时间窗约束下的车辆路径问题遗传算法外文翻译可编辑.docx

时间窗约束下的车辆路径问题遗传算法外文翻译可编辑.docx

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时间窗约束下的车辆路径问题遗传算法外文翻译可编辑

时间窗约束下的车辆路径问题遗传算法外文翻译

外文翻译

原文

GeneticAlgorithmsfortheVehicleRoutingProblemwithTimeWindows

MaterialSource:

SpecialissueonBioinformaticsandGeneticAlgorithmsAuthor:

OlliBr?

ysy

1Introduction

VehicleRoutingProblemsVRPareallaroundusinthesensethatmanyconsumerproductssuchassoftdrinks,beer,bread,snackfoods,gasolineandpharmaceuticalsaredeliveredtoretailoutletsbyafleetoftruckswhoseoperationfitsthevehicleroutingmodel.Inpractice,theVRPhasbeenrecognizedasoneofthegreatsuccessstoriesofoperationsresearchandithasbeenstudiedwidelysincethelatefifties.Publicservicescanalsotakeadvantageofthesesystemsinordertoimprovetheirlogisticschain.Garbagecollection,ortowncleaning,takesaneverincreasingpartofthebudgetoflocalauthoritiesAtypicalvehicleroutingproblemcanbedescribedastheproblemofdesigningleastcostroutesfromonedepottoasetofgeographicallyscatteredpointscities,stores,warehouses,schools,customersetc.Theroutesmustbedesignedinsuchawaythateachpointisvisitedonlyoncebyexactlyonevehicle,allroutesstartandendatthedepot,andthetotaldemandsofallpointsononeroutemustnotexceedthecapacityofthevehicleTheVehicleRoutingProblemwithTimeWindowsVRPTWisageneralizationoftheVRPinvolvingtheaddedcomplexitythateverycustomershouldbeservedwithinagiventimewindow.AdditionalcomplexitiesencounteredintheVRPTWarelengthofrouteconstraintarisingfromdepottimewindowsandcostofwaitingtime,whichisincurredwhenavehiclearrivestooearlyatacustomerlocation.Specificexamplesofproblemswithtimewindowsincludebankdeliveries,postaldeliveries,industrialrefusecollection,school-busroutingandsituationswherethecustomermustprovideaccess,verification,orpaymentupondeliveryoftheproductorservice[SolomonandDesrosiers,1988].

Besidesbeingoneofthemostimportantproblemsofoperationsresearchinpracticalterms,thevehicleroutingproblemisalsooneofthemostdifficultproblemstosolve.Itisquiteclosetooneofthemostfamouscombinatorialoptimizationproblems,theTravelingSalespersonProblemTSP,whereonlyonepersonhastovisitallthecustomers.TheTSPisanNP-hardproblem.Itisbelievedthatonemayneverfindacomputationaltechniquethatwillguaranteeoptimalsolutionstolargerinstancesforsuchproblems.Thevehicleroutingproblemisevenmorecomplicated.Evenforsmallfleetsizesandamoderatenumberoftransportationrequests,theplanningtaskishighlycomplex.Hence,itisnotsurprisingthathumanplannerssoongetoverwhelmed,andmustturntosimple,localrulesforvehiclerouting.Nextwewilldescribebasicprinciplesofgeneticalgorithmsandsomeapplicationsforvehicleroutingproblemwithtimewindows.

2Generalprinciplesofgeneticalgorithms

TheGeneticAlgorithmGAisanadaptiveheuristicsearchmethodbasedonpopulationgenetics.Thebasicconceptsaredevelopedby[Holland,1975],whilethepracticalityofusingtheGAtosolvecomplexproblemsisdemonstratedin[DeJong,1975]and[Goldberg,1989].Referencesanddetailsaboutgeneticalgorithmscanalsobefoundforexamplein[Alander,2000]and[Mühlenbein,1997]respectively.Thecreationofanewgenerationofindividualsinvolvesprimarilyfourmajorstepsorphases:

representation,selection,recombinationandmutation.Therepresentationofthesolutionspaceconsistsofencodingsignificantfeaturesofasolutionasachromosome,defininganindividualmemberofapopulation.Typicallypicturedbyabitstring,achromosomeismadeupofasequenceofgenes,whichcapturethebasiccharacteristicsofasolution.

Therecombinationorreproductionprocessmakesuseofgenesofselectedparentstoproduceoffspringthatwillformthenextgeneration.Itcombinescharacteristicsofchromosomestopotentiallycreateoffspringwithbetterfitness.Asformutation,itconsistsofrandomlymodifyinggenesofasingleindividualatatimetofurtherexplorethesolutionspaceandensure,orpreserve,geneticdiversity.Theoccurrenceofmutationisgenerallyassociatedwithlowprobability.Anewgenerationiscreatedbyrepeatingtheselection,reproductionandmutationprocessesuntilallchromosomesinthenewpopulationreplacethosefromtheoldone.Aproperbalancebetweengeneticqualityanddiversityisthereforerequiredwithinthepopulationinordertosupportefficientsearch.

AlthoughtheoreticalresultsthatcharacterizethebehavioroftheGAhavebeenobtainedforbit-stringchromosomes,notallproblemslendthemselveseasilytothisrepresentation.Thisisthecase,inparticular,forsequencingproblems,likevehicleroutingproblem,whereanintegerrepresentationismoreoftenappropriate.Weareawareofonlyoneapproachby[Thangiah,