美赛.docx

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美赛

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2015MathematicalContestinModeling（MCM）SummarySheet

（Attachacopyofthispagetoyoursolutionpaper.）

Typeasummaryofyourresultsonthispage.Donotinclude

thenameofyourschool,advisor,orteammembersonthispage.

IsItSustainable

Summary

Sustainabledevelopmentisanewdevelopmentstrategy.Itinvolvesmanyfieldsofnaturalscienceandsocialscience,andhasobtainedthewidespreadattentionoftheinternationalcommunity.Inthispaper,wechosethemutualrelationsamongeconomy,environmentandsocietyasthemainline,respectivelyusingtheAHPmodel,thecorrelationanalysis,sensitivityanalysisandBPneuralnetworkmodel,andcombinedwithMatlab,SPSScomputersoftwaretoanalyzeandforecastnationalsustainabledevelopment.

First,weconstructanevaluationmodelbasedonAHPmethodofnationalsustainabledevelopment.Thenwecalculatedtheweightsofthreesub-systemsand10sub-categories.Next,weexaminetheconsistencyoftheweights,andeventuallyarriveatacomprehensiveevaluationofnationalsustainabledevelopmentindexformulaandevaluationcriteria.

Nextwerankedthe48countriesgivenintask2byPIindexandchoseAfghanistan.Measuring20indicatorsbycorrelationtest,wechose8keyindicators.Basedontheseeightkeyindicators,wecreateda20yearsustainabledevelopmentplanAfghanistantomovetowardsamoresustainablefuture.

Finally,weputadditionalenvironmentalfactorsintoconsiderationandthenhadtheeightkeyindicatorsforsensitivityanalysis.Byrankingtheirsensitivitycoefficients,weevaluatedourplan.ThenwepredictandanalyzePIofAfghanistannext20yearswithBPneuralnetworkmodel.Intheendofthepaper,wepresentamethodtoenhancethemodelandthestrengthsandweaknessesofourmodels.

.Introduction

SustainableDevelopmentisanumbrellathatattemptstobridgethedividebetweeneconomicgrowthandenvironmentalprotection,whiletakingintoaccountotherissuestraditionallyassociatedwithdevelopment.Itseekstodevelopmeansofsupportingeconomicgrowthwhilesupportingbiodiversity,relievingpovertyandwithoutusingupnaturalcapitalintheshorttermattheexpenseoflongtermdevelopment.Whilemanydefinitionsofthetermhavebeenintroducedovertheyears,themostcommonlyciteddefinitioncomesfromthereportOurCommonFuture,morecommonlyknownastheBrundlandReport,whichstatesthatsustainabledevelopmentisdevelopmentthat”meettheneedsofthepresentwithoutcompromisingtheabilityoffuturegenerationstomeettheirownneeds”.

Sustainabledevelopmentisoftenmisinterpretedasfocusingsolelyonenvironmentalissues.Inreality,itisamuchbroaderconceptassustainabledevelopmentpoliciesencompassthreegeneralpolicyareas：

economic，environmentalandsocial.Insupportofthis,severalUnitedNationstexts,mostrecentlythe2005WorldSummitOutcomeDocument,refertothe“interdependentandmutuallyreinforcingpillars”ofsustainabledevelopmentaseconomicdevelopment,socialdevelopmentandenvironmentalprotection.

Sustainabledevelopmentisanotoriouslyambiguousconcept,asawidearrayofviewshavefallenunderitsumbrella.Theconcepthasincludednotionsofweaksustainability,strongsustainabilityanddeepecology.Differentconceptionsalsorevealastrongtensionbetweenecocentrismandanthropocentrism.Thus,theconceptremainsweaklydefinedandcontainsalargeamountofdebateastoitsprecisedefinition.

.Problemrestatement

TheInternationalConglomerateofMoney（ICM）,whoareinterestedindevelopingcountries,hashiredyoutohelpthemusetheirextensivefinancialresourcesandinfluencetocreateamoresustainableworld.

●Task1:

wearerequiredtodevelopamodelforthesustainabilityofacountry.Asamodel,itshouldprovideameasuretodistinguishmoresustainablecountriesandpoliciesfromlesssustainableones.Furthermore,itcanalsoservetoinformtheICMonthosecountriesthatneedthemostsupportandintervention.Somefactorsaretakenintoaccount.Finally,themodelshouldclearlydefinewhenandhowacountryissustainableorunsustainable;

●Task2:

wehavetoselectacountryfrom48LDClist.AtthebasisofTask1,wecreatea20yearsustainabledevelopmentplan,whichconsistsofprograms,policiesandaidthatcanbeprovidedbyICM.

●Task3:

wearesupposedtoevaluatetheeffectofyour20-yearsustainabilityplanatthebasisofTask1.Basedonyourselectedcountry,weneedtoconsideradditionalenvironmentalfactorssuchasclimatechange,developmentaid,foreigninvestment,naturaldisastersandgovernmentinstability;

●Task4:

Besuretodetailthestrengthsandweaknessesofthemodel.ConfirmingthattheICMwilluseyourreporttoinvestinsustainabilitydevelopmentinterventionstrategiesforspecificLDCcountries.

