2012年美赛论文B题

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东方文化培训中心经营方案CampingalongtheBigLongRiverAbstractInthispaper,wetrytosolvetheproblemofschedulingrivertourismwhichcontainsdifferenttourdurationsandvariousspeedsofpropulsion.Weproposeaplantoutilizethecampingsitesasmuchaspossible,andguaranteethattwodifferentteamsdonotmeetduringalltheirtrips,inordertoprovidetouristswiththewildnessexperience.Inmodelconstruction,underaseriesofnecessaryassumptionsincludingtripdurationandcampsitestates,wemakethediscretedynamicprogrammingontheBigLongRiveroperationusingtheconstraintsandobjectivefunctions.Moreover,amatrixformisintroducedtodescribethestatesofcampsitessuccinctlyandcomprehensibly.Weimproveparticleswarmoptimization(PSO)toInteger-PSOalgorithmwhichcansolvethelarge-scaleintegeroptimizationproblems.Thentheoptimumsolutionisobtainedunderourassumptions.Throughcarefulcalculation,wehaveprovedthatthisoptimumsolutionsatisfiesthebasicrequirementofthetopic.Whenthereare20campsites,wefigureoutthattheoptimalsolutionis43trips.Withthefurtherdiscussionaboutthedifferentdemandsoftouristsandmanagers,weimprovethecurrentmodelandtakemorefactorsintoaccountsuchasutilizationpercentageanddifferentcampsitequantity.Wemakethescheduleofteamsandfindthelawofscheduletopologystructurewhichhelpsuscertifyourmodelandsuggestabettertheory.Wetesttherobustnessandsensitivityofthemodelsbyaccuratesimulationaboveandobtainsometheoreticalconclusionsofthearrangementforrivertourism.Theobtainedoptimalsolutionperformspromisinglywhenconsideringdifferentconditions.Therefore,the页脚内容25

1东方文化培训中心经营方案theoreticalguaranteeandthesimulationresultareconsistentwitheachother,andtogetherindicatethefeasibilityandreliabilityofoursolutiontosomeextent.Keywords:PSO,discretedynamicprogramming,topology,campsite页脚内容25

2东方文化培训中心经营方案CONTENT1PROBLEMSTATEMENT22PROBLEMANALYSIS22.1BackgroundandApproaches22.2OurOwnUnderstanding22.3OutlineofOurAnalysis33ASSUMPTIONSANDNOTATIONS43.1Assumptions43.2Notationsandsymbols54MODELINGANDSOLUTIONS64.1Modeling64.1.1Simplifyingconditions64.1.1.1PreliminarySimplification64.1.1.2MatrixExpression64.1.2Establishmodeling74.1.2.1UnderstandingofInfluencingFactors74.1.2.2ConstraintConditionsandObjectiveFunctions84.2Solutions124.2.1IntroductionofPSOAlgorithm124.2.2TheProcedureofRevisedPSO144.2.3OptimalSchedule164.2.4TheRelationbetweentheOperationScheduleandY18页脚内容25

3东方文化培训中心经营方案5CONCLUSIONS205.1Strengths205.2Weaknesses205.3Improvements206REFERENCES21页脚内容25

4东方文化培训中心经营方案1ProblemStatementIn this paper, we try to solve the problem of scheduling river tourism to utilize the campsites in the best way possible. Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The only way to enjoy it is to take a river trip that requires several days of camping. Passengers take either oar-powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river. The manager of this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel on the Big Long River during a six month period every year. There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river campsites and no two sets of campers can occupy the same site at the same time. Problem: How many more boat trips could be added to the Big Long River’s river season in order to utilize the campsites in the best way possible?2ProblemAnalysis2.1BackgroundandApproachesThisproblemhasaclosecontactwithpeople’slifeandproduction.Thebackgroundofthisproblemishowtoplanthetravellingroutesforthemanagersoftherivertomakehigherprofits,andtheansweroftheproblemcanbeappliedtothefieldofcityplanning,publictransportationandproductionlogistics.However,lowandoverexploitationoftravelresourcesarecommondrawbacksinthefieldofrivertourism,partlybecauseofthelackoftheoreticalfoundationsinscientificcalculation.Therefore,thediscussionandsolutionofthisproblemisofgreatimportanceforsociety.页脚内容25

