AIRCRAFT LANDING SCHEDULING USING EMBEDDED FLOWER ... · Aircraft landing scheduling is an important issue in the air traffic management, that aim s to decide the best allocation

AIRCRAFT LANDING SCHEDULING USING EMBEDDED FLOWER POLLINATION ALGORITHM

Ayman A.Ataher Mahmud

Research Scholar , Department of Computer Science. SHUATS, Allahabad , Uttar Pradesh, India

[email protected]

Dr. Satakshi (Co-Advisor)

Assistant Professor Department of Mathematics & Statistics. SHUATS, Allahabad, Uttar Pradesh, India

[email protected]

Prof.(Dr.) W. Jeberson

Advisor and Head of Dept. Computer Science & I.T. SHUATS, Allahabad, Uttar Pradesh, India

[email protected]

ABSTRACT:

Aircraft landing scheduling is an important issue in the air traffic management, that aims to

decide the best allocation considering the landing time for assigning to a sequence with limit the

aggregate of the deviation of the actual as well as target landing time under the state of safe

landing. The paper presents an Embedded Flower Pollination Algorithm (EFPA) for aircraft

landing schedule. The aircrafts are categorized depending on the class of each aircraft, small,

large and heavy. Considering every single aircraft classes, runway occupation profile, landing

time and separation time computation are done. EFPA is used to schedule the arrival of the

airplanes. Context cognitive learning and runway balance methodology are contrived to upgrade

the searching ability. Experimental outcomes demonstrate that the proposed EFPA outperforms

compared with other existing strategies.

Keywords: Aircraft Landing Scheduling, Embedded Flower Pollination Algorithm, Landing time,

Separation time, Runway occupation profile, Runway balance strategy.

1. INTRODUCTION

With the swift globalization in economies, the aviation business has assumed a vital part of

social and economic frameworks [1]. Air transport has turned into the crucial modes of

transportation for individual and business voyaging and business delivery, In this way the request

of air transportation is expanded for numerous purposes. The increment in the number of aircraft

departures and arrivals within a given time period at a certain airport causes risk air traffic [2].

Over the preceding few years, air transport has encountered expanded rivalry. These

circumstances requires airline companies to improve their frameworks keeping in mind that the

ultimate goal is to advance the planning of aircraft maintenance [3]. The test lies in

simultaneously accomplishing safety, productivity, and equity which are regularly contending

goals [4]. Because of constrained space for further infrastructural expansion, enhancing the

productivity of air traffic management winds up basic for the aviation business to adapt to the

normal request surge [5]. Due to this the airline companies are required to improve their

frameworks. Numerous researchers distinguish airport as the bottlenecks of the air transport

frameworks, where an applicable offer of the delays is frequently created by a wasteful

management of the runway restrictions [6].

International Journal of Pure and Applied MathematicsVolume 119 No. 16 2018, 1719-1735ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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The airline business works in a strongly competitive environment where aircraft companies plan

to give best services at lower expenses [7]. The productivity of the air traffic framework is a

considerable traffic since air traffic delays have been costing billions of dollars to airlines every

year. Two issues engaged with modern air traffic framework are, air traffic control (ATC) and

air traffic flow management(ATM) [8]. ATC is a set of services returned by the air traffic

controllers to aircraft, to help in the protected, quick and effective execution of the flights. The

fundamental motivation behind air control is to prevent the crashes between the airplanes and the

ground or vehicles and collision in between the aircrafts [9]. Aircraft Landing Problem (ALP) is

one of the significant characteristics of air traffic flow management to keep up smooth air traffic

from airspace to the corresponding airport [10]. The Aircraft Landing Scheduling (ALS) issue is

choosing a landing time for each plane to such extent that each plane lands within a foresaid

time window. The separation criteria between the landing of a plane and of next progressive

plane is also considered. ALS in terminal zone essentially affects decreasing flight delays, so it is

one of the critical pieces of the air traffic management [11]. The issue turns out to be more

noteworthy for busy airports where loads of aircraft are expected to land at each time period and

at the same time these are limited resources(or runways) [2].

