数学建模美赛论文.docx

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数学建模美赛论文.docx

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数学建模美赛论文.docx

数学建模美赛论文

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Acomputational-intelligencesystemfortheRiverTrip

TheBigLongRiveriswellknownasoneofthenaturalwondersworldwide.Besidesviewingthespectacularlandscape,anextremelyattractiverecreationalactivityisriverraftingontheBigLongRiver.Giventheriseinpopularityofriverrafting,theparkmanagershavebeenaskedtoallowmoretripstotraveldowntheriver.

ThepaperdevelopsamethodtoprovideamanagementstrategybyusingstatisticaldataandComputational-Intelligence-System（CIS）.CISisacomputerprogramthatmodelscomplicated,dynamiccampsites’numberYinteractionsintherivercorridoroftheBigLongRiver.Thesystememploysadataacquisitionandsimulatorsystem.Thedatabaseisa18×13matrixwhichgiveseverytrip’stravelarrangement.Thecomputersimulationcontainsdataanalysisandartificialintelligenceincreatinganindividual-basedmodelingsystem.

ThepapermainlyusethemodeloftheComputational-Intelligence-System（CIS）tosearchforhowtomaketheoptimalmanagementstrategieswhichmainlycontaintwoparts:

Thefirstpart:

theoptimalschedule

CISobeytheprinciplesofnotwosetsofcamperscanoccupythesamesiteatthesametime.CIScanputoutthespecificdistributeofthecampingsites,andtheoptimalschedulesaccordingtothevalueofthevariables.

Thesecondpart:

TransferProblem

Accordingtotheresultsofthefirstpart,thetableaboutchangingboatscanbeobtainedthroughcalculation.

Finally,usingprogram,assumeY=25,wegainaoptimalschedule,namedtable4.Thetableshowsthattheparkentertains318traveltripsinatouristseason,andthechoiceofshiptypesalsoisshowedintheTable5.

Contents

AnalysisoftheSweetSpot1

1Introduction1

1.1Background1

1.2problem1

2Assumptions2

3SymbolsandDefinitions2

4Model2

4.1Analysisoftheissue12

4.1.1Whatisthe“carryingcapacity”oftheriver2

4.1.2Thesituationsthatadaptthe“CarryingCapacity”3

4.1.3Resultoftheissue13

4.2Analysisoftheissue23

4.2.1Whatisthemeaningoffullyusedcampingsites?

4.2.2Howtomakethebestarrangement?

4.2.3Resultoftheissue27

4.3Analysisoftheissue311

4.3.1Whyshouldpassengersneedtochangeboats?

4.3.2Howtodecidewhichboatshoulduse?

4.3.3Resultoftheissue312

5StrengthsandWeaknessoftheModel13

6References13

7APPENDIX14

8Memo17

1Introduction

TheBigLongRiveriswellknownasoneofthenaturalwondersworldwide.Besidesviewingthespectacularlandscape,anextremelyattractiverecreationalactivityisriverraftingontheBigLongRiver.Rivertripsaredirectedbyschedules,whichshowthedaytripsstart,thenatureofanypassengerexchangesthatoccur,andthedayandlocationwherethetripsover.Themodelinthisstudywillhelptheparkmanagersmakeadeterminetoallowmoretripstotraveldowntheriver.

1.1Background

TheBigLongRiver（225miles）isinaccessibletohikers,ifyouwanttoexperienceawildernesslife,youhavetotakearivertripthatrequiresafewdays'camping.AlltripsmustbestartfromFirstLaunchtoFinalExitend.Thetripshavedifferenttypes,youcanselect6to18nightseitherway.Besides,youcanalsochoosetwodifferenttravelways,oneisoar-poweredrubberraft,whichtravelsonaverage4mph,theotherismotorizedboat,whichtravelsonaverage8mph.

1.2Problem

Thegrowingnumberoftouristsinrecentyears,scenicareasneedaprogramsothatmorevisitorscanenjoythemselves.Thequestionasksustoscheduleanoptimalmixoftripsandmakesurethecampsitescouldbeutilizedinthebestwaypossible,nomatterwhichkindofboats.

CurrentlythereareYcampsitesontheBigLongRiver,whichdistributedfairlyuniformlythroughouttherivercorridor.AndtheBigLongRiveracceptedXtripseachyear,butitopenedonlysixmonthseachyearbecauseofthecoldforrivertripsintherestmonthoftheyear.

Inadditiontotheaboveconditions,weshouldrememberthatnotwosetsofthecamperscanoccupythesamesiteatthesametimeandwithminimalcontactwithothergroupsofboatsontheriver.

Ultimately,takingintoaccounttheaboveconditions,weshouldgiveareasonabletimeschedulesothatthemoretripscantraveldowntheBigLongRiver.

Infact,thequestionsinclude3partsasfollows:

◆HowtobalancethecarryingcapacityoftheBigLongRiver?

◆Howbesttomakefulluseofthecampingsites?

◆Whenshouldpeoplechangeboats?

2Assumptions

●Supposethatthecampingsitesonlyfairlydistributealongonesideoftheriver.

●Supposethatallthetripsobeythearrangementsofthescenicwhentravelling.

●Supposethattheweatherofthescenicisgoodin6months.

●Supposethatdriftingonlyduringthedaytime,peoplemuststayatthecampingsitesduringthenights.

