CN107016462B - A kind of multirunway field flight landing cooperative optimization method based on genetic algorithm - Google Patents
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Abstract
The invention discloses a kind of multirunway field flight landing cooperative optimization method based on genetic algorithm, includes the following steps：1) description flight lines up to form；2) flight priority is set；3) preferred number of flight on single runway is set；4) it establishes multirunway field and cooperates with Optimized model into departure from port Ground Holding Problem；5) setting collaboration optimizing evaluation standard；6) Local search heuristics strategy is proposed；7) design of genetic algorithm；Present invention seek to address that ground delay decision multirunway field into, departure from port Ground Holding Problem in application problem, delay expense is reasonably distributed between outgoing flight queue, the model that the present invention establishes compared with prior art realizes the collaboration optimization of loss of delay to reduce loss of delay as target；Using the loss of equivalent flight mean delay as heuristic information, guiding local search is carried out towards set direction, avoids the blindness of search, and the collaboration optimization to being delayed expense is significantly improved.
Description
Technical field
The present invention relates to the optimization methods that a kind of reduction flight is delayed expense, more particularly to one kind being based on genetic algorithm
Multirunway field flight landing cooperative optimization method.
Background technology
With China's rapid development of economy, air shipping needs amount persistently rises, and thus brings Chinese Aviation Transportation
The rise and fast development of industry.2014, China's airfield handling capacity indices recorded high again, and wherein passenger throughput is
391950000 person-times, the amplitude increased than 2013 is 10.7%, and only domestic air route just completes 360,400,000 person-times, wherein north
Capital, Shanghai and three big city Airport passenger Throughput of Guangzhou account for the 28.3% of whole Airport passenger Throughputs.Due to air traffic
The surge of flow, the existing air transportation facilities and administration technology in China become difficult to adapt to；The peak of the magnitude of traffic flow in the air
Phase, it may appear that serious air traffic congestion is delayed so as to cause flight large area.2014, the natural rate of interest of China's flight was only
It is 68.37%, flight delay had both caused huge economic loss, also brought security risk to aircraft flight.The U.S. every year because
For economic loss caused by flight is delayed up to 3,000,000,000 dollars, European situation is worse, and becoming by increasing is presented in loss of delay
Gesture.The flight loss of delay in three key airline companies of China trunnion knob center Beijing, Shanghai, Guangzhou is also huge, while flight delay is also tight
The normal life of passenger is affected again.
Ground delay decision is the current main method for solving air traffic congestion, because Ground-Holding waits for expense more in the air
High with low and safety coefficient, basic thought is to determine the best departure time of aircraft, passes through the Ground-Holding tune of original base
The flight flow of air traffic networks is saved, the delay time at stop is reduced, to reduce loss of delay, and ensures the safety and standard of flight
When.As all there is a plurality of race in rise of the more runway construction in airport, such as the capital in China, Pudong, Guangzhou, Chengdu airport etc.
Four runways are invested to build in road, Anhui construction and the Hefei new bridge airport plan in having put into effect, these airports constitute China's boat
The defeated core force of air transport.However, coordinate operation more sophisticated of the flight in multirunway field landing process, except Beijing, on
Except sea and Guangzhou airport, the run time of the most of multirunway fields in China is not grown, and is accumulated experience also insufficient, especially in pipe
Seem more weak in terms of the research of system strategy, operation regulation and specification.For the present situation of Chinese Aviation Transportation industry development, it is based on
The research almost blank of flight landing problem in the multirunway field of ground delay decision.
Ground Holding Problem (Ground-holdingProblem, GHP) becomes the research object of numerous scientific research institutions,
Richetta etc. expands a series of analysis, research to Ground Holding Problem (Ground-holdingProblem, GHP), carries
Model and derivation algorithm out of joint, these work all surround the flight that approaches and discuss, and often only consider single
Track object airport.However, any airport all exist flight into, departure from port, and process influences each other, Gilbo consider airport into
The curved line relation of field and capacity of leaving the theatre realizes airport mutually converting into departure from port capacity by adjusting the preferred number of flight,
The Research foundation into departure from port Ground Holding Problem (Arrival-Departure GHP, ADGHP) is established；The positive equality of horse is herein
On the basis of model, the transition times requirement of continuation of the journey flight is considered, it is proposed that in conjunction with the ADGHP dynamics of RBS and Compress thoughts
Programming evaluation algorithm；However these models have ignored the difference of delayed flight expense, Zhang Honghai is on the basis of considering the factor
By being rationally transformed into capacity of leaving the theatre, in conjunction with Coordination Decision thought, the collaboration for realizing delay expense between each airline is excellent
Change.Above-mentioned ADGHP models are based on single flight road or runway is considered as system analyzes, with flourishing for aircraft industry,
More runways become the hot spot of current GHP researchs into departure from port Ground Holding Problem (Multi-RunwayADGHP, MRADGHP).Luo Xi
Actor is according to the occupation mode of runway, respectively to the description of approach flight and outgoing flight formalized into departure procedure,
Deterministic type and stochastic pattern MRADGHP are discussed, are at present about the more comprehensive achievement in research of the problem.However the model
It is not used in mixed way runway to landing to be analyzed and described, and flight preferred number is not in contact with the practical feelings into outgoing flight
Condition, influences the reasonable distribution of airfield runway resource, in addition has ignored the tardiness cost difference of flight.Some large airports are gathered around at present
There is a plurality of runway, if China Capital Airport is provided with three runways, two of which is respectively used to the takeoff and landing of aircraft, another
The landing that item is then used for aircraft according to actual needs is used in mixed way.Obviously, establishing a kind of effective MRADGHP Optimized models has
Highly important realistic meaning.
MRADGHP is a new class of combinatorial optimization problem, increasingly complex compared with GHP, ADGHP, is NP complete, is solved
Difficult point is that the collaboration optimization of expense is assigned and be delayed into outgoing flight to the runway of flight.According to conventional algorithm such as linear gauge
The method of drawing solves problems, and there are algorithm operations to take the defects of longer, solution quality is difficult to ensure.Genetic algorithm (Genetic
Algorithm, GA) many engineering fields are widely used in its good ability of searching optimum, such as the solution of GHP, however
Weaker local search characteristic is easy that algorithm is made to be absorbed in local optimum, and can not ensure the quality of solution.Kazarlis, which is proposed, to be drawn
Enter the GA of climbing method, and uses it for the solution of optimization problem；It revives etc. according to problem characteristic, it is proposed that efficient local search
Operator, and combined with GA, the problems such as batch process production scheduling, detection of large-scale complex Web Community, is solved, is optimized
It is with obvious effects.With the continuous development of production, problems faced understands more sophisticated in engineering, makes great efforts to solve energy the problem of improving GA
Power, enhancing local search ability become a kind of trend of GA researchs.