Scheduling of aircraft is a regular dynamic scheduling with numerous strong constraints, for

example, time urgency, space constraint, and resources limitation etc. Also there exist numerous

vulnerabilities and disturbances amid the scheduling procedure [12]. Due to the quick expand of

flights and passengers, the finite airport resources regularly can't satisfy the demand at busy time

interim, causing conceivable serious congestion and potential task safety-risk events. Instructions

to viably ensure high operation performances have grown to be a significant issue if there arises

an occurrence of airport congestion regarding the security [13]. Airport operations force

numerous difficulties because of complex procedures and vulnerabilities. The requirement to

enhance airport operations as far as operational proficiency, predictability, and throughput have

drawn much consideration [14]. Extensively the scheduling and resource allocation optimization

can decrease operation cost, they are generally utilized as a part of different territories of the

aviation industry. Among these applications, flight scheduling, routing, and timetable

optimization are the most attractive research to fairs [1]. Since an immense number of aircraft

arrive at a bustling terminal region consistently, it is incompetent to consider such a major

number of aircraft simultaneously centered on the vast search space. Thus, the need to outline a

strategy that could solve the real-time arrival sequencing and scheduling issue vigorously, viably

and productively, is the topic of further research [15].

2. LITERATURE REVIEW

Bo Xu [16] proposed an Ant Colony (AC) algorithm with the Wake Vortex Modeling (WVM)

technique aimed at Aircraft Scheduling Problem (ASP). AC was considered in this problem ant

in AC specifically restored a sequencing system, which was a conceivable decision to build the

precision of the approximation technique. They initially created a rank 2 matrix (denoted by

MST) by the WVM technique. At that point, MST was approximating to the actual minimum

separation time (MST), where the ideal solution concerning MST′ was anything but difficult to

discover when the airplane ready time constraint was ignored. At long last, they utilized AC to

advance the ASP while considering the contrasts amongst MST and MST′ and included the

aircraft ready time constraint. Numerical outcomes approved that the projected technique would

International Journal of Pure and Applied Mathematics Special Issue

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be advised to performance than CPLEX, general AC algorithm, an approximation algorithm. It

was a promising method to enhance the competence of the aircraft scheduling framework in new

of theoretical perspective.

B.S. Girish [17] suggested a hybrid particle swarm optimization algorithm in a rolling horizon

system to take care of the ALP. ALP was an essential optimization issue in ATC and was proved

as NP-hard. The issue comprised of allotting the arriving aircraft to runways at an airport and

assigning a landing time to each aircraft. Every aircraft had an optimum target landing time

decided centered upon its most fuel effective airspeed and a deviation from it caused a penalty,

which was proportional to the measure of deviation. The landing time of every aircraft was

compelled within a predetermined time window and must fulfill minimum separation time

necessity with its former airplanes. The goal was to limit the aggregate penalty cost because of

deviation of landing times of aircraft from the individual target landing times. The suggested

algorithm's performance was evaluated on a collection of benchmark cases included up to five-

hundred aircraft along with 5 runways. Computational outcomes presented that the suggested

algorithm was efficient in solving the issue in short computational time.

Marcella Sama et. al [18] tended to the real-time aircraft routing and scheduling issue at a

bustling terminal control area (TCA) if there should be an occurrence of traffic congestion. The

issue of successfully overseeing TCA operations was especially challenging since there was a

consistent development of traffic demand and the TCAs were turning into the obstacle of the

whole ATC. That work tended to the issue by means of development of mixed-integer linear

programming plans that consolidated the security rules with high modeling precision and target

elements of viable intrigue in light of the minimization of the aggregate travel time and the

largest delay because of possible aircraft clashes. Computational experiments were done on real-

world data as of Roma Fiumicino, the biggest airport in Italy as far as passenger demand. Traffic

disturbances were produced by simulating groups of arbitrary landing/departure aircraft delays.

Near-optimal solutions of practical-size instances were figured in a brief span by means of a

business solver. The computational analysis empowered the selection of those solutions offering

the finest trade-off among the distinctive objectives.