●BoatspeedisdefinedhereastheaverageofthespeedoftheBigLongRiver.

3SymbolsandDefinitions

◆Xrepresentsthetotaltripsin6months.

◆Yrepresentsthetotalnumbersofthecampingsites.

◆Nisthetotaltimesthatcampingsitestobeusedin29days.

◆Misthenumberofcampingsiteswhichcouldbeusedin29days.

◆WistheCampingpointofutilization.

◆

isthenumbersoftheIthteams

◆Kisthenumberofalltheteamsin29daystravel.

4Model

4.1Analysisoftheissue1

4.1.1Whatisthe“carryingcapacity”oftheriver?

Whatisthescientificdefinitionforcarryingcapacity?

Carryingcapacityreferstothemaximumpopulationthatagivenenvironmentandresourcebasecansustain.Understandingtheimpactsofhumanrecreationonnaturalresourcesisofcriticalimportanceinconstructingeffectivemanagementstrategies.Accordingtothisproblem,itmeansthatthemaximumnumberoftripboatscanbeacceptedbytheBigLongRivereverhalfofayear.

Theexperiencetellsusthatifthemachineworksalldaywithoutrest,itwillsoongetsometrouble.Soallmachineshaveregularworkingtime.ItissimilartotheBigLongRiver.

4.1.2Thesituationsthatadaptthe“CarryingCapacity”.

Clearly,lesstripboatsmakebettercarryingcapacity.Butitwillgetlessincomeforthescenic.Soweusethe"machineworking"modeltodescribetheriver's"CarryingCapacity".Eachmonththeparkhasonedayclosed.Thus,theBigLongRivercanbothacceptmorepeopleandits"CarryingCapacity"isstillmaintainabalance.

4.1.3Theresultofissue1

ConsideringtheopendaysoftheBigLongRiver,weassumethatdriftinginthesamewayineachmonth.Thatistosaythetripsareincycleforeverymonth.That'smoreeasierformanagertoarrangethedriftingplan.Alsoweassumetheopendaysofeachmonthis29days.Sotheopendaysofthescenicare174days（29×6=174）eachyearintotal.

InthiswaytheRivercouldgettheopportunitytorelievestress,andthesceniccouldearnasmuchaspossible.Afterall,theenvironmentalfactorsareveryimportant.

4.2Analysisoftheissue2

4.2.1Whatisthemeaningoffullyusedcampingsites?

Accordingtothefirstproblem,thetripsareincycleforeverymonth.Alltripsneedtotravelinthedaytime,sothecampingsitesshouldbeusedasmanyaspossibleatnight.Andthenthescenicwouldhavemuchchancetooffertravelerbetterservice.

4.2.2TheapplicationoftheCIS（Computational-Intelligence-System）

Obeyingtheprinciplesofnotwosetsofcamperscanoccupythesamesiteatthesametime,AComputational-Intelligence-System（CIS）isacomputerprogramthatmodelscomplicated,dynamiccampsites’numberYinteractionsintherivercorridoroftheBigLongRiver.Thesystememploysadataacquisitionandsimulatorsystem.Thedataacquisitionisa18*13matrixwhichgiveeverytrip’stravelarrangementatnightwithintheextentoftheBigLongRiverService.Thecomputersimulationcontainsdataanalysisandartificialintelligenceincreatinganindividual-basedmodelingsystem.

ThepapermainlyusethemodeloftheComputational-Intelligence-System（CIS）tosearchforhowtomakethebestmanagementstrategies

Weknowthereare18campingsitesalongtheriveratleast.Inordertosimplifytheproblem,assumingthatatotalof25spacinguniformdistributionofcampingsites.Accordingtotheprinciplesofdriftingthesamedistanceeveryday.Wecanalsofindout13differenttypesoftrips,whichhavedifferenttraveldays,from6to18nights.

Nowwecanlist13differentdriftmodeofcampinglocations.ShowninTable1.

Table1

TheCampingLocationsof13DifferentDriftMode

Traveltypes

Campingsites

6nights

4,8,13,17,21,25

7nights

4,7,11,1418,21,25

8nights

3,6,9,13,16,19,22,25

9nights

3,6,8,11,14,17,19,22,25

10nights

3,5,8,10,13,15,18,20,23,25

11nights

2,5,7,9,11,14,16,18,20,23,25

12nights

2,4,6,8,10,13,15,17,19,21,23,25

13nights

2,4,6,8,10,12,13,15,17,19,21,23,25

14nights

2,4,5,7,9,11,13,14,16,18,20,21,23,25

15nights

2,3,5,7,8,10,12,13,15,17,18,20,22,23,25

16nights

2,3,5,6,8,9,11,13,14,16,17,19,20,22,23,25

17nights

1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,25

18nights

1,3,4,6,7,8,10,11,13,14,15,17,18,19,21,22,24,25

Thenweneedtocalculatethescheduleofoptimalmixoftrips,ofvaryingdurationonthebasisofnotwosetsofcamperscanoccupythesamesiteatthesametime.

ForthispurposeweestablishthemodelofComputational-Intelligence-System（CIS）.Thevalueofsimulationmethodsasatoolforunderstandingandmanagingnaturalresourcesisevident.

wesetcycleoftheschedule29days

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