristic I stage, expanding a search range, jumping out a local optimal solution, and searching a result close to global optimal in a larger range, wherein the tabu-simulated annealing algorithm comprises a tabu table for recording a historical optimal solution to guide the direction of algorithm search, and specifically comprises the following steps:
step 3.3.1: initialization tabu table M2Setting the iteration parameter m as 0, setting the search termination times c and the initial solution X1Temperature control parameter r, TfTo terminate the temperature, the historical optimum solution X*=X1The solution set S is an empty set
Figure 915827DEST_PATH_IMAGE022
The meta-heuristic type II phase termination condition is temperature T<TfThe initial value of the temperature T is T0；
Step 3.3.2: a random strategy is used to obtain a new solution and add it to the solution set S, m = m + 1.
Step 3.3.3: judging whether the iteration parameter m is larger than c; if yes, selecting the optimal solution in the solution set S, and updating X*、M2(ii) a Otherwise, returning to the step 3.3.2;
step 3.3.4: judging whether the meta-heuristic type II stage termination condition is met: if yes, outputting the optimal solution X2=X*，X2In order to satisfy all the hard constraints and optimize the solution that the maximum value of the objective function is closest to the global optimum, the algorithm is ended; otherwise T = T r, S =
Figure 137861DEST_PATH_IMAGE022
Go back to step 3.2.2 and concatenate iteration parameter m = 0.
Wherein the random strategy of step 3.2.2 and step 3.3.2 is: generating a random number, the value of which belongs to the interval [0,1 ]; the generation of random numbers can accord with normal distribution and uniform distribution; if the random number is greater than or equal to a fixed probability value, the fixed probability value is a preset value, and the value belongs to an interval (0,1), adopting a swap operator, wherein the swap operator is as follows: randomly selecting two or more flights from the flight set, and exchanging the positions allocated by the selected flights two by two to generate a new solution; if the random number is less than or equal to the fixed probability value, adopting a change operator, wherein the change operator is as follows: randomly selecting a flight from the flight set, and randomly allocating another flight in the allocable stop set corresponding to the flight to generate a new solution.
The SA (Simulated Annealing) algorithm has the advantages of high iterative search efficiency and capability of jumping out of a locally optimal solution to some extent, and has been proved to be a global optimization algorithm converging on a globally optimal solution. Under the condition of limited solving time, in order to improve the local searching capability of the SA algorithm, a smaller temperature control coefficient is usually set, and multiple searching steps are performed at the same temperature, but the global searching capability of the SA algorithm is reduced. Aiming at the problem, a tabu table is introduced for the SA algorithm, and the historical optimal solution is recorded to guide the searching direction of the algorithm. The input of the current stage is the optimal solution of the previous stage, and the output is the historical optimal solution and the corresponding objective function.
The purpose of the meta-heuristic I stage is to quickly find a solution satisfying all hard constraints, the length of a tabu table is small, and the obtained result is a locally optimal solution. The purpose of the meta-heuristic stage II is to expand the search range, jump out the local optimal solution and search a result close to global optimal in a larger range on the basis of the meta-heuristic stage I.
The three-stage meta-heuristic parking space allocation optimization method can quickly obtain a high-quality parking space allocation scheme under large-scale and multi-constraint conditions of an airport, core indexes such as bridge rate, corridor bridge rate, allocation satisfaction and the like are greatly improved compared with the traditional method, and the method has good adaptability under continuously changing service scenes.
The present invention has been described in detail with reference to the embodiments, and those skilled in the art can make various modifications to the present invention based on the above description. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention. Therefore, certain details of the embodiments are not to be interpreted as limiting, and the scope of the invention is to be determined by the appended claims.