Xiao-Peng Ji et. al [19] handled aircraft arrival sequencing along with scheduling issue as a

dynamic optimization issue. An evolutionary approach, in particular, dynamic sequence

searching and assessment, was suggested. The suggested approach utilized an evaluation of

distribution algorithm along with a heuristic search strategy to look for the optimal landing series

of flights. In the dynamic Aircraft Sequencing and Scheduling, the most punctual arriving flights

ought to be first considered in the scheduling operation. In the event that new flights were

landing at the terminal area (TMA) amid that timeframe, they should hold up until the point that

the last scheduling process was finished and afterward taken part in the subsequent scheduling

operation along with those holding up flights. At the point when there was not any new plane to

be scheduled, the scheduling operation would hang up till the point when new flights were

landing at the TMA Compared with other related algorithms, the suggested technique performed

much better on some test occurrences including an instance acquired from the real data of the

Beijing Capital International Airport.


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Marcella Sama et. al [20] presented various algorithmic upgrades executed in the AGLIBRARY

solver (a best in class optimization solver to manage complex routing along with scheduling

issues) so as to ameliorate the probability of discovering great quality solutions rapidly. The

presented structure began with a decent initial solution for the aircraft scheduling issue with

fixed routes (given the resources to be navigated by every aircraft), computed through a

truncated branch and bound algorithm. A metaheuristic was then connected to enhance the

solution by rerouting some airplane in the terminal control territory. New metaheuristics, in view

of variable neighborhood look, tabu search together with hybrid schemes, were presented.

Computational experiments were done on an Italian terminal control region under different sorts

of disturbances, comprising numerous aircraft delays together with a briefly disrupted runway.

The metaheuristics accomplished solutions of amazing quality, within a little computation time,

contrasted with a commercial solver and with the past variants of AGLIBRARY.

K.K.H. Ng et. al [21] regarded the aircraft sequencing together with scheduling issue under the

vulnerability of entry and also departure delays aimed at multiple heterogeneous mixed-mode

parallel runways. To upgrade runway versatility, runways operations ought to stay robust to

moderate the impacts of delay propagation. The primary target of that research was to distinguish

an optimal schedule by assessing the robustness of feasible solutions under its particular most

dire outcome imaginable. An artificial bee colony algorithm was created and checked by

experimental results. The recommended efficient artificial bee colony algorithm gets close-to

optimal outcomes with fewer computational exertions as to an hour flight traffic planning

horizon. Concerning the solution strategy of the robust optimization utilizing the min-max regret

approach, the recommended proficient artificial bee colony algorithm could be an advantage to

ATC to acquire the close-to-optimal schedules within a sensible calculation time for practical

utilization. The computational outcomes showed the adequacy of the recommended algorithm by

contrast with other meta-heuristic methodologies on produced occasions. The recommended

algorithm outflanked other meta-heuristic methodologies in regards to target function and

calculation time.

3. AIRCRAFT LANDING SCHEDULING (ALS) USING EFPA

The goal of ALS is to decide the best combination of doling out the sequence and relating

landing time for a given set of aircraft to a runway. In another word, the scheduling algorithm of

ALS aims to limit the total of the deviations of target landing times and the real arrival times of

aircraft while fulfilling the minimum separation time between two adjoining airplane landing on

the same runway. This paper presents an EFPA for aircraft landing schedule. The standard FPA

is a persistent optimization algorithm. Nonetheless, when managing discrete optimizations like

ALS issue, its deficiencies for discrete optimization will be uncovered straightforwardly. EFPA

is a combination of FPA and runway balance technique. At first, the aircraft are partitioned as

separate classes, for example, small, large and heavy classes. For every aircraft classes, runway

occupation profile, landing time and separation time are computed, EFPA is used to plan the

landing of the aircraft as presented in Figure 1.


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Figure 1: The Proposed Framework

3.1 Parameter Calculation

The runways can be possessed by just a solitary aircraft at once each, and a division time

should be guaranteed between any combination of the airship. A minimum partition between each pair of progressive aircraft focused on the sort and relative spots of the two aircraft must be guaranteed for scheduling reason. For processing the assessed time entry of aircraft it is critical to know the bits of knowledge about landing and minimum separation times between each aircraft classes. Minimum separation time is the security distance betwixt the aircraft that can be translated in a separation time by considering the distinctive aircraft speeds. Expected that the runways are self-governing, inferring that the flight ways for all runways being utilized are confined sufficiently, so the runways can be dealt with independently. Amid the planning time frame the runway considered might be utilized for arriving flights. 3.1.1 Runway Occupation Profile (ROP).