5东方文化培训中心经营方案1.1OurOwnUnderstandingSimilartotheoperationoftrains,thetouristschoosetheirspecifictravelplanfrommanypredeterminedschedulesmadebymanagersoftheriver.Thatistosay,managerscouldpickupthespecifictouristsaccordingtotheirchoicesofdifferenttypesofboatsandduration.Thereforewecannotadoptqueuingmodeltosolvetheproblem.Ourgoalistohelpthemanagerstoobtainthehighestprofits,inotherwords,thehighestnumberofthetrips.Atthesametime,wearerequiredtorespectthetouriststogivethemthemaximumwildexperience,whichmeanswetrytoavoidthesituationthattwoormoreteamsmeetwitheachotherinthetour.Wetakethesetwofactorsasobjectivefunctions,andtrytogetconstraintconditionsfromtherealpracticalsituationofthisproblem.Inthisway,weuseoptimizationmethodtogettheoptimalsolutionofthisproblem.Howeverforreasonsofconvenience,ifwedonotmakesomenecessarylimitsandassumptionsoftheproblem,wewillhaveafairlytoughjobondataprocessinganditisnoteasyforustogettheavailableresults.Therefore,inoursolutionpart,wehavetomakereasonableconstraintsandlimitssoastogetthecompleteandfeasibleexpressioninmathematics.Forexample,wepresumethatthereisnotranscendencebetweenboats,showingthattwodifferentteamscouldnotmeetduringtheirtrips.Also,forthesakeofsimplicityofmathematics,wesupposethattheboatsarealwaysattheconstantspeedoncestarting[1].Thetwotypesofboatscanberepresentedbytwoparametersinmathematics,andatacertainnighttherearetwostatesforeverycampsite:withorwithoutteamstaying.Inmathematics,wecanrepresentthemwith1and0.Accordingtotherequirementoftheproblem,everycampsitehasatmostonetravelingteamtooccupy,sowejusttrytoassurethevalueofcampsitestateisnomorethan1withinonenight.Andtosatisfytherequirementofnoencounterbetweenteams,weneedtoguaranteethatthecourseoftheboatinfrontisalwayslargerthantheboatbehind.1.2OutlineofOurAnalysisSynthesizingtheinformationthatwehave,wegettoknowthatthewayfortouriststoselectthedurationandthetypeoftheboatsneedstobeconsideredbymanagerswhentheyaremakingplan.Alsothemanagerneedstoensurethatthelocationoftheboatinfrontcanmakeaneffectontheboatbehind.Tofullymakeuseofthecampsitesinordertoaccommodatemoretourists,thetravelagencyneedstoworkouta页脚内容25

6东方文化培训中心经营方案well-calculatedplanaboutthenumberoftoursthathavedifferentdurationandtheircorrespondingtripstartdates.Wealsonoticethatitisnotlikelythateverycampsitehasateamtooccupyeveryday[2].Bymeansofthisseriesofprocessing,weestablishandoptimizeourmathematicalmodel.AndfinallywegettheoptimalresultofX.Inaddition,aimingatthedistinctgoalsofthetouristsandmanager,wecanmakefurtheroptimizationbyconstructinganotherdestinationfunction.1AssumptionsandNotations1.1Assumptions●Assumingthatthesixmonthsmentionedintheproblemequalstocontinuous180days.●Oneorafewteamscanstarttheirtripsinadayandtheymuststarttogether.●Everyteamtravelsthesamemilesperday.Butdifferentteamcantraveldifferentmilesinaday.●Everyteamstrictlyconformstothepredeterminedplanmadebythemanager.●Theintervalofeverytwoneighboringcampsitesremainsstrictlyuniform.●Weconsiderbothoar-poweredrubberraftsandmotorizedboatssailsonaconstantspeed,includingtheacceleratingpartatthebeginningandthedeceleratingwhenfinishes.●Theflowspeedoftherivermaintainssteady,andtheweathersituationdoesnotaffectthespeedoftheboats.●Everyboatcanonlystayonenightatthesamecampsite.●Theboatsbehindcouldnevertranscendtheboatsinfront.●Everyteamcanonlychooseonekindofboat,whichmeansthetravelingspeedoftheboatofeveryteamdoesnotchangeduringthecourse.●Theteamcannotreturntothecampsitesbehind;theycouldonlymoveforwardalongthetourroute.页脚内容25

