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ISSN:0974-7435Volume10Issue21BioTechnologyAnIndianJournalFULLPAPERBTAIJ,10(21),2014[13306-13312]ArrivalflightschedulingbasedonroughsettheoryandfuzzycomprehensiveevaluationGaoWei,ZhangYun-Xia*CollegeofAirTrafficManagement,CivilAviationUniversityofChina,Tianjin300300,(CHINA)E-mail:yxzhang20@126.
comABSTRACTTheefficientutilizationofterminalareaairspaceandrunwayresourceplaysanimportantroleinincreasingtheefficiencyofairtrafficflowmanagement(ATFM).
Arrivalflightschedulingisoneofthekeypartsofmakinguseofthisresource,soitisnecessarytostudytheproblemofarrivalflightscheduling.
Consideringseveralinfluencefactorsofactualsequencingprocessingbycontrollersandsomefactorswereneverconsideredbypreviousstudy,thispaperstudythisproblemwithfuzzycomprehensiveevaluationmethod,whichcouldtradeofftheimportanceofeachfactor.
Butthemembershipfunctionandweightnumberofeachfactorweredifficulttodetermine.
Tosolvethisdifficulty,weusedroughsettheorytoobjectivelycalculateweightnumberandcombineditwithfuzzycomprehensiveevaluationmethod.
Inthispaper,weanalysearrivalflightsequencingprocessbycontrollersfirstlyandproposefiveinfluencefactorstoconstructindexsystem,thenrepresenthowtousethismethodtosequenceflightandapplythismethodtoarealitycasetoverifyeffectivenessandfeasibility.
Theexperimentalresultshowsthatarrival-rateisimprovedandtimeofdelayisdecreasedobviously.
KEYWORDSTerminalarea;Arrivalflightscheduling;Roughsettheory;Fuzzycomprehensiveevaluation.
BTAIJ,10(21)2014GaoWeiandZhangYun-Xia*13307INTRODUCTIONWiththerapiddevelopmentofChina'saviationtransportationindustry,theproblemsoftheairtrafficflowmanagementgrowlargerandlarger.
Thedelaysofflights'take-offandlandinghavebeenarousedbyincreasingairtrafficflowandlimitedresourceofterminalareaairspaceandrunway.
Butthecurrentairtrafficcontrollacksaneffectivelyassistantdecision-makingtool.
Accordingtotheexpectedlandingtime,thecontrollersusuallycommandflightslandingonthefirst-come-first-servedbasis(FCFS),whichmainlydependsoncontrollers'experience.
Althoughthismethodofflightschedulingiseasytooperate,itdoesnotinvolveanyoptimizationandwillproducemoredelays.
Therefore,effectivemethodsofarrivalflightschedulingaresignificanttoflowmanagementinterminalarea.
Inthisrespect,domesticandforeignscholarshaveconductedextensiveresearches.
Therearemanykindsofmethodhavebeenputforwardtosolvethisproblem,including[1-8]positionexchangeconstraint,depth-firstsearchingalgorithm,fuzzytheory,combinatorialoptimizationmethod,controltheorycombinedwithintelligentalgorithm(suchasgeneticalgorithmandantcolonyoptimization)andsoon.
Buthowtodescribethisproblempreciselyisthekeytoschedulingarrivalflight.
Fuzzyintegratedjudgemethodcanbalanceelementsintheprocessofflightschedulingandmakedecisionsbyconsideringallelements'function.
Consequently,fuzzyintegratedjudgemethodwillbeadoptedtostudytheproblemofarrivalflightscheduling.
However,it'shardtoobjectivelydeterminemembershipfunctionsandeveryelement'sweight.
Roughsettheorycandigtheoriginalflightdataanddetermineattributes'weightallbytheregularityofdataitself.
Accordingly,thispaperwillcombinetheroughsettheoryandfuzzyintegratedjudgemethodtostudytheproblemofterminalareaarrivalflightscheduling.
