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b mcm论文.docx

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bmcm论文

CampingalongtheBigLongRiver

Abstract

Whendriftingteamsincreasing,ourprimarytaskistodeterminethenumberofboatscouldbeaddedtotheriver,todevelopanoptimalschedule,andthecarryingcapacityoftheriver.

Tosolvetheseproblems,wefirsthypothesesthatbothmotorizedboatsandrubberraftsdrift4hoursperday,andweshouldlimitthenumberofcampsites.Besides,wesupposethatthebeginningandendoftheriverhavenocampingpoint.Accordingtocampingpointaveragedistributionprincipleandspeedconditions,weobtainthattheinitialnumberofcampsitesis13.Thenwedetermine8wayofthetravel（seetable2）.

Sincewedon’ttakeintoaccountsomethingunexpectedwhichleadtothefailureofreachinggoals.Toaddressthisproblem,weputforwarddifferentadjustmentstrategyandadjustmentmodelbasedontheGeneticAlgorithm.Inthisprocess,wedefinetheFitnessFunction

andseveralconstraintconditions.Wesolvetheadjustmentmodelthroughanalysisandcalculation,andobtainadriftingschedule（seestable3）.

However,theschedulewehaveobtainedisbasingontheconditionthatboatshavenochancepullintoshoreonlywhentheyarriveatthecampsinevening,whichmeansthatthismodels’resultshavemanylimitations.Thus,wefurtheradjustthemodelbyallowingtheboatspullintoshoreeveninthemidway.Inordertostrivetoinsertthemostships,weuse0-1programmingbyincreasingthenumberofcampsites.Finally,weobtainthatthenumberofcampingsitesYis56,X（thenumberofdriftingteamsacceptedinsixmonthsperyear）is392,andwegettheoptimaldriftingschedule（seetable4）.

Keywords:

GeneticAlgorithms0-1ProgrammingFitnessFunction

Contents

1.Introduction3

2.Assumptions3

3.Model4

3.1Determinedriftingtimeontheriver4

3.2Themethodofsettingcampsites.4

3.3Determinethewaytotravel5

3.4Adjustmentmodelbasedonthegeneticalgorithm7

4.Improvementofthemodel10

5.Modelevaluation12

5.1StrengthensoftheModel12

5.2WeaknessesoftheModel12

References12

Memo...........................................................................................................................13

1.Introduction

ThereisaphenomenonthatmoreandmorepeoplechoosetohaveatriponBigLongRiver.Theycanenjoythebeautifulscenicandwhitewaterrapids.Theriverisinaccessibletohikers,sotheonlywaytoenjoyitistotakearivertripthatrequiresseveraldaysofcamping.Passengerstakeeitheroar-poweredrubberraftsormotorizedboats.

Giventheriseinpopularityofriverrafting,weshouldsetmodelstoallowmoretripstotraveldowntheriver.Tosolvethisproblem,wefurtherclassifythisproblemintofourcomponentsasfollows:

●DeterminethenumberofboatsshouldbeaddedtotheBigLongRiver’sraftingseason.

●Developthebestschedulefortherivermanagers.

●Determinethepropulsion（motororoar）.

●Determinethecarryingcapacityoftheriver.

Throughanalysisandcalculation,wefinallysetseveralsuitableadjustmentmodels.Inourmodel,wetakeintoconsiderationthefollowingbasicrequirements:

●Oar-poweredrubberraftstravelonaverage4mphandmotorizedboatstravelonaverage8mph.

●Thetripsrangefrom6to18nightsofcampingontheriver,starttofinish.

●Notwosetsofcamperscanoccupythesamesiteatthesametime.

Wehavesuccessfulsolvedthegivenproblem.Besides,ouralgorithmisnotonlyfastingeneratingsolutions,butalsoflexibleindifficulttasks.

Wefirstadjustsailingschedule,inordertoincreasethenumberofboatstomeettherequirementofdriftingamateurs,andsetthetime（launchandcamp）properly,avoidingtheirarrivinglatetothecamp.

Accordingtotheexternalfactorsmadeontheboats,wecanputtheadjustmentproblemsintotwocategories.

●Irreversiblelatefactors.Suchasthecircuitdamage,devastatingnaturaldisasters（earthquake….）.

●Reversiblelatefactors:

thedamageisslight,andadministerscanrecovertheboatsthrough“accelerateinpart”.

Tocopewiththeincreaseoftravelerswewillleadinmoreboats,anddeterminethecarryingcapacityoftheriver.

2.Assumptions

（1）Everytourismteamisonlyallowedusingoneboat.

（2）Visitorscanonlytransferonceandexchangethesametypeship.

（3）Thebeginningandendoftheriverhavenocampingpoint.

（4）Aslongasboatspass,visitorscangooutofthescenicspot.

（5）Allcampsitesuniformlydistributeononesideoftheriver.

Table1.Descriptionofthevariables.

oar-poweredrubberrafts’driftingdistanceperday

motorizedboats’driftingdistanceperday

oar-poweredrubberrafts’drifttime

motorizedboats’drifttime

thenumberoftripteams

thecampsite

symbolfunction.