In view of the above-mentioned problems, the present invention mainly takes following strategy to be resolved：(1) using multirunway field as scene, root
According to the practical composition and runway planned assignment situation into outgoing flight, the preferred number of flight is set, to reach to mixing runway
Reasonable distribution, adjust the load capacity of private track；(2) a kind of MRADGHP is established to the use priority of runway according to flight
Event-driven Optimized model realizes that loss of delay is delayed between outgoing flight while reducing flight total delay expense
The collaboration of expense optimizes；The many factors such as cost of flight delay difference, continuation of the journey flight transition times are considered simultaneously, with more fully
The characteristic of this problem is described；(3) according to MRADGHP the characteristics of, it is proposed that a kind of Local search heuristics strategy, according into from
Distribution and loss of delay situation of the port flight in each runway, the mobile flight between runway, so that loss of delay is into departure from port
Reasonable distribution between flight；For the complex nature of the problem, which is combined with GA, formed a kind of Hybrid GA (HybridGA,
HGA), and for the solution to problem model.
Local search heuristics strategy is embedded in Genetic Algorithms in the present invention, to form a kind of effective Hybrid GA pair
MRADGHP is solved, and gained optimum individual is the schedule flight plan met the requirements.Genetic operator specification：
Selection opertor：Individual is replicated using fitness ratio selection strategy, high fitness individual is answered with high probability
System.In addition, the randomness of genetic algorithm may cause some excellent individuals to be lost, so in conjunction with essence retention mechanism, it is outstanding
Worst individual in individual substitution group, is directly entered the next generation.
Crossover operator：Herein for more track features of problem, using document " based on adaptive more local searches
More runway Ground Holding Problems of memetic algorithms solve [J] the system engineering theorys and practice, 2012,32 (11):2523-
Ordered crossover operator in 2532. " carries out crossover operation to individual, and detailed design process is referring to the document.
Mutation operator：In document " An efficient genetic algorithm withuniform crossover
for airtraffic control[J].Computers&Operations Research,2009,36(1):245-259.”
On the basis of propose following mutation operator：1) early period of algorithm, point-to-point transmission flight gene in certain runway that backward randomly selects；
The later stage of algorithm exchanges the neighboring gene on certain runway randomly selected；2) two genes in different runways are randomly selected, and
Exchange their position；Or the flight gene on certain runway is moved to the tail portion of another runway series of flights.
Intersect, mutation probability：The probability that individual participates in intersecting, making a variation uses fixed form.
Invention content
The purpose of the invention is to overcome the deficiencies of the prior art and provide a kind of more races based on genetic algorithm
Road air station flight landing cooperative optimization method, to solve the unreasonable distribution of flight mixing runway in the prior art, private track
The bad adjusting of load capacity and loss of delay into unreasonable distribution between, outgoing flight the technical issues of；
The technical solution adopted by the present invention is as follows：The invention discloses a kind of multirunway fields based on genetic algorithm
Flight landing cooperative optimization method, which is characterized in that include the following steps：
1) description flight lines up to form
The unit interval tardiness cost of flight reflect when the flight is delayed will caused by economic loss, the unit interval prolongs
Accidentally the loss of delay that the flight should undertake is also presented simultaneously in cost；To, into, departure from port queue flight composition be represented by
The superposition of flight unit interval tardiness cost in respective queue claims the demand for services amount for being superposed to queue, institute for sake of convenience
The demand for services amount for stating queue is defined as follows：
Definition 1 is set forms queue FS by M frame flights, enables CDmIndicate the unit interval ground delays loss system of aircraft m in FS
Number enables
If demand for services amount reflect queue flight by be delayed it will cause loss of delay amount, i.e., queue flight use
The total desired value of runway, while also embodying the loss of delay that the queue flight should undertake；
2) flight priority is set
Flight embodies air traffic control personnel to the tendentiousness of flight type, multirunway field to runway using priority
The priority of middle landing flight considers following two factors：
A. queue service demand
Queue service demand is divided into two parts, i.e., the current demand Buddhist monk serviced demand to be serviced is shown
The aggregate demand of queue where the priority of right flight duty runway is proportional to and the demand for waiting service, are inversely proportional to the team
The demand serviced is arranged, because demand for services amount embodies runway resource whithin a period of time by the queue service condition；
B. the composition of private track and mixing runway
Flight carry out landing when, airport be its distribute private track or mixing runway, and in airport into, departure from port private track
And there may be differences for mixing runway number, so for the loss of delay of balanced flight queue, flight is run in special and mixing
A rational runway is selected to carry out landing in road；
Therefore, the preferred number of flight nrm on runway rm is mixed
Wherein, FRMA, FRMD and FRM are respectively the flight that approaches, outgoing flight and all flights mixed on runway, FAQ
For queue of approaching, FDQ is departure from port queue；
Wherein, the private track that will approach in (2) formula is considered as a system, with Dtrans (FAQ) in special and mixing runway
On preferred number of the allocation proportion as corresponding flight, to adjust the queue FAQ that approaches in distribution special, on mixing runway；
Using allocation proportions of the Dtrans (FDQ) on special and mixing runway as the preferred number of corresponding flight, to adjust departure from port team
FDQ is arranged in distribution special, on mixing runway；
In practice, due to the difference of approach private track number RA and the private track number RD of departing from port, advanced optimize to obtain into
Port flight preferred number is Dtrans (FRA)/RA/Dtrans (FAQ), excellent on private track with balanced respective queue flight
It first weighs, wherein FRA is the flight that approaches on private track；For mixing runway, the flight preferred number that approaches is its demand for services amount
With the ratio for mixing runway service aggregate demand, i.e. Dtrans (FRMA)/Dtrans (FRM)；
3) preferred number of flight on single runway is set
It enables
Preferred number using cr (r) as flight on runway r is corresponded to when flight loss of delay is larger on runway r
Preferred number it is then larger, vice versa, so passing through the load capacity that runway r is adjusted in coefficient cr (r)；In formula,Indicate that flight nr is in the time on runway rGenerated ground delays expense when duty runway r；Kc is normal
Amount；
4) it establishes multirunway field and cooperates with Optimized model into departure from port Ground Holding Problem