Firstly,theindexsystemoffuzzyintegratedjudgemethodwillbesetup.
Then,theprocessoffuzzyintegratedjudgebasedonroughsettheorywillbeintroduced.
Finally,thesimulationresultwillbeprovided,andthefeasibilityandeffectivenessofthismethodwillbetestedandverified.
ROUGHSETTHEORYDefinition1AknowledgebaseisdefinedasarelationshipsystemK=(U,R),whereU≠(isemptyset)isthesetoffiniteobjects(theuniverse),Risafinitesetofattributes[9].
Definition2TetradisusedtodefinetheinformationsystemS=U,A,V,f,whereU={x,x,…,x}representsnon-emptysetoffiniteobjects,calledtheuniverse;A={a,a,…,a}isafinitesetofattributes;V=σV∈meansthesetofattributesvalue;f:U*A→Vrepresentsinformationfunction.
ForeveryattributesubsetB,ind(B)isdefinedastheindiscerniblebinaryrelation(equivalencerelation),i.
e.
indB={(x,y)|x,y∈U,a∈B,fx,a=f(y,a)}.
indB(B∈A)representsakindofdivision,notedas(B)orU/B.
Definition3IfaknowledgebaseK=(U,R),r∈Risaequivalencerelation,wecalledGDRasgrainsizeofknowledger∈R.
Definition4IfaknowledgebaseK=(U,R),r∈Risaequivalencerelation,wecalledDis(R)asdiscernibilityofknowledger∈R.
DisR=1GDR=1||||=1||||(1)SupposedS=U,A,V,fisinformationsystem,A=C∪D,X∈Cisaattributesubset,x∈Xisaattribute,consideratingtheimportanceofxforX,whichmeansthataddingtheattributextoXimprovesthediscernibility.
Ifthisimprovementisheavier,attributexismoreimportantforX.
Definition5SupposedX∈Cisanattributesubset,x∈Cisanattribute,notedìxastheimportanceofxforX.
ìx=1|∪()|||(2)Supposed|()|=={x,x,…,x},thenX=indX=σ|X|.
INDEXSYSTEMFortheterminalareaarrivalflightschedulingproblem,itisassumedthatthereisonlyoneairportintheterminalareaanditsarrivalanddepartureflowhasbeenisolated,onlyconsideringthearrivalflight.
Thesearrivalflightsenterterminalareafromtheplanedwaypointindifferentdirections,withpredeterminedapproachandlandingprocedures.
Controllersscheduledthesearrivalflightsbetweenthestartandstopschedulingboundarysortboundariestooptimizetheflightqueueorder,reducedelays,avoidconflictandensureflightsafetybyadjustingthespeedandchangetheapproachroute.
Afterflightleftthestopboundary,theorderinthelandingqueuewillnotchangeandwillberemovedfromtheschedulingqueue,showninFigure1.
13308ArrivalflightschedulingbasedonroughsettheoryandfuzzycomprehensiveevaluationBTAIJ,10(21)2014Figure1:TerminalareastructureToavoidthecollisionbetweentheaircraftsoraircraftandobstaclesandensuretheflight'ssafe,efficientandorderlylandingattheairport,controllersusuallyuseradartoguideaircraftsenteringtheterminalareaandlanding.
ThereareseveralfactorsaffectingATCtoschedulingflight,whichneedtobecomprehensivelyconsidered.
Butoneofdifficultytotakeintothesefactorsisthattheycouldnotbeaccuratelydescribedwiththelanguageofmathematics.
Soweuseroughsettheorybasedandfuzzycomprehensiveevaluationmethodarrivalflightschedulingmodeltosolvethisproblem.
Throughanalysisofalargenumberofinfluentfactors,these5kinds'factorsareconsideredmuchmoreimportantthanothers.
Weconstructtheindexsystemasfollow:ThedistancetoIntermediateapproachFix(IF),notedasS:WhenflightpassIF,theorderinlandingqueueusuallymightnotbechanged.