7东方文化培训中心经营方案1.1NotationsandsymbolsTab.1NotationsandsymbolsNotationMeaningthecampdurationofonetripwhosetripnumberisthespeedofoneraftorboatwhosenumberisthesequencenumberofcampsitewhereNo.tripstaysatmomenttravellingtimeofNo.everydaytravellingmilesofNo.everydaythetotalofcampsiteswhichTeamNo.passesbybutdoesnotstaythedatethatTeamNo.startsutilizationpercentageofthecampsiteNo.页脚内容25

8东方文化培训中心经营方案thetotalnumberofcampsitesthemaximaltotalnumberoftripstheaveragenumberofboatsstartedperdaythefrequencyofNo.campsiteoccupiedwithin6months号营地的频率占用6个月内 1ModelingandSolutions1.1Modeling1.1.1Simplifyingconditions1.1.1.1PreliminarySimplificationDuringthewholejourney,everyteamcouldstayatonlyonecampsitepernightandcouldnotbetranscendedbyotherteams.Throughsimplecalculations,weknowthatanyboatwillfinishtheirtraveliftheysailtenhoursadaywithinsixdays.Obviously,theteamsarenotallattheirfullspeedmovingforwardinthetravelprocess.Afterfurtheranalysis,wedecidetodefinetheindexoftheprogressofthetravelintermsofthelocationofthecampsites.Thatistosay,oneboatcannottranscendanotherboatwhichisclosertothetermination.Accordingtotheproblem,18days-longtourisallowed,apparentlythenumberofthecampsitesYisnolessthan18.Ifnot,theriverwillnotbeabletosupplysufficientcampsitestoaccommodate[3].Andsincenotalltheallthetypesofthetouris18dayslong,thereexistthecampsitethathasnoteamstaying.Inaddition,wearesupposedtomakeuseofcampsitesasmuchaspossible.Thuswecanseethisconditionastheconstraintsoftheoptimizingproblem.1.1.1.2MatrixExpressionBasedontheseconsiderationsabove,weutilizethematrixtodenote页脚内容25

9东方文化培训中心经营方案thestateofthespecificcampsiteatthespecificnight.Thereareonlytwoelementsinthematrix:0and1.0representsthattheboatdoesnotstayatthiscampsiteatthenight;1indicatesthattheboatstaysatthecampsitethisnight.Inthisway,atthecertaintime,alltheboatsintheirtripscanberepresentedbythematrixwithXrowsandYcolumns.Andthedurationtimeofthetripcanbeindicatedbythenumberofchangeofthematrixfromthebeginningtotheendoftheirtrips.Forexample,onecertaincampsiteatthecertainnightcouldbepresentedbythefollowingtable:Tab.2ExampleofStateofCampsite000…010000…000…………………010…000001…000100…000Themostoriginalmatrixisthezero-matrix,denotingnoteamstartstheirtravel.Aftertheoriginalquietstate,everyrowofthematrixbeginstohaveelement1andcontinuouslymovingtowardstherightrow.untiltheelementsoftherowbecomeall-zero,whichmeanstheboathasfinishthetravelandarriveatthetermination.Addingallthematrixes,wegetthesumoftherowelementsofthematrixandthevalueisbetween6and18.Inthiswaywegetallthecampsitesandboatsstatesduringallthetravelperiod.Meanwhile,the6-month-longdurationcallsforverylargeamountofcomputation,andbringsdifficultyinfeasibilitytoapplythismethod.Forthesakeofsimplifyingtheproblem,wemightdividethe180daysinto10periods,with18daysperperiod.Inthelaterdiscussion,wecouldexertourmodelinarelativelysmallperiod,soastoreducetheverboseamountofcomputationandmakeoursolutionsavailable.页脚内容25