Based on priority of the flight into depart from port private track and mixing runway, multirunway field is established into departure from port ground
Face waiting problem cooperates with Optimized model, object function to be described as follows：
In formula, RA, RD are respectively approach private track number and departure from port private track number；RM is mixing runway number；NrTo divide
The flight number being fitted on runway r；Indicate distribution fall times of the aircraft p when carrying out landing on runway r；
5) setting collaboration optimizing evaluation standard
After GA generates new individual by genetic manipulation, calculate the individual into, departure from port delay expense, be denoted as CPA and
CPD；Due to the demand for services amount for defining Dtrans (FS) in 1 and reflecting queue FS, its flight composition cannot be intuitively expressed,
Therefore on the basis of the definition 1, existing equivalent flight concept is redefined, is defined as follows：
It defines 2 and sets FQ as a flight queue, appoint and take flight p ∈ FQ, on the basis of it, then the equivalent of flight q ∈ FQ is two
The ratio between person's unit interval ground delays expense：
ν (p, q)=CGq/CGp (5)
The equivalent flight sum of FQ illustrates the flight composition situation of the queue, to which the flight composition into departure from port queue is poor
It is different to be illustrated by the comparison between queue equivalent flight sum, remember into, the equivalent flight of depart from port queue FAQ, FDQ it is total
Number is respectively V (p, FAQ) and V (p, FDQ)；
Define the equivalent flight mean delay damage that the ratio between delay expense and its equivalent flight sum of 3 queues is known as the queue
It loses；
Under flights arrangement plan s into, departure from port queue equivalent flight mean delay loss be respectively CPA/V (p, FAQ) and
CPD/V (p, FDQ), and it is denoted as even (s, FAQ) and even (s, FDQ) respectively；When even's (s, FAQ) and even (s, FDQ)
It is worth closer, illustrates that the delay expense allocation of s is more reasonable, it is on the contrary then illustrate unfairness；
Define 4 set even (s, FAQ) and even (s, FDQ) be respectively s correspond into, departure from port equivalent flight mean delay damage
It loses, enables：Distance (s)=| even (s, FAQ)-even (s, FDQ) |, distance (s) is referred to as point for planning s losss of delay
With homogeneity deviation；
6) Local search heuristics strategy is proposed
As even (s, FAQ)>When even (s, FDQ), the queue that illustrates to approach assumes responsibility for excessive loss of delay, needs at this time
The mixing runway access right as public resource is adjusted, there are two types of schemes：A, a flight is chosen from the private track that approaches to move to
Mix runway；B, it chooses an outgoing flight from mixing runway and moves to departure from port private track；Both schemes both increase the boat that approaches
Class is to the access right of mixing runway, if flight and target location are chosen properly, option A can reduce the delay damage for queue of approaching
It loses, option b then while queue loss of delay is approached in reduction, increases the loss of delay of departure from port queue, two methods can
Reduce the gap of even (s, FAQ) and even (s, FDQ)；As even (s, FAQ)<When even (s, FDQ), illustrate that departure from port queue is held
Excessive loss of delay has been carried on a shoulder pole, has also needed to adjust the mixing runway access right as public resource, Adjusted Option at this time：C, from
The a certain position that a flight moves to mixing runway is randomly selected on departure from port private track；D, from mixing runway on randomly select one into
Port flight moves to a certain position approached on private track；Correspondingly, both schemes both increase outgoing flight and are run to mixing
The access right in road, and while reducing departure from port queue loss of delay, increase the loss of delay for queue of approaching, reduce
The gap of even (s, FAQ) and even (s, FDQ)；
Individual x is enabled to represent a kind of schedule flight scheme of arrangement of MRADGHP, the Local search heuristics at temperature t
Step is described as follows, and the local search number at each temperature is Lst：
Step 1 initializes searching times k=1；
Step 2 executes the local search under temperature t；
Step 2.1 calculate individual x into, departure from port queue even (s, FAQ) and even (s, FDQ)；
2.2 random output choice=rand () %2 of Step, if choice=0, embodiment A, otherwise embodiment party
Case B, specific Step is as follows：
Step 2.3 determines the private track r for participating in local search, and r is randomly choosed in private track, meets：If
Choice=0 and even (s, FAQ) ＞ even (s, FDQ) or choice=1 and when even (s, FAQ) ＜ even (s, FDQ),
R is the private track that approaches, and is otherwise private track of departing from port；
Step 2.4 determines that flight gene removes runway RoutWith immigration runway RinIf choice=0, Rout=r, Rin
Arbitrarily to mix runway；If choice=1, RoutArbitrarily to mix runway, Rin=r；
Step 2.5 is in RoutMiddle selection gene g, if RinFor private track, then gene g corresponds to flight and needs to meet runway
Use attribute；In runway RinSeries of flights in randomly generate a position, gene g is inserted into, new individual y is obtained；
Step 2.6 calculates adaptive value H (x), the H (y) of x and y, if H (x) ＜ H (y), x=y；If H (x)=H (y), turn
Step 3；
Step 2.7 calculates the acceptance probability pa=exp (- (H (y)-H (x))/t) when y is inferior to x；
Step 2.8 generates random number pr=random (0,1), if pa ＞ pr, x=y, H (x)=H (y)；
3 k=k+1 of Step turn Step2 and continue to execute if k≤Lst, otherwise stop the local search under temperature t；
7) design of genetic algorithm
Local search heuristics strategy in step 6) is embedded in Genetic Algorithms, to form a kind of effective Hybrid GA pair
MRADGHP is solved, and gained optimum individual is the schedule flight plan met the requirements；The Hybrid GA to MRADGHP into
The process that row solves is as follows：
Step 1 generates the initial population pop that scale is popsize, and which part individual presses the plan of flight duty runway
Time-series generates, remaining individual is random to be generated, and the fitness function value of individual is calculated；It is initial that simulated annealing is set
Temperature ts, final temperature te, temperature lapse rate td and Lst；The maximum evolutionary generation maxgen of setting, crossover probability Pc, variation
Probability P m and optimum individual substitution enable algebraically g=1 as the worst number of individuals Subn in former generation；
Step 2 chooses the individual into mating pond using above-mentioned fitness ratio selection strategy from pop, and to mating
Individual in pond intersected, mutation operation, generates new individual and the interim population temp_pop of composition；
Step 3 executes simulated annealing local search to all x ∈ temp_pop；
Step 3.1 initializes temperature t=ts；
Step 3.2 executes the simulated annealing local search under temperature t using local searching strategy in step 6) to x, finds
Fitness function value higher, loss of delay into, departure from port queue between distribute more reasonably individual replace x；
Step 3.3 moves back warm t=td*t；
If 3.4 t ＜ te of Step, terminate the local search of individual x；Otherwise turn Step3.2 described in this step to open again
Local search under beginning Current Temperatures t；
Step 4 enables pop=temp_pop, obtains population of new generation；
Step 5 executes essence retention strategy, with Subn worst individuals in the optimum individual substitution pop in group；
6 g=g+1 of Step；
If 7 g ＞ maxgen of Step, terminate algorithm, otherwise turn Step2 described in this step and continue to execute.