HenceSisasignificantfactorthatinfluencestheorderoftheapproachqueue.
TheseflightsclosedtoIFhavepriority.
Thedifferenceofvelocityofsuccessiveaircrafts,notedasV:Atthesamealtitude,apairofaircrafthavedifferentvelocity,thecasethatthefasteraircraftwasbehindthesloweronemightleadtoagreatdelay.
Ifthefastonecouldbequeuedinfrontoftheslowone,thedelaycouldbedecreasedeffectively.
Atthissituation,changingtheorderofsuccessiveaircraftswhichhavedifferentvelocitycouldoptimizetheflightqueue.
Standardtimeseparation,notedasT:Thetimeseparationofsuccessiveaircraftpassedfinalapproachfix(FAF)isrelatedtotheaircrafttype.
Theinternationalcivilaviationorganization(ICAO)prescribedtheminimumtimewakeseparationundertheconditionofnowindbetweentwosuccessivedifferenttypesofaircraft,asshowninTABLE1.
Thegreaterthedifferencebetweenintervalandstandard,thegreaterthechanceofadjustflightsequencing.
Theformulais:T=()(3)Theimportanceofflight,notedasP:Themoreimportanttheflightis,theearliertheflightshouldbeguidetoland.
TABLE1:Theminimalwakeseparationofdifferentaircrafttype(unit:s)AircrafttypeThebehindaircraftHeavy(H)Large(L)Small(S)ThebeforeoneHeavy(H)94114167Large(L)7474138Small(S)747498Thewaylinkedtobaseleg,notedasL:Iftheaircraftisindownwind,itcouldimplementdelaybyextendingdownwind.
Thiswayisconvenientandflexibleforcontrollertodirectflightinotherpositionofthecircletoinsetbaselegandland.
Thelinkedwaywithbaselegcouldinfluencetheorderofarrivalsequence.
COMPREHENSIVEEVALUATIONMETHODEstablishingthedatatablebasedonoriginaldataInordertomakeuseofroughsettheorytodeterminetheweightofeachevaluationindexintheprocessofaircraftsequencing,thefirstthingistoestablishevaluationindexsystemdatatableaccordingtotheoriginaldata.
EstablishingadecisiontableTheremightbedifferencesbetweendimensionandorderofmagnitudeevaluationindex.
Inordertoeliminatethesedifferences,standardizationisneeded.
Indicatorsaredividedintopositiveonesandreverseonesaccordingtothechangeofdirection.
Thegreaterthevalueofpositiveindicatoris,thebettertheindicatoris,whilethereverseoneisthesmallertheBTAIJ,10(21)2014GaoWeiandZhangYun-Xia*13309better.
Duetopoortransformationmethodhastheattributethatstandardizedindexesaretransformedin[0,1]interval,thismethodisadoptedtostandardizeindexes.
[10]Forpositiveindexes,wehave:y=(4)Forreverseindexes,wealsohave:y=(5)UsingroughsettheorytodeterminetheweightofvariousevaluationindexesAccordingtothedefinitionofattributeimportanceinroughsettheory,theimportanceofevaluationindexesìxiscalculatedandnormalizedtobetheobjectiveweightoftheindex[11].
ù=ìσì∈(6)FuzzycomprehensiveevaluationMarkingforeveryindexaccordingtoevaluationcriterionandflightoriginaldata,weusefuzzycomprehensiveevaluationmethodtosequencearrivalflights.
TABLE2:EvaluationofeveryindexIndexValueofevaluationindexS0—55—1010—1515—20Above200.
90.
70.
50.
30.
1V40—5030—4020—3010—20Below100.
90.
70.
50.
30.
1T0—0.
50.
5—1.
01.
0—1.
51.
5—2.
0Above2.
00.
90.
70.
50.
30.
1P100.
90.
5L100.
70.
3APPLICATIONThetargetofarrivalflightsequencingistominimizetotalarrivaldelayinterminalarea.