10东方文化培训中心经营方案1.1.1Establishmodeling1.1.1.1UnderstandingofInfluencingFactorsFromthemanager’spointofviewofmakingprofits,thepossiblelargestnumberoftripteamsispreferred.Wearerequiredtohelpmanagertogivetheoptimalrivertripsutilizationplan.Accordingtothedescriptionoftheproblem,therearealotofconstraintstolimitthemotivationofteams.Whatweshoulddoistoexertthemaximumutilizationpercentageofthecampsitesinthefinitetime.Thetravelplanoftheboatsbehindispartlyaffectedbytheteaminfront.Forexample,theTeam2shouldavoidmeetandstayatthesamecampsiteatthesametimeastheTeam1.Similarly,fortheTeam3,4andmore,theirrunningstates,involvingtherunningspeedandtravelingtime,arepartlyinfluencedbytheboatsinfront[4].Fromthis,werealizewecouldusethetimeseriesmodeltosolvetheproblem.Theplanoftheboatsinfrontisrelevanttotheonesbehind,andtheinfluencecouldbeaccumulatedlittlebylittle,resultinginthelargefluctuationofthewholeplanofmanagingtheriver.Withoutthecarefullycalculation,theadministratoroftheriverwilllosequitealotprofits.Therefore,weneedtooptimizethemethodofincreasingthenumberoftheteam,onthebasisofthepreviousone.Forthepurposeofthis,wemightaswelllaymoreemphasisondirectlyplanningthenumberoftheteam.Inotherwords,weneedtoconsidertheoperatingschemeofeveryboatinthesixmonthlongtravelseason,beforetheseasonbegins.Thuswecouldmaketherivertrafficmoreefficientandrational.1.1.1.2ConstraintConditionsandObjectiveFunctionsWeknowthatthetraveldurationofeveryboatislimitedin6to18nightsandweassumethatnoteamisallowedtostayinthesamecampsitesmorethan1night.SothenumberofcampsitesYmustsatisfy：(1)ForXteams,wedetermineeveryteamwillstaynights,whichmeanstheywillarriveatatotalofcampsitesduringtheirtripsmustobey:(2)页脚内容25

11东方文化培训中心经营方案Thevelocityofeveryboatis:(3)Togettheoptimaltravelplan,weneedtomakefurtherinstructionsandimprovementandintroducemorevariablestorepresentthepossiblepracticalproblemsinoperation.Fortherivermanager,thedurationandstartdateplanofeveryteamisextremelyimportant.Soitisnecessaryforustoprovidethespecificdurationanddate.Tosimplifyingtheproblem,weassumethatoneorafewteamscanstarttheirtripsinadayandtheymuststartatthesametime,forexample8:00a.m.Wesupposethedateofeveryteamisanditmustsatisfy:(4)Wealsoneedtoobtainhowmanynightsthetripstaysandwhereitlocates.Andweexpectatablelikebelow:Tab.3ExampleofFinalConclusionofOurExpectation…………………Alltheequationsabovemeet:(5)Tosimplifyandcalculatethevariablesabove,weneedtoadoptatotalofaquitenumberofvariables.Thenumberofvariablesis:(6)Apparently,eveniftheoperatingscaleisnotlarge,westillhavethousandsofvariablestodealwith.Thereforewewilltrytodecreaseitbasedonourreasonableassumptions。页脚内容25

12东方文化培训中心经营方案Wesupposethattheeveryboatsailsthesametimeeverydayintheirtrips,whichmeanstheysailsthesamemilesperday.Andweassumethateveryboatsailsatfrom8amto18am.Apparentlytheleasttimeofeverydaysailingis,here(mph).Thuswehave:(7)Themilesthateachteammovesforwardeveryday：(8)Andweget:(9)and,(10)Alsothenumberofcampsitesthattheteampassesbybutdoesnotstayis：(11)FirstFinalCampsiteFig.1SimulationofTravelProcessThenumberofcampsitesbetweeneverytwoneighboringteamsaccordingtoFig.1:(12)And(13)页脚内容25