The invention discloses a kind of multirunway field flight landing cooperative optimization method based on genetic algorithm, this hair
It is bright to has the following advantages compared with prior art：A kind of more runways are established into departure from port GHP Optimized models, the model is to reduce delay
Loss is target, and by the adjusting of flight preferred number, will reasonably distribute as the mixing runway of public resource be fed from
The collaboration optimization of loss of delay is realized in port queue.In view of the complexity of problem model, a kind of Local search heuristics calculation is devised
Son, using the loss of equivalent flight mean delay as heuristic information, guiding local search is carried out towards set direction, to keep away
The blindness of search is exempted from.The operator is embedded in GA, HGA is formed to problem solving, passes through the meter carried out to exemplary simulation example
It calculates, the results showed that carried model and problem-solving approach, which optimize the collaboration for being delayed expense, to be significantly improved.
Specific implementation mode
Embodiment 1
Embodiment 1 discloses a kind of multirunway field flight landing cooperative optimization method based on genetic algorithm,
It is characterized in that, includes the following steps：
1) description flight lines up to form
The unit interval tardiness cost of flight, which reflects, will cause economic loss, heavy machine, the world when flight is delayed
Flight etc. generally has higher unit interval tardiness cost, usually gives the higher runway of such flight and uses priority.So
And other flights can be caused to undertake excessive loss of delay in this way, lose it is just and sound, so unit interval tardiness cost simultaneously go back body
The loss of delay that the flight should undertake is showed.To which the flight composition into departure from port queue is represented by flight in respective queue
The superposition of unit interval tardiness cost claims the demand for services amount for being superposed to queue, is defined as follows for sake of convenience：
Definition 1 is set forms queue FS by M frame flights, enables CDmIndicate the unit interval ground delays loss system of aircraft m in FS
Number enables
If demand for services amount reflect queue flight by be delayed it will cause loss of delay amount, i.e., queue flight use
The total desired value of runway, while also embodying the loss of delay that the queue flight should undertake；
2) flight priority is set
Flight embodies tendentiousness of the air traffic control personnel to flight type to runway using priority, usually according to elder generation
Carry out first service strategy or the flight that approaches gives higher priority.However, these measures will be unable to reduce the total delay of flight
Loss, and do not account for the flight composition of departure from port queue.The priority of landing flight considers following two in multirunway field
Factor：
A. queue service demand
Queue service demand is divided into two parts, i.e., the current demand Buddhist monk serviced demand to be serviced is shown
The aggregate demand of queue where the priority of right flight duty runway is proportional to and the demand for waiting service, are inversely proportional to the team
The demand serviced is arranged, because demand for services amount embodies runway resource whithin a period of time by the queue service condition；
B. the composition of private track and mixing runway
Flight carry out landing when, airport be its distribute private track or mixing runway, and in airport into, departure from port private track
And there may be differences for mixing runway number, so for the loss of delay of balanced flight queue, flight is run in special and mixing
A rational runway is selected to carry out landing in road；
Therefore, the preferred number of flight nrm on runway rm is mixed
Wherein, FRMA, FRMD and FRM are respectively the flight that approaches, outgoing flight and all flights mixed on runway, FAQ
For queue of approaching, FDQ is departure from port queue；
Wherein, the private track that will approach in (2) formula is considered as a system, with Dtrans (FAQ) in special and mixing runway
On preferred number of the allocation proportion as corresponding flight, to adjust the queue FAQ that approaches in distribution special, on mixing runway；
Using allocation proportions of the Dtrans (FDQ) on special and mixing runway as the preferred number of corresponding flight, to adjust departure from port team
FDQ is arranged in distribution special, on mixing runway；
In practice, due to the difference of approach private track number RA and the private track number RD that departs from port, above-mentioned Distribution Strategy is not to the utmost
Rationally.The mean value of flight demand for services amount is advanced optimized as the preferred number of flight using on private track in the present embodiment
Obtain approaching flight preferred number for Dtrans (FRA)/RA/Dtrans (FAQ), with balanced respective queue flight in private track
On priority, wherein FRA is to approach flight on private track；For mixing runway, the flight preferred number that approaches services for it
Demand services the ratio of aggregate demand, i.e. Dtrans (FRMA)/Dtrans (FRM) with runway is mixed；To avoid because approaching
The extruding of private track flight preferred number, and mixing runway is made to share the excessive flight that approaches；Similarly, it can define departure from port boat
The preferred number of class.In addition, mixing runway in flight preferred number setting can also according to distribution mixing runway on into
It departs from port demand for services amount, and flight order is adjusted with this.Private track is usually carried out whole consideration by the prior art, can be caused
Some runway overloads, therefore the preferred number of the runway is set according to the loss of delay of flight on every runway, to reach equal
The purpose of even distribution flight.
3) preferred number of flight on single runway is set
It enables
Preferred number using cr (r) as flight on runway r is corresponded to when flight loss of delay is larger on runway r
Preferred number it is then larger, vice versa, so passing through the load capacity that runway r is adjusted in coefficient cr (r)；In formula,
Indicate that flight nr is in the time on runway rGenerated ground delays expense when duty runway r；Kc is constant；BecauseIt is worth too small, introducing constant kc；
4) it establishes multirunway field and cooperates with Optimized model into departure from port Ground Holding Problem
Based on priority of the flight into depart from port private track and mixing runway, multirunway field is established into departure from port ground
Face waiting problem cooperates with Optimized model, object function to be described as follows：
In formula, RA, RD are respectively approach private track number and departure from port private track number；RM is mixing runway number；NrTo divide
The flight number being fitted on runway r；Indicate distribution fall times of the aircraft p when carrying out landing on runway r；
5) setting collaboration optimizing evaluation standard
After GA generates new individual by genetic manipulation, calculate the individual into, departure from port delay expense, be denoted as CPA and
CPD；Aimed in embodiment into, departure from port queue be delayed expense collaboration optimization, due to flight queue composition difference, so
Equalization CPA and CPD is difficult to reach the reasonable distribution of delay expense.