The rectangular ranges of an aerodrome arranged for the arrival and also depart are of the airship is a runway. Which is most imperative piece of an airfield. A mischance on a runway will influence the air terminal accessibility and any mishap on a runway typically causes a few reasons of harm and wounds. Runway occupation time is the measure of time for which every

airplane occupies the runway. ROP is characterized as a vector RR cTcT ,......, 11 that contains

the time RT and aircraft class Rc of the newest landing on every runway. A runway without any

operations scheduled is meant in a ROP as (-1,-1). Estimation of runway occupation profile is quickly talked about in [22]. The runway occupation profile can be evaluated by the accompanying condition (1)

)( 21 TTTROP R (1)


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3.2 Embedded Flower Pollination Algorithm(EFPA).

The standard FPA is a continuous optimization algorithm. However, when dealing with discrete optimizations like ALS problem, FPA may not be suitable, so Embedded FPA is introduced which is a combination of FPA and runway balance strategy. Suppose if there are ten aircraft to be scheduled and three runways available aimed at assigning, then the candidate solution should be a ten-dimensional vector and every decision variable should be one, two or three.

Figure 2: Pseudocode for EFPA The pseudo code for embedded FPA with runway balance strategy is presented in Figure 2.

Begin

Initialize Z of P flowers

\\ Each flower represents a scheduling sequence for an aircraft landing

instance.

Find the Best Solution O in the initial population.

Define a switch probability 1,0q

While Generationt max

For Pu :1 (all the flowers in the population)

If qrand

(Global Search Process)

Carryout context cognitive learning and get the via Eq.2;

Else

(Local Search Process)

Carryout walking one strategy and get the via Eqs.3-5;

End if

(Turbulent Process)

Carryout turbulent operator and get xT

(Runway Balance)

Carryout the runway balance and get xB

Find the best one from 1t

ux , xT and xB ,then set it to 1t

ux ;

Evaluate the scheduling sequence 1t

ux ;

If t

u

t

u xfitnessxfitness 1

Update flower ux

End if

End for

Find the current best scheduling sequence O

End while

Output the best scheduling sequence

End


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Initialization: In the initialization process relied upon runways, P candidate solutions are produced, where P is the populace size and set to ten on account of ten aircraft. For each solution, a Latest Active Time (LAT), whose initial value should be zero and a Target Landing

Time uT of the considerable number of aircraft, should be arranged in ascending sequence, which

says that Target Landing Time of the former aircraft in sorted sequence might be after the

preceding one. The chief aircraft 1u will land at an arbitrary runway. For every sorted aircraft

ku and 1ku , if11 ,

kkkk uuuu STT , aircraft 1ku is assigned to the runway that ku lands on and the

last dynamic time of the runway which 1ku lands on are to be updated and its value has got to be

set to1kuT . Otherwise, the airplane 1ku should be appointed to another runway with smallest last

active time and the last active time of this runway is set to1kuT . In particular, aircraft ku and

1ku are allotted to various runways. This generated procedure of initialization repeats until

P candidate solutions are generated.

Context Cognitive Learning: In nature, the biotic pollination process of flowers often resorts to

pollinator and honeybees are a good instance of pollinator. Honey bees get pollen as of one

flower and then take it to another flower with same species to help the plants to finish the biotic

pollination after flying a long distance. When the honeybees complete the transportation mission,

they will get together and communicate amongst themselves to share the experience of nectar

resources and biotic pollination. By sharing the experience, honeybees will understand better

places for pollination in the subsequent time. Namely, this ability of pollinators is described as

context cognition.

For simplicity, better solutions are defined as the finest solutions in the population. This

subset is named as ES (Elite Set) and the ES size is set to P3.0 . The context cognitive learning

is depicted using the equation given in (2).

SizeESkAvPuotherwisex

randrandex

t

vu

t

vkt

vu _1,1,1,,

,

,

21,1

,

(2)

At this time, t

vke , is the thv variable of thk the individual in ES and the evolution generation is t .

The t

vke , should be chosen randomly which could enhance the diversity of the population to some

extent. t

vux , is the thv variable of thu individual of the population at tht generation.