13东方文化培训中心经营方案Howistheobjectivefunctionofoptimizationmodeldetermined?Asweknow,sincemanagersalwayswishmoretouriststojoininthetravel,themostdirectobjectivefunctionisthetotaltripnumberXwhichisalsothevariablethatistobefiguredout.Thus,wedefinetheutilizationpercentageofcampsite:(14)Obviously,themoreteamsareinvolvedintravelinafinitetimeperiod,thehigherutilizationpercentageisattained.Therefore,wecandefineanotherobjectivefunction:(15)Wealsohave：(16)Thus,wedefinethefinalobjectivefunction:(17)Aswestateabove,theboatsbehindcouldnevertranscendtheboatsinfront.Sowegettheconstraintconditions:(18)Finallyweyieldtheoptimizingmodel:页脚内容25

14东方文化培训中心经营方案(19)Inaddition,because6-month-longtimespanbringsaboutlargeverbosecalculation,weneedtodecreasethetimespananddividethewholecomplexproblemintoafeweasierquestionstodealwith.However,simplysplittingthetopicwillresultinthetremendouserrorsofoptimalresults[5].Asweknow,onemonthisacommonperiodforpeopletorecordevents.Weassumethatitisalsoconvenientformanagerstomaketheschedule,andweuseonemonthastheperiodtodiscuss.Bysolvingproblemsinthesmallerperiod,wesimplifytheamountofcalculation.1.1Solutions1.1.1IntroductionofPSOAlgorithmPSOalgorithmisoneofthecommonswarmintelligencemethodstosolveproblemsaboutparameteroptimization,parameterdesignandcombinatorialoptimization.Ithasbeenachievedbyprogramsandhasimpressiveoptimizationefficiencybecauseofthecombinationofswarm页脚内容25

15东方文化培训中心经营方案intelligenceandlearningfunction.Asaresult,PSOiswidelyusedinscienceandtechnologyresearches.ThecoreideaofPSOisderivedfromtheprocessofsimulatingsocialbehavior.Asastylizedrepresentationofthemovementoforganismsinabirdflockorfishschool,itisametaheuristicasitmakesfewornoassumptionsabouttheproblembeingoptimizedandcansearchverylargespacesofcandidatesolutions[6].ThemathematicalmodelofPSOisfollowing:(20)(21)Tab.4NotationforModelExpressionabovethespeedofeveryparticleattime;thepositionofeveryparticleattime;w(t)inertiaweight;,personalfactors,socialfactors;PbestthebestpositionofeveryindividualsofarGbestthebestpositionofglobalparticlessofar,randomnumberswhichareuniformlydistributedbetween0and1页脚内容25

16东方文化培训中心经营方案Fig.2SchemaoftheSearchingProcessforOptimalSolutionofPSOIfavalueofthedecisionvariablesisinteger,theproblemiscalledanintegerprogrammingproblem.Inthispaper,ourassumedvariablesareallintegers.Forequations(18)integerprogrammingproblems,wecanhaveoptimalsolutionbyapplicationofthedynamicprogrammingfundamentally.However,sinceoptimizationproblemsbecomelargerandmorecomplicate,ahighspeedandaccurateoptimizationmethodisexpected.Asforthisrivertripproblem,althoughthenumberofvariablesdecreasesalotbyourreasonableassumptionsandsimplification,theconstraintconditionsandcalculationamountsstillremainquitecomplex.Thereforeweadoptparticleswarmoptimization,toobtainourresultsasaccuratelyaswecaninafinitetime[7].However,thevalueobtainedbythemoveschemeofthePSOmethodisnonintegervalue,wecannotapplythePSOmethodtononlinearintegerprogrammingproblems.Thus,werevisethedecisionvariablestoapplytononlinearintegerprogrammingproblemsbytheroundingofvaluesobtainedbythemovescheme.Ontheotherhand,wecannotregardthePSOmethodadequatelyonaccuracyofsolutions.Thus,weanalyzetheprocessofPSOmethodindetail,andwefindoutthatapartoftheswarmdoesnotmoveonthesearchprocess.[8]Thisisattributedtoallelementsbecoming0whenwerevisesearchdirectionvectorelementintoanintegervalue.Thereforewerevisemovemethodstomakecertainthatallparticlesmovewhenallelementsofthesearcharedirectionvector.Tobeconcrete,wereviseinto1or-1dependingontheplusandminusontheelementthattheabsolutevalueismaximumintheelementofbeforerevisinganintegervalue.[9]页脚内容25