Weusedactualarrivalflightdataofanairportbetween8amto9amascasetocalculatethearrivalflightsequencingproblemwithroughsettheory.
TheoriginaldataisshowninTABLE3.
TABLE3:OriginaldataofarrivalflightFlightnumberFlighttypeImportancelevelVelocity(NM/H)DistancetoIF(NM)WhetherpassingdownwindEstimatedarrivaltimeA1L0200019:00:44A2L0220309:01:18A3L0230719:01:58A4L0220719:02:30A5L02501319:04:30A6L12301509:05:20A7L02202019:06:18A8H02502009:08:30A9L02502619:09:22A10H02502709:12:0013310ArrivalflightschedulingbasedonroughsettheoryandfuzzycomprehensiveevaluationBTAIJ,10(21)2014EstablishingindexsystemofarrivalflightEstablishingindexsystemtableasTABLE4accordingtoTABLE3,where"↑"representspositiveindex,"↓"representsreverseindex.
Tiscalculatedwithformula(3);theimportanceofflightP'svaluewillbe1iftheflightisspecialplane,otherwiseis0;linkedwaywithbaselegL'svaluewillbe0iftheflightpassthedownwind,otherwiseis1.
TABLE4:IndexsystemdataFlightnumberS(↑)V(↑)T(↓)P(↑)L(↑)A10……00A23100.
4601A37100.
5400A47150.
4300A513201.
6200A61500.
6811A720100.
7200A820101.
8500A926100.
7401A1027151.
8900DiscretizationandstandardizationDimensionsandordersofmagnitudeofindicatorsarenotconsistentinTABLE4andneedtobestandardizedanddiscretized.
WestandardizepositiveindexS,VandPwithformula(4)andreverseindexH,DandLwithformula(5).
Iftheindexisapositiveindex,thegreaterthevalueis,thehigherthepriorityis.
Andiftheindexisreverse,thesituationisopposite.
IndextableafterdiscretizationisshowninTABLE5.
TABLE5:DecisiontableofweightFlightnumberS(↑)V(↑)T(↓)P(↑)L(↓)A210001A310000A411000A511100A600011A700000A800100A900001A1001100CalculatingweightofindexWeightcalculationprocessisshownasfollows:CalculatetheindiscernibilityrelationUind(R)={A2,A3,A4,A5,A6,A7,A8,A9,A10}Uind(R-S)={{A2,A9},{A3,A7},A4,{A5,A10},A6,A8}Uind(R-V)={A2,{A3,A4},A5,A6,A7,{A8,A10}A9}Uind(R-T)={A2,A3,{A4,A5},A6,{A7,A8},A9,A10}Uind(R-P)={A2,A3,A4,A5,{A6,A9},A7,A8,A10}Uind(R-L)={{A2,A3},A4,A5,A6,{A7,A9},A8,A10}BTAIJ,10(21)2014GaoWeiandZhangYun-Xia*13311CalculationtheimportanceSupposedX={V,T,P,L},accordingtothedefinitionofindeximportance,computingmethodoftheimportanceofindexSisasfollow:|X|=3^2+1^2+1^2+1^2+1^2+1^2+1^2=15|X∪{S}|=1^2+1^2+1^2+1^2+1^2+1^2+1^2+1^2+1^2=9ì_R(S)=1-(|X∪(S)|)/(|X|)=6/15ThesamecanbeobtainedìV=,ìT=,ìP=,ìL=.
Accordingtotheformula(6),eachindeximportanceisnormalized,afterthisprocessingwecangettheweightas:ù=0.
266,ù=0.
204,ù=0.
204,ù=0.
122,ù=0.
204A=(0.
266,0.
204,0.
204,0.
122,0.
204)SequencingarrivalflightTheindexisscoredaccordingtotheindexesofevaluationcriteria(TABLE2)andthesinglefactorevaluationvectorisasfollows:R1=[1,1,1,0.
5,0.
3]R2=[0.
8,0.
1,0.
85,0.
5,0.
5]R3=[0.
7,0.
