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1、PublicTransp(2009)1:253273DOI10.1007/s12469-010-0016-7ORIGINALPAPERAmulti-objectivemetaheuristicapproachfortheTransitNetworkDesignProblemAntonioMauttone·MaríaE.UrquhartPublishedonline:11February2010©Springer-Verlag2010AbstractWestudytheproblemoftheoptimaldes
2、ignofroutesandfrequenciesinurbanpublictransitsystems,theTransitNetworkDesignProblem(TNDP),whichismodeledasamulti-objectivecombinatorialoptimizationproblem.Anewheuris-ticbasedontheGRASPmetaheuristicisproposedtosolvetheTNDP.Asamulti-objectivemetaheuristic,itpr
3、oducesinasinglerunasetofnon-dominatedsolutionsrepresentingdifferenttrade-offlevelsbetweentheconflictingobjectivesofusersandoperators.Previousapproacheshavedealtwiththemulti-objectivenatureoftheprob-lembyweightingthedifferentobjectivesintoasingleobjectivefunct
4、ion.ThecaseproposedbyMandlisusedtoshowthatthemulti-objectivemetaheuristiciscapableofproducingadiversesetofsolutions,whicharecomparedwithsolutionsobtainedbyotherauthors.Weshowthattheproposedalgorithmproducesmorenon-dominatedsolutionsthantheWeightedSumMethodwi
5、ththesamecomputationaleffort,usingthecaseofMandlandanotherrealtestcase.KeywordsTransitNetworkDesignProblem·Multi-objectivecombinatorialoptimization·GRASP1IntroductionTheplanningofurbanpublictransitsystemsmaybedecomposedinasequenceofactivities,namely,networkd
6、esign,frequencysetting,timetabledevelopment,busanddriverscheduling(CederandWilson1986).AtthenetworkdesignlevelasetofroutesA.Mauttone()·M.E.UrquhartOperationsResearchDepartment,UniversidaddelaRepública,J.HerrerayReissig565Piso5,Montevideo,Uruguaye-mail:mautt
7、one@fing.edu.uyM.E.Urquharte-mail:urquhart@fing.edu.uy254A.Mauttone,M.E.Urquhartisdefined,whereeachrouteisasequenceoflinksoftheroadnetwork.Thisactiv-ityisperformedinthecontextofstrategicplanning,takingdecisionsinalongtermhorizon(DesaulniersandHickman2007),usual
8、lyregulatedbytheauthorities.Inthemostgeneralcase,routeandfrequencydefinitionhastotakeintoaccounttheinter-estsofusers(peoplewhoemployorneedtoemploypublictransport)andoperators(companieswhoownthere