17东方文化培训中心经营方案1.1.1TheProcedureofRevisedPSOTheprocedureoftherevisedPSOproposedinthispapersummarizedasfollowsandisshowninFig.3[10].Step1:FindanintegerfeasiblesolutionbyPSOinconsiderationofthedegreeofviolationofconstraints,anduseitasthebasepointofthehomomorphousmapping,.LetandgotoStep2.Underthepremiseofassumptions,ifthereisonemotorboatteamstartingitstraveleveryday,thereareatmost30motorteamsinamonth.Theysailssamemileseverydayandtheystayatthesamecampsites,andbecausetheirstartingdatesdiffersonedayonebyone,theydonotcontradictwitheachotherinthewholetravel.So,wecangetagroupoffeasiblesolutions(assumingthereare20campsites):Step2:Generatefeasibleinitialintegersearchpositionsbasedonthehomomorphousmapping.GotoStep3.Step3:Iftheparticledoesnotmovesincethecurrentsearchpositionandthenextsearchpositionarethesameeither,reviseto1or-1dependingontheplusandminusontheelementthattheabsolutevalueismaximumintheelementofbeforerevisinganintegervalue.GotoStep4.Step4:Checkifthecurrentsearchpositionofeachparticleinthesub-swarmwithrepairbasedonthebisectionmethod,,isfeasible.Ifnot,repairittobefeasibleusingthebisectionmethod,andgotoStep5.Step5:Evaluateeachparticlebythevalueofobjectivefunctionfor.GotoStep6.Step6:Iftheevaluationfunctionvalueisbetterthantheevaluationfunctionvalueforthebestsearchpositionoftheparticleinitstrack,updatethebestsearchpositionoftheparticleinitstrack.Ifnot,letandgotoStep7.Step7:Iftheminimumofisbetterthantheevaluationfunctionvalueforthecurrentbestsearchpositionoftheswarm,updatethebestsearchpositionoftheswarm.Otherwise,letand页脚内容25

18东方文化培训中心经营方案gotoStep8.Step8:Iftheconditionofthesecessionissatisfied,applythesecessiontoeveryparticleaccordingtoagivenprobability,andgotoStep9.Step9:Finishift=Tmax(themaximalvalueoftime).Otherwise,letandreturntoStep3.页脚内容25

19东方文化培训中心经营方案Fig.3FlowChartoftheProcedureoftheRevisedPSO页脚内容25

20东方文化培训中心经营方案1.1.1OptimalScheduleUsingPSOalgorithmtooptimizethetopic,wefigureoutthefollowingoptimalresultsasthescheduleoffirstmonth:Tab.5OptimalScheduleOptimalX43No.NightsStartingDayNo.ThesequenceNo.ofCampsitewhichtheteamfirststayBoatTypeTravelhourperday11414M321311M331123O441133O451143O461453M371463M381062O491474M3101184O4111082O4121092O41311103O41411104O41511103O41611104O41710112O41811124O41911123O42010131O42113142M32211144O42313151M32410161O42510162O42613172M3279174O22813182M32910192O43011203O43111213O4页脚内容25

21东方文化培训中心经营方案3213211M33310222O43410232O43513231M33614234M33711244O43810252O43910261O44011274O44111283O44210292O44311303O4Theaverageofeachboat’sstop:(22)Thenumberofeverydayboatsstarted:(23)WeintroduceamatrixwithXrowsandYcolumnstodescribethestateofeverycampsiteandteamandwegetthecampsitesnumber:页脚内容25