Due to the demand for services amount for defining Dtrans (FS) in 1 and reflecting queue FS, its flight cannot be intuitively expressed
Composition, therefore on the basis of the definition 1, existing equivalent flight concept is redefined, is defined as follows：
It defines 2 and sets FQ as a flight queue, appoint and take flight p ∈ FQ, on the basis of it, then the equivalent of flight q ∈ FQ is two
The ratio between person's unit interval ground delays expense：
ν (p, q)=CGq/CGp (5)
The equivalent flight sum of FQ illustrates the flight composition situation of the queue, to which the flight composition into departure from port queue is poor
It is different to be illustrated by the comparison between queue equivalent flight sum, remember into, the equivalent flight of depart from port queue FAQ, FDQ it is total
Number is respectively V (p, FAQ) and V (p, FDQ)；
Define the equivalent flight mean delay damage that the ratio between delay expense and its equivalent flight sum of 3 queues is known as the queue
It loses；
Under flights arrangement plan s into, departure from port queue equivalent flight mean delay loss be respectively CPA/V (p, FAQ),
CPD/V (p, FDQ), and it is denoted as even (s, FAQ) and even (s, FDQ) respectively；When even's (s, FAQ) and even (s, FDQ)
It is worth closer, illustrates that the delay expense allocation of s is more reasonable, it is on the contrary then illustrate unfairness；
Define 4 set even (s, FAQ) and even (s, FDQ) be respectively s correspond into, departure from port equivalent flight mean delay damage
It loses, enables：Distance (s)=| even (s, FAQ)-even (s, FDQ) |, distance (s) is referred to as point for planning s losss of delay
With homogeneity deviation；
The size of distance (s) reflects the reasonability that s corresponds to loss of delay distribution.In individual local search procedure
In, distance (s) can be made to tend to 0 by the movement of flight gene；It navigates into departure from port so distance (s) can be used as
The evaluation criterion of class's queue delay expense collaboration optimization.
6) Local search heuristics strategy is proposed
As even (s, FAQ)>When even (s, FDQ), the queue that illustrates to approach assumes responsibility for excessive loss of delay, needs at this time
The mixing runway access right as public resource is adjusted, there are two types of schemes：A, a flight is chosen from the private track that approaches to move to
Mix runway；B, it chooses an outgoing flight from mixing runway and moves to departure from port private track；Both schemes both increase the boat that approaches
Class is to the access right of mixing runway, if flight and target location are chosen properly, option A can reduce the delay damage for queue of approaching
It loses, option b then while queue loss of delay is approached in reduction, increases the loss of delay of departure from port queue, two methods can
Reduce the gap of even (s, FAQ) and even (s, FDQ)；As even (s, FAQ)<When even (s, FDQ), illustrate that departure from port queue is held
Excessive loss of delay has been carried on a shoulder pole, has also needed to adjust the mixing runway access right as public resource, Adjusted Option at this time：C, from
The a certain position that a flight moves to mixing runway is randomly selected on departure from port private track；D, from mixing runway on randomly select one into
Port flight moves to a certain position approached on private track；Correspondingly, both schemes both increase outgoing flight and are run to mixing
The access right in road, and while reducing departure from port queue loss of delay, increase the loss of delay for queue of approaching, also reduce
The gap of even (s, FAQ) and even (s, FDQ)；
Individual x is enabled to represent a kind of schedule flight scheme of arrangement of MRADGHP, the Local search heuristics at temperature t
Step is described as follows, and the local search number at each temperature is Lst：
Step 1 initializes searching times k=1；
Step 2 executes the local search under temperature t；
Step 2.1 calculate individual x into, departure from port queue even (s, FAQ) and even (s, FDQ)；
2.2 random output choice=rand () %2 of Step, if choice=0, embodiment A, otherwise embodiment party
Case B, specific Step is as follows：
Step 2.3 determines the private track r for participating in local search, and r is randomly choosed in private track, meets：If
Choice=0 and even (s, FAQ) ＞ even (s, FDQ) or choice=1 and when even (s, FAQ) ＜ even (s, FDQ),
R is the private track that approaches, and is otherwise private track of departing from port；
Step 2.4 determines that flight gene removes runway RoutWith immigration runway RinIf choice=0, Rout=r, Rin
Arbitrarily to mix runway；If choice=1, RoutArbitrarily to mix runway, Rin=r；
Step 2.5 is in RoutMiddle selection gene g, if RinFor private track, then gene g corresponds to flight and needs to meet runway
Use attribute；In runway RinSeries of flights in randomly generate a position, gene g is inserted into, new individual y is obtained；
Step 2.6 calculates adaptive value H (x), the H (y) of x and y, if H (x) ＜ H (y), x=y；If H (x)=H (y), turn
Step 3；
Step 2.7 calculates the acceptance probability pa=exp (- (H (y)-H (x))/t) when y is inferior to x；
Step 2.8 generates random number pr=random (0,1), if pa ＞ pr, x=y, H (x)=H (y)；
3 k=k+1 of Step turn Step2 and continue to execute if k≤Lst, otherwise stop the local search under temperature t；
7) design of genetic algorithm
Above-mentioned Local search heuristics strategy is embedded in Genetic Algorithms, to form a kind of effective Hybrid GA pair
MRADGHP is solved, and gained optimum individual is the schedule flight plan met the requirements.Genetic operator specification：
Selection opertor：Individual is replicated using fitness ratio selection strategy, high fitness individual is answered with high probability
System.In addition, the randomness of genetic algorithm may cause some excellent individuals to be lost, so in conjunction with essence retention mechanism, it is outstanding
Worst individual in individual substitution group, is directly entered the next generation.
Crossover operator：Herein for more track features of problem, using document " based on adaptive more local searches
More runway Ground Holding Problems of memetic algorithms solve [J] the system engineering theorys and practice, 2012,32 (11):2523-
Ordered crossover operator in 2532. " carries out crossover operation to individual, and detailed design process is referring to the document.