Claims (6)

1. A three-phase meta-heuristic method for optimizing the allocation of stand-off positions is characterized by comprising the following steps:
preprocessing the data to obtain a mapping relation between flights and positions;
establishing an aircraft stop allocation model according to the mapping relation between the flights and the aircraft stops;
adopting a three-stage meta-heuristic optimal solution search to obtain a machine position distribution scheme;
the three-stage meta-heuristic optimal solution search comprises:
and a heuristic stage: under the condition of minimum number of violating hard constraints and maximum optimization objective function, a greedy algorithm is used for allocating flight positions for each flight to obtain an initial solution X0；
Meta-heuristic stage I: obtaining a locally optimal solution using a delayed-tabu search algorithm under conditions that all hard constraints are met and the tabu table length is short, wherein the delayed-tabu search algorithm comprises a delayed acceptance table;
meta-heuristic stage II: using a tabu-simulated annealing algorithm, on the basis of a meta-heuristic I stage, expanding a search range, jumping out a local optimal solution, and searching a result close to global optimal in a larger range, wherein the tabu-simulated annealing algorithm comprises a tabu table;
the meta-heuristic I phase includes:
(a) initialization tabu table M1A delay receiving table N, iteration parameters m and N are 0, the search termination times a, the meta-heuristic I stage termination times b and the initial solution X are set0History optimal solution X*＝X0The solution set S is an empty set
Figure FDA0002668426770000011
(b) Obtaining a new solution by adopting a random strategy and adding the new solution into a solution set S, wherein m is m + 1;
(c) judging whether the iteration parameter m is larger than a: if yes, selecting the optimal solution in the solution set S, and updating the historical optimal solution X*Tabu watch M1And a delayed acceptance table N; otherwise, returning to the step (b);
(d) judging whether the iteration number n is greater than b: if yes, the algorithm is ended and X is output1＝X0Otherwise n is n +1, solution set
Figure FDA0002668426770000012
Resetting m to 0 and returning to step (b);
the meta-heuristic stage II includes:
(a) initialization tabu table M2Setting the iteration parameter m as 0, setting the search termination times c and the initial solution X1Temperature control parameter r, TfTo terminate the temperature, the historical optimum solution X*＝X1The solution set S is an empty set
Figure FDA0002668426770000013
Meta-heuristic phase II termination condition is temperature T<TfThe initial value of the temperature T is T0；
(b) Obtaining a new solution by adopting a random strategy and adding the new solution into a solution set S, wherein m is m + 1;
(c) judging whether the iteration parameter m is larger than c; if yes, selecting the optimal solution in the solution set S, and updating X*、M2(ii) a Otherwise, returning to the step (b);
(d) judging whether the meta-heuristic type II stage termination condition is met: if yes, outputting the optimal solution X2＝X*,X2In order to satisfy all the hard constraints and optimize the solution that the maximum value of the objective function is closest to the global optimum, the algorithm is ended; otherwise T ═ T × r, solution set
Figure FDA0002668426770000014
Setting the iteration parameter m to 0 and jumping to the step (b).
2. The method of claim 1, wherein the data comprises: flight constraint rules and flight position constraint rules;
the constraint rule comprises a weight value representing the importance degree of the constraint rule;
the flight constraint rules include: flight number, model, time of arrival, time of departure, vip grade, route, task type, airline company, terminal building to which it belongs, number of passengers;
the machine position constraint rule comprises the following steps: whether the machine position is close to the aircraft station, the station building to which the machine position belongs, the serial number of the aircraft station and the category of the aircraft station can contain a machine type set;
the machine position categories include: the non-combined machine position, the father machine position in the combined machine position and the son machine position in the combined machine position.
3. The three-stage meta-heuristic aircraft stand allocation optimization method of claim 2, wherein the preprocessing the data to obtain the mapping relationship between flights and stands comprises:
obtaining an allocable seat set corresponding to each flight according to the flight constraint rule and the seat constraint rule;
filtering the positions where each flight can not be parked to obtain a distributable position set corresponding to each flight
Figure FDA0002668426770000021
Obtaining the weight value of each flight stopping at the corresponding allocable stop according to the flight constraint rule and the stop constraint rule, and obtaining the allocable stop set corresponding to each flight
Figure FDA0002668426770000022
Adding a weight value of an allocable seat corresponding to each flight to obtain a mapping relation between each flight and the seat;
wherein n isfThe number of flights to be allocated.