22东方文化培训中心经营方案Fig.4StateofEveryCampsiteandTeamByanalyzingthefiguresabove,withtheincreasingnumberofcampingsites,moreteamscanbeallowedtostarttheirtrips,andtheblacksquareinthefigurebecomeslesscompressed.Becausetheteamhasmoreoptionstostaywhentherearemorecampsites,bythecoordinationofthemanager,moreboatshaveopportunitiestostarttheirtrips.Itiscertifiedthatoursimulationresultisreasonable.Infact,theresultofouroptimizationmodelaccordstothesequenceofthecodeelementtableweaddressabove.Ourdestinationofoptimizationistoaddthetotalnumberofrowsasmuchaspossible,sothattoaddmoreteamsinthetraveloperation.Italsoindicatesusthatwecouldfirsttransformtheproblemanddealwithitinaddressingthecodetable.Inthisway,wecoulddirectlyfigureoutthecampsitesstateswhichtheboatstayandobtainthemaximumtotalnumberofrows.Thusweavoidfacedirectlywiththecomplexdynamicprogrammingproblem.页脚内容25

23东方文化培训中心经营方案1.1.1TheRelationbetweentheOperationScheduleandYApparently,Yhasthedecisiveeffectonthescheduleformulation,andthecampsitescouldrepresentthecarryingcapacityoftheriver.UsingPSOalgorithms,wemakeoptimizationonthecircumstancesofdifferentvaluesofY.Accordingtotheoptimizationresult,weobtainthecurve-fittingresult:Fig.5FittingCurveofDataofXandYTheresultshowsthatcampsitetotalnumberandthemaximumnumberofteamshavethefollowingrelation：(24)Basedonthefittingresults,wededucethatthereislinearrelationbetweenXandY.However,lackingofenoughreferencedata,thereexistsdifferentpracticalsituation.Theaveragequantitiesofstartingteamsperdayalsoincreasesaccordingly：Tab.6AverageofStartingTeamsperDay2021222324252627282929页脚内容25

24东方文化培训中心经营方案1.431.571.731.771.92.032.172.272.302.332.371Conclusions1.1StrengthsInourmodel,wemakesomereasonableassumptionstodecreasethenumberofunknownvariables.Therefore,wetransformthecomplexproblemsintosolvablemathematicalmodelofnon-linearprogramming.Thetimespanintopicis6months.Wereducethescopeofourdiscussionsoastoobtaintheresultsmorequicklyandaccurately.Takingadvantageofthemethodofswarmintelligenceandlearningfunction,weadoptandimprovethePSOalgorithmtosolvetheproblem.Weproposethecoderepresentationtorepresentalltripschedules,andthinkupaninnovativeandmeaningfulthoughtofthetopic.1.2WeaknessesWhileourmodelsattempttogetareasonableandconvincingresult,therealsoexistlimitations.Forexample,weassumethateachteamtravelssomemileseveryday,andwedonotallowdifferentteamstomeetatthetravelcourse.Inalgorithmsaspect,thePSOalgorithmitselfhaslimitationsindealingwithlargescaleoptimization,whichprobablyfallsintolocaloptimumsituation.Ourfinalresultshowsthatonaveragetherewillbe1.6teamsstartingtheirtravel,nottakingaccountoftheconsiderationsondifferentweatherandseasons.页脚内容25