.Problemanalysis

ThekeyofthispaperistohelpICMusetheirextensivefinancialresourcesandinfluencetocreateamoresustainableworld.Inaword,ourstudyaimstodeveloponeormoremodelstoassessthefollowingquestions:

●Whetherisacountrysustainableornot?

●Howcanyoucreatea20yearsustainabledevelopmentplan,whichconsistofprograms,policiesandaid?

●Howcanyouevaluatetheeffectofyourplanbasedonthesustainabilitymeasure?

●Whatarethestrengthsandweaknessesofyourmodel?

Inordertosolvetheseproblems,firstweestablishanAHPmodelasameasurablemodeltojudgeacountryissustainableornot.Thenwehaveordered48countriesgivenintitleandchoosethehighestone.Nextcorrelationanalysisiscarriedoutontheselectedcountries,selectingevaluationindexofhighrelevanceasakeyindicator.Combinedwiththekeyindicator,wecreatea20yearsustainabledevelopmentplan.Then,takingtheadditionalfactorsintoaccount,weconductsensitivityanalysisonkeyindicator.Accordingtothechangeoffactors,wecanmakeacommentontheplan.Atthesametime,BPnetworkisappliedtopredictthechangeoccurredoverthe20yearsinthefuture.Lastly,wedetailthestrengthsandweaknessesofthemodel.

.Modelassumption

●Forallcountries,thecomprehensiveevaluationindexofsustainabledevelopmentisonlyrelatedtoeconomy,environmentandsociety.

●Thedataweuseareallrealandeffective;

●Theindexwedonotchoosehaveanegligibleimpactonthenationalsustainabledevelopment;

●Inadditiontothetopicgivenintheplusfactors,theinfluenceofotherfactorsarenegligible.

.Models

SymbolsandDefinitions

variable

Meaning

CI

consistencyindexofJudgmentmatrix

CR

randomconsistencyindexofjudgmentmatrix

W

variousweight

PI

developmentindex

threshold

n

thenumberofnode,

N

thenumberofsample

ω

correspondinglink

5.1ModelOne

5.1.1Modelpreparation

Inordertoevaluatethesustainabledevelopmentsystem,wedividethesustainabledevelopmentsystemintothreemajorsubsystems,tensub-categoriesandalotofindexs,whicharefullyequippedtocarryoutaclearAHPanalysis.Ingenerally,AHPanalysisshouldbebuiltforeachlevelofjudgmentmatrix,andfurtherfordeterminingtheweightsandconsistencytests,andfinallythewholesystemischeckedbyoverallconsistencytesttoverifytheeffectivenessofweightdetermination.Inthispaper,takingthecomplexityofthesystemandthesimilarityoftensub-categoriesintheindexintoaccount,itisdifficulttodeterminetheimportantdegreeofsubjective.Therefore,forindexsinAHPanalysis,wenolongerexpand,butgivethemtherighttotheequivalentweight.WeonlycompeltheAHPanalysistothreemajorsubsystemsandtensub-categories.

5.1.2Modelestablishment

●Establishahierarchy

First,wedividethecomplexproblemintomoreelementsofthevariouspartsandformdifferentlevelsasfollow（Fig1）:

Fig1Hierarchicalanalysismodeldiagram

●constructJudgmentmatrix

Accordingtotherelevantguidelines,the1-9indirectcalibrationmethodareusuallycarriedouttoconstructthejudgmentmatrixtocomparethevariouslevelsofallelementswhichelementismoreimportant,andgiventheimportancetoacertainmagnitude.Thejudgementmatrixisasfollow（Tab1）:

Tab1JudgementMatrix

Scaling

Definition

1

3

5

7

9

2,4,6,8

thescalelistedabove

twoelementsareequallyimportant

oneisalittlemoreimportantthantheother

oneisobviouslymoreimportantthantheother

oneisstronglymoreimportantthantheother

oneisextremelymoreimportantthantheother

intermediatevaluesbetweentwoadjacentjudgments

theoppositesituationdescribedinabovedefinition

Inordertodeterminetherelativeobjectivejudgmentmatrixforsustainabledevelopment,wedecidedtousetheexpertquestionnaire.Letthemanalyzetheimportanceofthreemajorsubsystemsand10subcategoriesaboutthesustainabledevelopmentofthecountryusingthe1-9calibrationmethod,thenwehavetheresultsofasimpleweightedaverage.Thejudgementmatrixgivenbyspecialistisasfollow（Tab2）:

Tab2JudgementMatrixgivenbyspecialist

specialist

one

two

three

four

five

six

seven

eight

nine

ten

SocialSystem

2

1

1

2

1

1

1

2

1

1

EnvironmentalSystem

1

3

2

1

2

2

2

1

3

2

EconomicalSystem

2

1

3

1

2

3

1

2

2

1

Regionalpopulation

2

1

1

2

1

1

2

1

1

1

Socialstability

4

5

6

5

4

6

5

5

6

4

Technologyprofessionals

4

3

5

2

3

4

3

3

2

4

infrastructure

3

2

3

2

2

3

2

2

3