4. The three-stage meta-heuristic aircraft stand allocation optimization method of claim 1, wherein the building of the aircraft stand allocation model according to the mapping relationship between flights and stands comprises:
establishing an optimization index, wherein the optimization index comprises a bridge approach rate Z1Corridor bridge ratio Z2Distribution satisfaction degree Z3；
Setting a hard constraint;
and combining the optimization indexes and the hard constraints to obtain an off-line position distribution model.
5. The three-stage meta-heuristic stand allocation optimization method of claim 4, wherein the establishing an optimization index comprises:
according to the weight corresponding to each optimization index, carrying out weighted summation on the optimization indexes to obtain an optimization objective function, wherein the optimization objective function is as follows:
Z＝αZ1+βZ2+γZ3(1)；
in the formula (1), α, β, γ are bridge-approaching ratios Z1Corridor bridgeRate Z2Distribution satisfaction degree Z3The weight coefficients α, β, γ corresponding to each optimization index are non-negative numbers, and the sum of the weight coefficients is equal to 1, that is:
α+β+γ＝1，α≥0，β≥0，γ≥0 (2)；
the bridge approach rate Z1According to the proportion of flights near the flight position to all reliable bridge flights distributed in a certain distribution result, the calculation formula is as follows:
Figure FDA0002668426770000031
the corridor bridge ratio Z2According to the proportion of the number of passengers on flights near the flight level to the number of passengers on all reliable bridges distributed in a certain distribution result, the calculation formula is as follows:
Figure FDA0002668426770000032
the distribution satisfaction degree Z3According to a weight value score in an assignmentikCalculated, the formula is:
Figure FDA0002668426770000033
wherein Maxscore and Minscore are constants, and are calculated by the following formulas respectively under the condition that only one stand can be allocated to one flight:
Figure FDA0002668426770000034
Figure FDA0002668426770000035
flight i belongs to F, F is a set of flights to be distributed, machine k belongs to G, G is a set of machine positions, nfFor the number of flights to be allocated, ngThe number of machine positions;
scoreikthe meaning of (1) is that the flight i stops at the corresponding weight value of the flight k;
sithe number of passengers on flight i;
xikthe meaning of (1) is that if the flight i stops at the station k, otherwise, the flight i is 0;
Figure FDA0002668426770000041
the flight identifier is a reliable bridge flight identifier, if the flight is a reliable bridge flight, the flight identifier is 1, otherwise, the flight identifier is 0, and the unreliable flight cannot be parked at a near airport;
Figure FDA0002668426770000042
the meaning of (1) is that if the machine position k is a near machine position, otherwise, the machine position k is 0.
6. The three-stage meta-heuristic stand allocation optimization method of claim 4, wherein the hard constraints comprise:
the uniqueness constraint is as follows: one flight must and can only stop at one flight level;
Figure FDA0002668426770000043
the exclusivity constraint: at most one flight can be parked on the same position at the same time;
Figure FDA0002668426770000044
and (3) combining machine position constraint: at the same time, the parent machine position and the child machine position in the combined machine position can not be used at the same time, but the child machine positions can be used at the same time;
Figure FDA0002668426770000045
safety constraint: a necessary safety time interval is required between two continuous flights distributed to the same position so as to ensure the safe leaving of the previous airplane and the safe entering of the next airplane;
Figure FDA0002668426770000046
wherein G is a set of stand, k is stand, k belongs to G, F is a set of flights to be allocated, i is a flight, i belongs to F, ngThe number of the stand positions is;
xikthe meaning of (1) is that if the flight i stops at the station k, otherwise, the flight i is 0;
xjkthe meaning of (1) is that if the flight j stops at the station k, otherwise, the flight j is 0; i is not equal to j;
Nijthe meaning of (1) is that if the time conflict exists between the flight i and the flight j, otherwise, the time conflict is 0;
Cewif the position is a combined machine position, the value is 1, otherwise, the value is 0;
if e is the parent station, w is the child station, xieThe meaning of (1) is that if the flight i stops at the parent station e, otherwise, the flight i is 0;
xjwmeaning is 1 if the flight j stops at the child station w, otherwise 0;
ETAiestimated time of arrival, ETD, for flight iiEstimated departure time, T, for flight ibufferMinimum safe time interval for the same machine position;
ETAjestimated time of arrival, ETD, for flight jjThe expected departure time for flight j.
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