Mutation operator：In document " An efficient genetic algorithm with uniform crossover
for air traffic control[J].Computers&Operations Research,2009,36(1):245-259.”
On the basis of propose following mutation operator：1) early period of algorithm, point-to-point transmission flight gene in certain runway that backward randomly selects；
The later stage of algorithm exchanges the neighboring gene on certain runway randomly selected；2) two genes in different runways are randomly selected, and
Exchange their position；Or the flight gene on certain runway is moved to the tail portion of another runway series of flights.
Intersect, mutation probability：The probability that individual participates in intersecting, making a variation uses fixed form.
Local search heuristics strategy in the step 6) is embedded in Genetic Algorithms, to form a kind of effective mixing
GA solves MRADGHP, and gained optimum individual is the schedule flight plan met the requirements；The Hybrid GA pair
It is as follows that MRADGHP carries out solution procedure：
Step 1 generates the initial population pop that scale is popsize, and which part individual presses the plan of flight duty runway
Time-series generates, remaining individual is random to be generated, and the fitness function value of individual is calculated；It is initial that simulated annealing is set
Temperature ts, final temperature te, temperature lapse rate td and Lst；The maximum evolutionary generation maxgen of setting, crossover probability Pc, variation
Probability P m and optimum individual substitution enable algebraically g=1 as the worst number of individuals Subn in former generation；
Step 2 chooses the individual into mating pond using above-mentioned fitness ratio selection strategy from pop, and to mating
Individual in pond intersected, mutation operation, generates new individual and the interim population temp_pop of composition；
Step 3 executes simulated annealing local search to all x ∈ temp_pop；
Step 3.1 initializes temperature t=ts；
Step 3.2 executes the simulated annealing local search under temperature t using local searching strategy in step 6) to x, finds
Fitness function value higher, loss of delay into, departure from port queue between distribute more reasonably individual replace x；
Step 3.3 moves back warm t=td*t；
If 3.4 t ＜ te of Step, terminate the local search of individual x；Otherwise turn Step3.2 described in this step to open again
Local search under beginning Current Temperatures t；
Step 4 enables pop=temp_pop, obtains population of new generation；
Step 5 executes essence retention strategy, with Subn worst individuals in the optimum individual substitution pop in group；
6 g=g+1 of Step；
If 7 g ＞ maxgen of Step, terminate algorithm, otherwise turn Step2 described in this step and continue to execute.
The present embodiment is tested using multi-group data in order to verify the validity of model and algorithm, achieves ratio
Preferable effect of optimization.This programme uses prerequisite variable FCFS, standard genetic algorithm (Standard to representational example
GA, SGA), the randomized local search genetic algorithm of no problem knowledge heuristic (Stochastic Local Search GA,
SLSGA) and HLSGA is calculated, and is analyzed to each algorithm result of calculation.
1, simulation example and algorithm parameter setting
By taking three strip airport flight datas as an example, two of which runway be respectively used to it is special into outgoing flight, another
To be used in mixed way runway, it is example to choose and reach 35 flights in 25 minutes, and the flight number that approaches, departs from port and continue a journey is respectively
17,18 and 5 frame.The calculating of ground delays expense is delayed explicit cost calculation formula using flight in the prior art：
The CG of flight ppBy the operation cost of the flightAirline's lost revenueAnd passenger's economic lossIt forms, p in formulap、vpAnd hpAverage fare, average rate of profit and the mean time of flight of flight p, value are indicated respectively
Respectively 750 yuan, 2.2% and 2h, npIndicate ridership, lpIndicate that the mean delay cost of every passenger, domestic passenger are 50
Member/h, international passenger are 100 yuan/h；Operation cost is set respectively according to the type (heavy (H), medium-sized (M), small-sized (S)) of flight
It is set to 4167,2916,208 yuan/h.Continue a journey the most short transition times TRM of flighthInternational Civil Aviation group is pressed for 20m, Sep (r, p1, p2)
Minimum safe wake forcing as defined in knitting is into between-line spacing, and coefficient k c takes 1.4 in formula (3).
HLSGA, SGA initial population scale are 180, wherein being by the number of individuals that duty runway chronological order generates
18, essence retention parameter is also 18.Maximum evolutionary generation was 50 generations, and crossover probability, mutation probability are respectively 0.94,0.25, was fitted
Response function constant C=50；Simulated annealing local search algorithm parameter, initial temperature：100, final temperature：0.001, at a temperature of
Drop rate：0.50, Lst=10.This programme realizes algorithm by tool of C language, is debugged in VC6.0, operation.Example Flight Information is such as
Shown in table 1, wherein the continuous number correspondence number for indicating flight before and after continuation of the journey flight.
1 simulation example flight data of table
2, simulation result and analysis
To being ranked up into departure from port problem using each algorithm in 25 minutes of 35 flights in table 1, flight uses race
The planned time and algorithm operation result in road are as shown in table 2.ETi indicates that the planned time of flight duty runway i, time use
Format：mm:Ss, STA, GT, GC indicate runway usage time, ground delays time and the expense after flight sequence respectively, wherein
Delay time at stop unit is s, and delay expense unit is member, and R represents the runway that flight uses.
2 emulation experiment ranking results of table
(1) effect of optimization of problem
Shown in table 1 into departure from port queue transportation service demand be respectively 57.19,104.41, using No. 21 flights as standard,
Then the equivalent flight sum of two queues is respectively 21.41 and 39.09.Each algorithm ranking results statistics is as shown in table 3 in table 2：
3 experimental data statistical result of table
The ranking results scheme of each algorithm of behalf in table, for sake of convenience, algorithm title used below represents the algorithm pair
The flights arrangement plan answered.It is shown and is known by 3 data of table：
1) relative to FCFS algorithms, total aircraft delay cost reduces 21.8%, 50.5% and respectively by SGA, SLSGA, HLSGA
60.1%, HLSGA, which correspond to tardiness cost and have, to be decreased obviously, and fall is maximum.
2) it is respectively 831.9 and 816.6 yuan that FCFS, which is corresponded into departure from port queue delay expense, and distribution is more equal, however due to
The difference of flight total unit causes equivalent flight mean delay to lose even (FCFS, FAQ) and even (FCFS, FDQ) respectively
It is 38.85,20.89, the former is nearly twice the latter.The even (HLSGA, FAQ) and even (HLSGA, FDQ) of HLSGA is respectively
10.95 and 10.82, the evenly distributed degree deviation distance (HLSGA) of loss of delay is down to 0.13 by the 17.96 of FCFS, delay
It loses and is obviously improved into the reasonability distributed between departure from port queue.SGA, SLSGA loss of delay fairness in distribution degree phase
It makes moderate progress for FCFS, but fainter.
