2015美赛D题获一等奖论文

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2015MathematicalContestinModeling(MCM)SummarySheet

Turnunsustainabilityintosustainability

Ajudgingsystemthatdeterminewhenandwhetheracountryissustainableornotcanprovidereferenceformakingareliabledevelopmentplan.Basedonthedefinitionofsustainabledevelopmentgiven,wechoose11indexesreflectingeconomical,social,cultural,thetechnicalissuestoactthemodel.

Webuildacountry-comprehensivescoringmodelbycombininggreyrelationalanalysisandclusteranalysistobuildthesystem.Then,enlargingthesamplebyRBFneutralnetworkandusingthissystemtotraintheBPneutralnetworktoscoreacountryweselected.

Fortask1,7countriesarepickedoutaccordingtothedevelopmentdegreefrom3levels.Thedataofeachindexofthesecountriesin2010-2012arenormalizedtobeanalyzedbyusinggreyrelationalanalysis.Scorethesecountriesandwewillgetaseriesofscoresbetween0and1.Theconclusionis:ifthescoregetshigherthan0.45,thecountryworthasustainableplan;

Fortask2,wechooseBangladeshastheexample.Itgetsthepointof0.3029,lowerthan0.45.Groundonthe3clustercentervalues,ourplanarepidedinto3partsforthefirst5years,thefollowing10years,andthenext5years.Onthefirststage,weaimatthoseindexeswhichgetlowerscorethanthe3rdclustercentervaluesuchasPercapitaforestareaandOil,thenraisethesevaluesuptothe3rdclustercentervalue.Aftertheimplementationoftheplan,thecountryscorereaches0.3349.Onthesecondstage,weconsidernotonlythoseindexes’scoreslowerthan2ndclustercentervaluelikePercapitaoutputofgrain,butalsocaretheindexwhichdidn’t‘makegreatprogress’afterthefirststageplanlikeOil.Weget0.4014bythisstage.Onthelaststage,wefocusmoreonthecomprehensiveimprovementofalltheindexes,especiallytheCrimerate.Thefinalscoreis0.4588afterthelongtermanditishigherthan0.45.

Fortask3,sensitivelyanalysisperformswellinstudyingtheinfluenceonthecountryscorewhenaindexvaluefloatsslightly.WefindthatPercapitaforestareacontributestothescorewhenitincreasestosomeextents.Torisethecountryscoreattheearlystage,wecanencouragetheinvestmentonforestplanting.However,aextremepointexistswhenmentionedthecontributionofBio-capacity/Ecologicalfootprinttothescore.Thescorewilldecreaseasthepointgetshigherthantheextremepoint.Inaword,itwillpreventthesustainableifwepayattentiontotheenvironmentprotectiononlywithoutconsideringthedevelopmentofindustryandagriculture.It’snecessaryforustoimproveotherindexesvalueforthereasonthattheyhelptoincreasethefinalscore.WereflecttheinteractionbetweenoutsidefactorsandtheindexeswegotabovesuchasnaturaldisastersinfluencethePercapitaoutputofgrain.Thesefactorshavedefinitelydifferentinfluenceonthefinalscore.

Fortask4andintheend,wediscussthestrengthsandweaknessesofourmodelforafurtherimprovement.

Contents

I.Introduction....................................................................................................................................3

1.1ProblemBackground.............................................................................................................3II.Symbols,DefinitionsandAssumptions......................................................................................3

2.1SymbolsandDefinitions.......................................................................................................32.2GeneralAssumptions............................................................................................................4III.Articulateourmetrics................................................................................................................4

3.1Collectdata............................................................................................................................43.2Preprocessdata......................................................................................................................6IV.Task1:Judgingasustainablecountry.......................................................................................7

4.1ModelI:GreyRelationGradeAnalysis................................................................................7

4.1.1Obtaintheindexweight.............................................................................................74.1.2Results&analysis......................................................................................................84.2ModelII:K-meansClusteringAnalysis...............................................................................9

4.2.1Modelingstep.............................................................................................................94.2.2Results&analysis......................................................................................................94.3ModelIII:RBF&BPneuralnetwork..................................................................................10

4.3.1Enlargetheamountofdata......................................................................................114.3.2Forecastthescore.....................................................................................................11V.Task2:Asustainabledevelopmentplan....................................................................................12

5.1Firststage............................................................................................................................135.2Secondstage........................................................................................................................145.3Thirdstage...........................................................................................................................15VI.Task3:Theadditionalenvironmentalfactors’influence......................................................15VII.Task4:TheStrengthsandWeakness.................................................................... …… 此处隐藏：20351字，全部文档内容请下载后查看。喜欢就下载吧 ……