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求解VRPSTW问题的参数优化蚁群算法.docx

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求解VRPSTW问题的参数优化蚁群算法 Introduction VehicleRoutingProblemwithTimeWindows(VRPSTW)isawell-knowncombinatorialoptimizationproblemthathasbeenwidelystudied.Theproblemistodeterminethebestpossibleroutingplanforafleetofvehiclestoserveasetofcustomerswithtimewindowsandcapacityconstraints.Theobjectiveistominimizethetotaldistancetraveledbyallthevehicleswhilerespectingtheseconstraints.TheVRPSTWproblemisanNP-hardproblem,andexactalgorithmsforsolvinglarge-scaleinstancesarecomputationallyintractable.Therefore,heuristicalgorithmssuchasAntColonyOptimization(ACO)havebeenproposedforsolvingthisproblem. AntColonyOptimization(ACO)isametaheuristicalgorithminspiredbytheforagingbehaviorofants.ACOhasbeensuccessfullyappliedtovariouscombinatorialoptimizationproblems,includingtheVRPSTWproblem.ACOisapopulation-basedalgorithmthatusesacolonyofartificialantstosearchfortheoptimalsolution.Thealgorithmischaracterizedbytwomajorcomponents:thepheromonetrailsandtheantbehavior. Inthispaper,weproposeaparameteroptimizationmethodfortheACOalgorithmtosolvetheVRPSTWproblem.ThemethodaimstofindtheoptimalvaluesoftheACOparametersthatcanimprovetheperformanceofthealgorithm.Therestofthepaperisorganizedasfollows:Section2providesabriefreviewoftheVRPSTWproblemandtheACOalgorithm.Section3describestheproposedparameteroptimizationmethod.Section4presentstheexperimentalresults,andSection5concludesthepaper. VRPSTWProblem TheVRPSTWproblemisavariantoftheclassicalVehicleRoutingProblem(VRP)thatimposesadditionalconstraintsontheproblem.IntheVRPSTW,thecustomershavespecifictimewindowsinwhichtheycanbeservedandcapacityconstraints.Theobjectiveistominimizethetotaldistancetraveledbyallthevehicleswhilesatisfyingtheseconstraints. Theproblemcanbedefinedasfollows:Givenasetofcustomerswithdemands,timewindows,andlocations,afleetofvehicleswithlimitedcapacity,adepot,andadistancematrix,theproblemistofindtheoptimalsetofvehicleroutesthatserveallthecustomerswithintheirrespectivetimewindowsandminimizethetotaldistancetraveledbyallthevehicles. ACOAlgorithm ACOisa