(2) loss of delay collaboration optimization analysis
Table 4 is the series of flights of each runway under FCFS is arranged, and even (FCFS, FAQ) is far above even (FCFS, FDQ).It calculates
Example in approach private track flight preferred number be 0.93, mixing runway approach flight preferred number be 0.47, thereby produce
The high pressure of flight priority.So HLSGA moves partly approach flight, such as FA between runway10、FA15Deng as a result such as table 5
It is shown.Although the flight that approaches mixed in table 4 and table 5 on runway is all 6 framves, transportation demand amount increases to 21.7 by 19.2, and
Outgoing flight is then down to 20.49 by 28.48, and the flight preferred number that approaches on private track and mixing runway is 0.86,0.53,
Tend to mitigate, the flight that illustrates to approach gives the higher mixing runway right to use.By optimization, flight loss of delay of approaching
831.9 are down to 234.5, and outgoing flight is down to 423.1 by 816.6, and fall is significantly less than queue of approaching, into departure from port queue
The loss of equivalent flight mean delay is respectively 10.95 and 10.82, and distance (HLSGA) is down to 0.13 by the 17.96 of FCFS.
Each runway series of flights of 4 FCFS of table
Each runway series of flights of 5 HLSGA of table
Known by the description of above table data, carried model and its derivation algorithm HLSGA are being reduced in this programme embodiment
Total aircraft delay cost all achieves more significant effect into departure from port queue loss of delay distribution etc., and solution procedure illustrates
The good optimizing abilities of HLSGA and convergence.
Claims (1)
1. a kind of multirunway field flight landing cooperative optimization method based on genetic algorithm, which is characterized in that including with
Lower step：
1) description flight lines up to form
The unit interval tardiness cost of flight reflect when the flight is delayed will caused by economic loss, unit interval delay at
The loss of delay that the flight should undertake is also presented simultaneously in this；To, into, departure from port queue flight composition be represented by it is corresponding
The superposition of flight unit interval tardiness cost in queue claims the demand for services amount for being superposed to queue, the team for sake of convenience
The demand for services amount of row is defined as follows：
Definition 1 is set forms queue FS by M frame flights, enables CDmIt indicates the unit interval ground delays loss coefficient of aircraft m in FS, enables
If demand for services amount reflect queue flight by be delayed it will cause loss of delay amount, i.e. queue flight duty runway
Total desired value, while also embodying the loss of delay that the queue flight should undertake；
2) flight priority is set
Flight embodies tendentiousness of the air traffic control personnel to flight type to runway using priority, is risen in multirunway field
The priority of drop flight considers following two factors：
A. queue service demand
Queue service demand is divided into two parts, i.e., the current demand Buddhist monk serviced demand to be serviced, it is clear that boat
The aggregate demand of queue where the priority of class's duty runway is proportional to and the demand for waiting service, have been inversely proportional to the queue
The demand of service, because demand for services amount embodies runway resource whithin a period of time by the queue service condition；
B. the composition of private track and mixing runway
Flight carry out landing when, airport be its distribute private track or mixing runway, and in airport into, departure from port private track and
Mixing runway number, there may be differences, so for the loss of delay of balanced flight queue, flight is in special and mixing runway
The rational runway of selection one carries out landing；
Therefore, the preferred number of flight nrm on runway rm is mixed
Wherein, FRMA, FRMD and FRM be respectively mix runway on the flight that approaches, outgoing flight and all flights, FAQ be into
Port queue, FDQ are departure from port queue；
Wherein, the private track that will approach in (2) formula is considered as a system, with Dtrans (FAQ) on special and mixing runway
Preferred number of the allocation proportion as corresponding flight, to adjust the queue FAQ that approaches in distribution special, on mixing runway；With
Preferred number of allocation proportions of the Dtrans (FDQ) on special and mixing runway as corresponding flight, to adjust departure from port queue
FDQ is in distribution special, on mixing runway；
In practice, due to the difference of approach private track number RA and the private track number RD that departs from port, advanced optimize to obtain the boat that approaches
Class's preferred number is Dtrans (FRA)/RA/Dtrans (FAQ), preferential on private track with balanced respective queue flight
Power, wherein FRA is the flight that approaches on private track；For mix runway, the flight preferred number that approaches be its demand for services amount with
Mix the ratio of runway service aggregate demand, i.e. Dtrans (FRMA)/Dtrans (FRM)；
3) preferred number of flight on single runway is set
It enables
Preferred number using cr (r) as flight on runway r, it is corresponding excellent when flight loss of delay is larger on runway r
First coefficient is then larger, and vice versa, so the load capacity of runway r is adjusted by coefficient cr (r)；In formula,It indicates
Flight nr is in the time on runway rGenerated ground delays expense when duty runway r；Kc is constant；
4) it establishes multirunway field and cooperates with Optimized model into departure from port Ground Holding Problem
Based on priority of the flight into depart from port private track and mixing runway, multirunway field is established into departure from port ground etc.