25东方文化培训中心经营方案1.1ImprovementsInourmodel,wedeterminethateachteamtravelssamemileseverydayandcannotmeetanyotherteams.Infact,itbringsdifferencesbetweenourmodelandpracticaltravelsituations.Loosingthiskindofassumptions,wecouldgetthebettersolutionthatkeepswiththereality.Inthispaper,wearemainlyonthesamesideofthemanagers,andignoringthesubjectiveroleoftouristsinthetourismservices.Inaddition,fromanecologicalstandpoint,over-explorationisnotbeneficialtotheenvironmentneartheriver.Therefore,weneedtointroducemorevaluablefactorstomakefurthermulti-objectiveoptimization,whichwillleadtoamoreconvincingandsignificantresult[11].Furthermore,indifferencetoourmodelwhichisbasedonthestatesoftheteams,wecouldalsoconstructourmodelfromtheviewofcampingsites.Thepossiblemethodistoseethecampingsitesasthefixednodesintopologicalstructure,tosolvetheproblemusingthegraphtheory.2References[1]J.A.Bieri,andC.A.Roberts,2000,UsingtheGrandCanyonRiverTripSimulatortoTestNewLaunchSchedulesontheColoradoRiver,AssociationforWomeninScience,29:6-10;[2]R.E.Borkan,andA.H.Underhill,1989,SimulatingtheEffectsofGlenCanyonDamReleasesonGrandCanyonRiverTrips,EnvironmentalManagement13:347-354;[3]C.A.Roberts,DougStallman,J.A.Bieri,2002,ModelingComplexHuman–EnvironmentInteractions:theGrandCanyonRiverTripSimulator,EcologicalModeling,153:181-196;[4]H.R.Gimblett,Roberts,C.A.Daniel,T.Mitner,M.Cherry,S.Kilbourne,D.Ratliff,M.Stallman,D.Bogle,R,2000b.IntelligentAgentModelingforSimulatingandEvaluatingRiverTripSchedulingScenariosfortheGrandCanyonNationalPark.IntegratingGISandAgentBasedModelingTechniquesforUnderstandingSocialandEcologicalProcesses.pp:245–275;[5]Bishop,I.D,H.R.Gimblett,1999.ManagementofRecreationalAreas:GeographicInformationSystems,AutonomousAgentsandVirtualReality.EnvironmentandPlanningBPlanningandDesign,27:423–435;[6]Xiu-juanLei,A-liFu,Jing-jingSun,2010,PerformanceAnalyzingandResearchingofImprovedPSOAlgorithm,ApplicationResearchofComputers,27(2):453-458;[7]J.KennedyandR.C.Eberhart,1997(b),ADiscreteBinary页脚内容25

26东方文化培训中心经营方案VersionoftheParticleSwarmAlgorithm.Proc.1997Conf.onSystems,Man,andCybernetics,4104–4109;[1]H.Yoshida,K.Kawata,Y.Fukuyama,andY.A.Nakanishi,ParticleSwarmOptimizationforReactivePowerandVoltageControlConsideringVoltageStability.InG.L.TorresandA.P.AlvesdaSilva,Eds.,Proc.Intl.Conf.onIntelligentSystemApplicationtoPowerSystems,RiodeJaneiro,Brazil,1999.pp.117–121;[2]VandenBergh,A.Engelbrecht,UsingNeighbourhoodwiththeGuaranteedConvergencePSO,2003IEEESwarmIntelligenceSymposium,2003:235-242;[3]M.ClercandJ.Kennedy,2002,TheParticleSwarm:Explosion,StabilityandConvergenceinaMulti-DimensionalComplexSpace,IEEETransactionaonEvolutionaryComputation,Vol.6,58-73;[4]ParsopoulosKEandVrahatisMN,2002,ParticleSwarmOptimizationMethodinMultiobjectiveProblems.ProceedingsACMSymposiumonAppliedComputing,pp.603-607;页脚内容25

27东方文化培训中心经营方案MEMOTo:ManagersoftheriverFrom:Team12911Date:13FebruarySubject:OptimizationonrivertripsplanWearewritingtoreportourkeyfindingsinthesefourdays.Findings1.WeareabletofigureoutthemaximumvalueoftripstotalnumberX,accordingtothegivenvalueofcampsitestotalnumberY.WhenYequalsto20,themaximumXis43.2.WiththeincreasingvalueofY,thecarryingcapacityoftheriverimproves,andXincreasesaccordingly.3.Toobtainthemoreaccuratesolution,weneedtointroducemoreusefulfactors.Thusthemulti-objectivemethodcouldbeutilized.Recommendations1.Forenvironmentalreasons,therivershouldnotbeoverexploited,sothevalueofYshouldnotbetoolarge.2.Forpersonalexperienceoftourists,toolargeXandYprobablydecreasetheRiver’sattractionandprofits.页脚内容25