1,0.
7,0.
5,0.
3]R4=[0.
65,0.
2,0.
85,0.
5,0.
3]R5=[0.
5,0.
3,0.
3,0.
5,0.
3]R6=[0.
4,0.
05,0.
6,0.
5,0.
5]R7=[0.
2,0.
1,0.
55,0.
9,0.
3]R8=[0.
2,0.
1,0.
2,0.
5,0.
3]R9=[0.
1,0.
1,0.
45,0.
5,0.
5]R10=[0.
1,0.
2,0.
2,0.
5,0.
3]SotheindexsetRforevaluationmatrixis:R=10.
80.
710.
10.
110.
850.
70.
650.
50.
40.
20.
30.
050.
850.
30.
60.
20.
20.
10.
10.
10.
10.
550.
20.
450.
10.
20.
20.
50.
50.
50.
30.
50.
30.
50.
90.
50.
30.
30.
50.
50.
50.
50.
30.
30.
50.
50.
3BymultiplyingtheweightingmatrixAusingroughsetstheorywithindexevaluationmatrixR,wecangetthefuzzycomprehensiveevaluationmatrix:=*=0.
79650.
56950.
47140.
50920.
37730.
45020.
30780.
23620.
30170.
2301Comparingthevaluesofmatrix,theorderofflightinlandingqueuecanbeobtained.
Itisbecausethegreaterthevalueis,theflightordershouldbenearthetop.
Underthecaseofmininaltotaldelayandconsideringminimalseparationconstrain,thesequencingresultisA1,A2,A4,A3,A6,A5,A7,A9,A8,A10.
ComparisontheresultcalculatedbyroughsettheorybasedfuzzycomprehensiveevaluationmethodwithFCFS,shownasTABLE6,thetotaldelaytimereducesfrom700secondsto676seconds.
FromTABLE6,wecanknowthattheorderofflightA4andA3isexchanged,becausevelocityofA4isfasterthanA3;theorderofflight5andA6isexchangedtoo,becauseA6isspecialplaneandhashigherpriority.
13312ArrivalflightschedulingbasedonroughsettheoryandfuzzycomprehensiveevaluationBTAIJ,10(21)2014Besides,theorderofflightA8andA9isalsoexchangedbecauseoftheirdifferentaircrafttypes,whichmeansdifferentwakeseparation.
Bychangingtheorderofthetwoaircraftscandecreasetheseparation.
CONCLUSIONThispapermainlystudiesthefuzzycomprehensiveevaluationbasedonroughsettheoryandtheapplicationthisalgorithminarrivalaircraftsequencing.
Consideringtheminimumsafetytimeintervalbetweensuccessiveflights,estimatedtimeofarrival,flightimportance,distancetoIF,speedandlinkedwaywithbaseleg,thisalgorithmismoreclosetotheactualoperationconditionandeffectivelysimulatestheprocessofreasoninganddecision-makingofcontroller.
Calculationofindexweightiscompletelybasedonthedata,whichismoreobjective.
Theresultofexperimentverifiestheeffectivenessandfeasibilityofthismethod.
Thetotaldelaytimeofsystemisdecreasedandarrival-rateofrunwayisimproved.
TABLE6:ResultofsequencingOriginaldataFCFSresultComprehensiveevaluationresultFlightnumberETAOrderSTADelay/sTotaldelay/sOrderSTADelay/sTotaldelay/sA19:00:44A19:00:4400A19:00:4400A29:01:18A29:01:584040A29:01:584040A39:01:58A39:03:1274114A49:03:124282A49:02:30A49:04:26116230A39:04:26148230A59:04:30A59:05:4070300A69:05:4020250A69:05:20A69:06:5494394A59:06:54144394A79:06:18A79:08:08110504A79:08:08110509A89:08:30A89:09:2252556A99:09:220509A99:09:22A99:11:16114670A89:10:54144648A109:12:00A109:12:3030700A109:12:2828676REFERENCES[1]R.
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