Wait for that problem cooperates with Optimized model, object function to be described as follows：
In formula, RA, RD are respectively approach private track number and departure from port private track number；RM is mixing runway number；NrIt is run to be assigned to
Flight number on road r；Indicate distribution fall times of the aircraft p when carrying out landing on runway r；
5) setting collaboration optimizing evaluation standard
After genetic algorithm (Genetic Algorithm, GA) generates new individual by genetic manipulation, the individual is calculated
Into, departure from port delay expense, be denoted as CPA and CPD；Due to the demand for services for defining Dtrans (FS) in 1 and reflecting queue FS
Amount cannot intuitively express its flight composition, therefore on the basis of the definition 1, existing equivalent flight concept is redefined,
It is defined as follows：
It defines 2 and sets FQ as a flight queue, appoint and take flight p ∈ FQ, on the basis of it, then the equivalent of flight q ∈ FQ is that the two is single
The ratio between position time ground cost of delays use：
ν (p, q)=CGq/CGp (5)
The equivalent flight sum of FQ illustrates the flight composition situation of the queue, to which the flight composition difference into departure from port queue can
To be illustrated by the comparison between queue equivalent flight sum, remember into, the equivalent flight sum of depart from port queue FAQ, FDQ point
It Wei not V (p, FAQ) and V (p, FDQ)；
Define the equivalent flight mean delay loss that the ratio between delay expense and its equivalent flight sum of 3 queues is known as the queue；
Under flights arrangement plan s into, departure from port queue equivalent flight mean delay loss be respectively CPA/V (p, FAQ) and CPD/V
(p, FDQ), and it is denoted as even (s, FAQ) and even (s, FDQ) respectively；When the value of even (s, FAQ) and even (s, FDQ) more connect
Closely, illustrate that the delay expense allocation of s is more reasonable, it is on the contrary then illustrate unfairness；
Define 4 set even (s, FAQ) and even (s, FDQ) be respectively s correspond into, departure from port equivalent flight mean delay loss, order：
Distance (s)=| even (s, FAQ)-even (s, FDQ) |, distance (s) is referred to as the evenly distributed of plan s losss of delay
Spend deviation；
6) Local search heuristics strategy is proposed
As even (s, FAQ) ＞ even (s, FDQ), the queue that illustrates to approach assumes responsibility for excessive loss of delay, needs to adjust at this time
The whole mixing runway access right as public resource, there are two types of schemes：A, it is moved to from private track one flight of selection that approaches mixed
Close runway；B, it chooses an outgoing flight from mixing runway and moves to departure from port private track；Both schemes both increase the flight that approaches
To mixing the access right of runway, if flight and target location are chosen properly, option A can reduce the delay damage for queue of approaching
It loses, option b then while queue loss of delay is approached in reduction, increases the loss of delay of departure from port queue, two methods can
Reduce the gap of even (s, FAQ) and even (s, FDQ)；As even (s, FAQ) ＜ even (s, FDQ), illustrate queue of departing from port
Excessive loss of delay is assumed responsibility for, also needs to adjust the mixing runway access right as public resource, Adjusted Option at this time：C、
The a certain position that a flight moves to mixing runway is randomly selected from departure from port private track；D, one is randomly selected from mixing runway
The flight that approaches moves to a certain position approached on private track；Correspondingly, both schemes both increase outgoing flight to mixing
The access right of runway, and while reducing departure from port queue loss of delay, increase the loss of delay for queue of approaching, also reduce
The gap of even (s, FAQ) and even (s, FDQ)；
Individual x is enabled to represent more runways into departure from port Ground Holding Problem (Multi-Runway Arrival-Departure
Ground-holding Problem, MRADGHP) a kind of schedule flight scheme of arrangement, the heuristic part at temperature t
Search step is described as follows, and the local search number at each temperature is Lst：
Step 1 initializes searching times k=1；
Step 2 executes the local search under temperature t；
Step 2.1 calculate individual x into, departure from port queue even (s, FAQ) and even (s, FDQ)；
2.2 random output choice=rand () %2 of Step, if choice=0, embodiment A, otherwise embodiment B,
Specific Step is as follows：
Step 2.3 determines the private track r for participating in local search, and r is randomly choosed in private track, meets：If choice=
0 and even (s, FAQ) ＞ even (s, FDQ) or choice=1 and when even (s, FAQ) ＜ even (s, FDQ), r is to approach
Otherwise private track is private track of departing from port；
Step 2.4 determines that flight gene removes runway RoutWith immigration runway RinIf choice=0, Rout=r, RinIt is arbitrary
Mix runway；If choice=1, RoutArbitrarily to mix runway, Rin=r；
Step 2.5 is in RoutMiddle selection gene g, if RinFor private track, then gene g corresponds to flight and needs to meet runway use
Attribute；In runway RinSeries of flights in randomly generate a position, gene g is inserted into, new individual y is obtained；
Step 2.6 calculates adaptive value H (x), the H (y) of x and y, if H (x) ＜ H (y), x=y；If H (x)=H (y), turns Step
3；
Step 2.7 calculates the acceptance probability pa=exp (- (H (y)-H (x))/t) when y is inferior to x；
Step 2.8 generates random number pr=random (0,1), if pa ＞ pr, x=y, H (x)=H (y)；
3 k=k+1 of Step turn Step2 and continue to execute if k≤Lst, otherwise stop the local search under temperature t；
7) design of genetic algorithm
Local search heuristics strategy in the step 6) is embedded in Genetic Algorithms, to form a kind of effective Hybrid GA pair
MRADGHP is solved, and gained optimum individual is the schedule flight plan met the requirements；The Hybrid GA to MRADGHP into
The process that row solves is as follows：
Step 1 generates the initial population pop that scale is popsize, and which part individual presses the planned time of flight duty runway
Precedence generates, remaining individual is random to be generated, and the fitness function value of individual is calculated；Simulated annealing initial temperature is set
Ts, final temperature te, temperature lapse rate td and Lst；The maximum evolutionary generation maxgen of setting, crossover probability Pc, mutation probability
Pm and optimum individual substitution enable algebraically g=1 as the worst number of individuals Subn in former generation；
2 fitness ratio selection strategies of Step are a kind of typical individual choice strategies, high fitness individual with high probability into
Row replicates, since the randomness of genetic algorithm may cause some excellent individuals to be lost, so in conjunction with essence retention mechanism,
Excellent individual replaces the worst individual in group, is directly entered the next generation, is selected using this fitness ratio for combining essence to retain
It selects strategy and chooses the individual for entering mating pond from pop, and the individual in mating pond is intersected, mutation operation, generated new
Individual simultaneously forms interim population temp_pop；
Step 3 executes simulated annealing local search to all x ∈ temp_pop；
Step 3.1 initializes temperature t=ts；
Step 3.2 executes the simulated annealing local search under temperature t using local searching strategy in step 6) to x, finds and adapts to
Degree functional value higher, loss of delay are replacing x into distributing more reasonably individual between, departure from port queue；
Step 3.3 moves back warm t=td*t；
If 3.4 t ＜ te of Step, terminate the local search of individual x；Otherwise turn Step3.2 described in this step to restart to work as
Local search under preceding temperature t；
Step 4 enables pop=temp_pop, obtains population of new generation；
Step 5 executes essence retention strategy, with Subn worst individuals in the optimum individual substitution pop in group；
6 g=g+1 of Step；
If 7 g ＞ maxgen of Step, terminate algorithm, otherwise turn Step2 described in this step and continue to execute.
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| CN107704949B (en) * | 2017-09-12 | 2021-09-03 | 中国船舶重工集团公司第七0九研究所 | Flight entering and leaving scheduling optimization method and system based on historical data drive |
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