Walking One Strategy: Standard FPA use mutation operator of differential evolution to do the

local search. The major purpose of the local search is to find a better solution in neighbor space.

Thus, walking one strategy is launched in this discrete version FPA. It simulates the local

cognitive behavior of pollen. In the local search process, a crossover rate CR is set to 0.01. the

complete process of walking one strategy is modeled by succeeding equations (3), (4) and (5).

randroundstepsize vu 21, (3)

1,mod ,,, RstepsizexmutVec vu

t

vuvu (4)


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otherwisex

CRrandmutVecx

t

vu

jit

vu,

,

,

,1

,

(5)

Where, AvPu 1,1 , R is the number of runways. From equation (3), it can be discovered

that the variable vustepsize ,can only be -1, 0 and 1. This ensures that the searching space of

walking one strategy is around the existing solution vux , . And vumutVec , is the mutation vector

after carried out the walking strategy and it is also an input variable of equation (5). The essence

of (5) is a crossover operator.

Turbulent Operator: Context cognitive learning and walking one strategy are used as the main

procedure of global search and local search in proposed EFPA. When facing large scales

scheduling, their limited searching ability makes it hard to jump out of the local optimal. Thus,

the turbulent operator is applied to the proposed EFPA to ameliorate the population diversity.

This turbulent process contains swap operator and inserts operator.

Runway Balance Strategy: Consider a scheduling task with 1000 aircraft and 3 runways for

handling. On account of its huge quantity of aircraft and little runways to assign, the load of

every runway may be severe unbalance. For example, if the current best solution shows 451

aircraft will land on the first runway and also a load of other two runways are 444 and 105. It can

be easily discovered that loads of three runways are not balanced. And nearly ninety percent

aircraft are assigned to first two runways. If scheduling the aircraft by using this best scheduling

solution, the first runway and the second runway are occupied for landing almost all the time, but

the third runway is unused in most portion of the scheduling process, which wastes many

resources is found. Thus, balancing the load of each provided runway is a vital problem to be

handled. Thus, runway balance strategy is designed here to balance the load of each runway.

Firstly, the number of aircraft on every runway should be calculated, an aircraft should be chosen

randomly from the runway which count value of landing aircraft is the maximum. Then the

runway with least aircraft to land on should also be found and assigned to chosen aircraft to land

on. If the quantity of airplanes on runways, minimum and maximum, is equivalent, then a

runway ought to be selected randomly. Furthermore, the process will continue until the deviation

of those runway count values is below one. The pseudocode of runway balance strategy is

presented in Figure 3.


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Figure 3: Pseudocode for Runway Balance Strategy

4. RESULT AND DISCUSSION

The proposed embedded flower pollination algorithm for aircraft landing scheduling is simulated

in JAVA platform and the dataset comprises of flight landing and also takeoff details for each of

the commercial flight inside the USA. So as to scrutinize the proposed work’s performance,

measured the different parameters on basis of the execution situation. Figure 4 reveals the

relative comparison of the proposed EFPA algorithm with prevailing KH optimization and

Cuckoo Search optimization. Table 1 shows the comparative analysis of the proposed EFPA and

the existing Krill Herd (KH) and Cuckoo optimization algorithms in term of CPU time.

Problem

Size

KH Cuckoo Proposed

EFPA

100 20 7 5

200 48 35 20

300 55 63 48

400 100 90 84

500 135 125 112

Table 1: CPU Time (seconds)

Begin

Read Rmax , Maximum number of Runways

Rmin Minimum number of Runways

Countmax , Number of aircrafts land on Rmax

Countmin , Number of aircrafts land on Rmin

Function res= Runway_Bal (solution)

[maxR, maxCount]= findMaxRunway (solution)

[minR, minCount]= findMinRunway (solution)

While 1minmax CountCount

Select an aircraft from Rmax randomly

Assign the selected aircraft to Rmin

Update the solution

[maxR, maxCount]= findMaxRunway (solution)

[minR, minCount]= findMinRunway (solution)

End while

res= solution

End


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Figure 4: Comparision of EFPA with existing Methods

. It is observed that as size increases , the CPU time for processing also increases. Among

the three compared techniques, the proposed EFPA outperforms as compared to existing

methods for the entire problem sizes.