3.Model

3.1Determinedriftingtimeontheriver

Inthistitle,passengerstakeeitheroar-poweredrubberrafts,whichtravelonaverage4mphormotorizedboats,whichtravelonaverage8mph.Thetripsrangefrom6to18nightsofcampingontheriver,starttofinish.

Inaddition,wegotsomeinformationfromtheInternet:

Breakfastisservedaround8AMandyouareonthewaterbyabout10AM.Therewillbeastopforlunchandsomeshorthikes.Visitorscanarriveatcampsitearound4to5PM.Theyareallowedtohikeandrelaxbeforeservingdinner.Combinedwiththisarticlesaid,inordertoletpassengersplayrelaxedandhappy.Afterintegrating,wefinallyhypothesesthatbothmotorizedboatsandoar-poweredrubberraftsdrift4hoursperday.

3.2Themethodofsettingcampsites.

Wesupposethatthebeginningandendoftheriverhavenocampingpoint.Accordingtocampingpointaveragedistributionprinciple,wefirstset14campingpointstomeettheaveragedistributionprinciple.

Considerofoar-poweredrubberraftstravelonaverage4mph,motorizedboatstrav-

elonaverage8mph,bothofoar-poweredrubberraftsandmotorizedboatsdrifting4hoursperday,andtheconditionthattripsrangefrom6to18nightsofcampingontheriver.Wecanrespectivelycalculateoar-poweredrubberrafts’andmotorizedboats’dri-

ftingdistanceperdayrespectively.

miles

miles

Since,thedistancebetweeneverytwocampsitesis15miles.

miles

miles

So,motorizedboatshavepastthesecondcampsiteaftertravelling4hoursontheri-ver.Similarly,wecandeducethatoar-poweredrubberraftsalsopastthecampsite4hourslater.

Inordertomaketwokindsofboatsjustarrivedatcampsites,notwastingoftimeandenergy.Weadjustthedistancebetweeneachtwocampsitesis16miles.Sowejustneed13campsites.Andbothoar-poweredrubberrafts’andmotorizedboats’driftingdistancejustarecampingpointspacingintegertimesafteradjusting,whichcanmeettherequirementthateitheroar-poweredrubberraftsormotorizedboatscanjustarrivedatcampsites

3.3Determinethewaytotravel

Tosolvethisproblem,weconsiderofaextremesituationthatoar-poweredrubberraftsandmotorizedkeepsailing.Inotherwords,don’thavearest.SincetheBigLongRiveris225miles,oar-poweredrubberraftstravelonaverage4mphandmotorizedboatstravelonaverage8mph.Wecaneasilycomputeoar-poweredrubberrafts’drifttime

andmotorizedboats’drifttime

:

h

h

What’smore,accordingtotheresultofdrifting4hoursperday,wecangetthelimitofthesailingdaysaboutoar-poweredrubberraftsandmotorizedboatsrespectively.

days

days

Consideroftherequirementthatdriftingtimeshouldbemeasuredinnightsontheriver.Sothroughtheunitwecanconversioncalculate:

days=13nights

days=6nights

Wefurtherclassifytheproblemintotwocases.

●Ignoretransfer:

Justhavetwokindsoftourismway,oneistravelingfor13nights,theotheroneistravelingfor6nights.

●Consideroftransfer.

Sincethespeedofmotorizedboatsistwiceasmuchasthespeedofoar-poweredrubberrafts.Wecanobtainthefollowingtransferschedule.

Table2.Transferschedule

Transfer

rubberrafts

motorizedboats

rubberrafts

motorizedboats

6night

motorizedboats

7night

8night

9night

10night

11night

12night

13night

rubberrafts

Intheabovetable,

rubberrafts

motorizedboats：

Visitorssailingbyrubberraftstransferatcampsite

motorizedboats

rubberrafts：

Visitorssailingbymotorizedboatstransferatcampsite

3.4Adjustmentmodelbasedonthegeneticalgorithm

Ideally,everydriftingteamsailsonthebasisofgivennavigationcharttoenjoythemselves.However,infact,somethingunexpectedmayoccurredwhichleadtothefailureofreachinggoals;meanwhile,boatscan’treachthecampsintimewhichbringingunnecessaryproblemstothetravelers.

Driftteamduringthedrivingprocessmaybeaffectedbysomeuncertainexternaldisturbances（suchaswind,storm,shipsoutfailureorhumanfactors）.Theseoftencausemanyteamsfailtoarriveatthecampingplaceatthepredeterminedtime,whichissimilartothelatetrain,thusbringingthevisitorssecuritythreat.Atthesametimesuchdisturbancescanbringbigtroublestomanagementadjustment.

Considerofaseriesoffactors,weputforwarddifferentadjustmentstrategyandadjustmentmodel.

Consideringtheconditionsabove,

thedistancebetweenpandqisdefinedasfollowing:

Where

Xisthenumberofteams

Yisthenumberofcampsites

istheplannedroutinemap,thatis,

Where

arethearrivinganddeparturetimeofteam

tocampsite

.

Gisthesetofallactualroutinemaps.

Obviously,

metthefollowingconditions

●

matchingit.

●Thesufficientandnecessaryconditionof

is

●

wecanconclude

A