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公交线路发车间隔优化的双层规划模型与算法(英文) OptimizationofBusRouteDepartureIntervalwithDouble-LayerPlanningModelandAlgorithm Abstract: Optimizingthedepartureintervalofbusroutesisanimportantissueinpublictransportationplanning.Tosolvethisproblem,adouble-layerplanningmodelandalgorithmisdevelopedinthispaper.Thefirstlayerisamacroscopicmodelthatconsidersthecharacteristicsofthetransitnetwork,andthesecondlayerisamicroscopicmodelthatfocusesonthetime-spacedistributionofbuses.Twoobjectives,i.e.,minimizingthetotalwaitingtimeofpassengersandminimizingtheoperationalcostofbusoperators,areformulatedastheoptimizationobjectivesoftheproposedmodel.Ahybridgeneticalgorithmandsimulatedannealingalgorithmisdesignedtosolvethemulti-objectiveoptimizationproblem.TheeffectivenessoftheproposedmodelandalgorithmisvalidatedthroughacasestudyofabusrouteinaChinesecity.Theresultsshowthattheoptimizeddepartureintervalcanreducethetotalwaitingtimeofpassengersandtheoperationalcostofbusoperators. Introduction: Theoptimizationofbusrouteshasattractedsignificantattentionfromtransportationresearchersandpractitioners,asitcanimprovetheefficiencyofpublictransportationsystemandprovidebettertravelexperienceforpassengers.Oneoftheimportantaspectsofbusrouteoptimizationisthedepartureinterval,whichdetermineshowfrequentlybusesaredispatchedalongaroute.Awell-designeddepartureintervalcanbalancethetradeoffbetweenthewaitingtimeofpassengersandtheoperationalcostofbusoperators. Theconventionalmethodforsettingthedepartureintervalistorelyontheexperienceoftransitplannersorthehistoricaldataofpassengerdemand.However,thismethodmaynotalwaysleadtooptimalresults,especiallywhenthetrafficconditionsorpassengerdemandchange.Toovercomethislimitation,manyoptimizationmodelsandalgorithmshavebeenproposedintheliterature.Forexample,Erdoganetal.(2018)proposedamathematicalprogrammingmodelforoptimizingthebusstoplocationsanddepartureintervals.Liuetal.(2017)developedabi-levelprogrammingmodeltojointlyoptimizethedepartureintervalandbusfrequency.However,mostofthesestudiesfocusedo