Aircraft Scheduling: The aircraft scheduling decides the best blend of assigning sequence also

corresponding landing time for a specified set of the airplane to a runway. The scheduling

algorithm of ALP should diminish the sum of the deviations of target landing times and the

actual landing times of aircraft by concurrently fulfilling the least separation time between two

adjacent airplane landing on the same runway.

Figure 5: Performance Analysis of Aircraft Scheduling


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Figure 5 analyzes the performance of aircraft scheduled for the proposed EFPA and the existing

KH and also Cuckoo optimization algorithms. The proposed EFPA outperforms both the KH and

cuckoo optimization techniques in term of effective aircraft scheduling.

Computation Time: Computation time (additionally called "running time") is the time span

required to play out a computational process. In aircraft schedule, the length of the time essential

to play out a schedule update is called as a computational time (The time difference between start

and end time of aircrafts schedule). The calculation times for the proposed EFPA and the

existing KH and Cuckoo optimization algorithms are depicted in Table 2.

Small Large Heavy

Problem

Size

KH Cuckoo Proposed

EFPA

KH Cucko

o

Proposed

EFPA

KH Cucko

o

Proposed

EFPA

100 0.414 0.354 0.302 0.413 0.353 0.342 0.413 0.353 0.337

200 0.464 0.404 0.341 0.463 0.403 0.364 0.464 0.403 0.356

300 0.471 0.411 0.352 0.471 0.411 0.385 0.471 0.411 0.402

400 0.483 0.423 0.365 0.483 0.423 0.402 0.483 0.423 0.411

Table 2: Comparative Analysis of Computation time for Small, Large and Heavy Aircrafts

Table 2, summaries all class of aircrafts and observed that the computation time varies for the small, large and heavy aircraft that are individually depicted.

(a) Small Aircraft


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(b) Large Aircraft

(c) Heavy Aircrafts Figure 6: Performance analysis of Computation time for the existing KH, Cuckoo and the

proposed EFPA for (a) Small aircraft (b) Large aircraft and (c) Heavy aircrafts

Figure 6 analyzes the performance concerning computation time intended for the existing KH, Cuckoo and the proposed EFPA for the small, large and heavy aircraft that are individually depicted. Figure 6(a) demonstrates the graphical portrayal of computation time for small aircraft. For any quantity of problem sizes, the proposed EFPA shows superior performance, that is, low computation time than the other conventional techniques. Figure 6(b) displays the graphical delineation of computation time for large aircraft. Here, on considering KH and the proposed EFPA, there is a vast variation, among which the proposed EFPA performs well. On considering Cuckoo and the proposed EFPA, though there is a slight variation in the computation time, the proposed EFPA outperforms the cuckoo technique. Figure 6(c) shows the graphical portrayal of computation time for heavy aircraft. Here, the existing Cuckoo optimization technique has


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computation time approximately equal to the proposed EFPA but the existing KH shows poor performance. When comparing all the three techniques, the proposed EFPA shows superior performance. 4.4 Aircraft Scheduling Distribution The scheduling of aircraft based on the target landing time is established in the graph displays in Figure 7.

Figure 7: Aircraft Scheduling Distribution based on Target Landing Time

It is deduced from the Figure 7 that these ten aircrafts are assigned to three runways. The aircraft1, aircraft 4, aircraft 7 and aircraft 10 will land at first runway. Aircraft 2, aircraft 5 and aircraft 8 will be assigned to the second runway. And the rest aircrafts will get the right to land at the third runway. 5. CONCLUSION The ALS problem at an airport has become exceptionally challenging on account of the expansion of air traffic. Customarily, this problem is broadly examined by defining it as an optimization model resolved by different operation research approaches. In any case, these methodologies are not ready to catch the dynamic nature of the ALS issue fittingly and handle vulnerability effectively. To overcome such demerits, this paper introduces an Embedded Flower Pollination Algorithm (EFPA) for aircraft landing scheduling, which embeds Runway Balance strategy with the FPA. The proposed EFPA is contrasted with the existing techniques with metrics CPU time, computation time and aircraft scheduling distribution. Experimental outcome established that the proposed EFPA is efficient to get optimal results when compared with other conventional techniques.


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