西工大数模公园内道路设计问题

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1、FormversusFunction:WalkingtheLineAmrishDeshmukh,NikoStahl,TarunChitraNovember18,20081AbstractTheArtsquadisaspacethatissubjecttoseveralcompetinginterests.Itsdesignisexpectedtooffertheopportunityforanindividualtomoveconvenientlyfromoneendtoanother,tokeepgene

2、ralmaintenancecostsfeasibleandtoallowforactivitiesrangingfromlecturestosnowballfights.Thispaperproposesamathematicalmodel,whichprovidesawayofintelligentlydesigningthepathnetworkofthequad.Thecenterpieceofourmodelisacostfunction,whichevaluatesthefeasibilityo

3、fagivenpathconfiguration.Toexplorethesetoffeasiblepathconfigurationwewroteanalgorithmthatrandomlygeneratessamplesofthisset.WethenimprovedonthissearchbyconstructinganoptimizationalgorithminspiredbyMarkovchainMonteCarlomethods.Webelievethisimprovedsearchhasfo

4、undalocalminimumpathconfiguration,asitappearsstableunderperturbation.2ContentsIIIIIIIVVVIProblemStatementTheArtsQuadrangleasaGraphTheLengthofaPathUnofficialPathInducedbyHumanBehaviorTheCostFunctionAssumptions:446789VIIVIIIIXAlgorithmsforFindingOptimalPath

5、ConfigurationsResults:RecommendedSolution91011XXIFutureWorkBibliography31516PartIProblemStatementThetaskistoredesigntheArtsquadwalkwaysusingamathematicalmodelthatwillhelpusdetermineapreferreddesign.Beyondthegeneralfactthatminimizingthetotallengthofthep

6、athsandmaximizingtheareasofcontiguouslawnsarepreferable,weareaskedtoconsiderthefollowingcriteria:·Pathmaintenancecosts·Landscapingcosts·Pedestriantrafficandbehavior·Thecreationofunofficialpathsanditsimpactonthelawn·ThegeneralappealofthequadToimplementthesecri

7、teriainourmodel,weareprovidedwiththefollowingprinciples:·Thepathmaintenancecostisproportionatetothetotalpathlength.·Thelandscapingcostdependsonthenumberofcontiguouslawns,thecreationofunofficialpaths(asaresultofpedestriansleavingthepavedpathstoarriveattheird

8、estinationmorequickly)andthegeometryofcontiguouslawn.·Ifthepathbetweentwopointsis15%longerthanthestraightlineconnectingthepoints,apedestrianwillleavethepathandcutacrossthequad.·Anaveragepedestrianmightleavethepathif