Ant Colony Optimization Algorithmto Solve Split Delivery Vehicle Routing

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1、*⫼㱕㕸ㅫ⊩∖㾷䳔∖ৃᢚߚ䔺䕚䏃ᕘ䯂乬椚槁㠾᧨➟┯䰞᧨䇧榖₫᧨⒧㪠⸘ϰ࣫໻ᄺᙃᄺ䰶⌕⿟ᎹϮ㓐ড়㞾ࡼ࣪ᬭ㚆䚼䞡⚍ᅲ偠ᅸˈ≜䰇ˈ110004E-mail:suilusi@163.comᨬ㽕:Ӵ㒳ⱘ䔺䕚䏃ᕘ䯂乬ᰃ㒘ড়Ӭ࣪ЁϔϾ݌ൟⱘNP䲒乬ˈ䛑؛䆒ᴵӊᅶ᠋䳔∖ϡৃᢚߚˈԚ೼ᅲ䰙ⱘ⠽⌕䖤԰Ёˈ᳝ᯊ䗮䖛䳔∖ⱘᢚߚৃҹ᳈དⱘ䰡Ԣ䖤䕧៤ᴀDŽᴀ᭛ᇱ䆩⫼㱕㕸ㅫ⊩ᴹ∖㾷䳔∖ৃᢚߚ䔺䕚䏃ᕘ䯂乬ˈ㒭ߎњ෎Ѣᭈ᭄㾘ߦⱘᦣ䗄ᮍ⊩˗䩜ᇍ῵ൟⱘ⡍⚍ˈᇍ㱕㕸ㅫ⊩䖯㸠њᬍ䖯ˈ䆒䅵њϔ⾡䩜ᇍ䳔∖ৃᢚߚ䔺䕚䏃ᕘ䯂乬ⱘᮄⱘ㱕㕸Ӭ࣪ㅫ⊩˄AntColonyOptimization-ACO˅DŽᑊᇍ䳔∖ৃᢚߚⱘ䔺䕚䏃ᕘ䯂乬˄SDVRP˅䯂乬

2、䖯㸠ӓⳳ䆩偠ˈᇚ݊㒧ᵰϢӴ㒳VRP԰↨䕗ˈᕫࠄњ⒵ᛣⱘ㒧ᵰDŽ݇䬂ᄫ:ৃᢚߚ䔺䕚䏃ᕘ䯂乬ˈ㱕㕸Ӭ࣪ㅫ⊩ˈ⠽⌕AntColonyOptimizationAlgorithmtoSolveSplitDeliveryVehicleRoutingProblemSUILu-si,TANGJia-fu,PANZhendongandLIUShu-anKeyLabofIntegratedAutomationofProcessIndustryofMOE,NortheasternUniversity,Shenyang,110004,ChinaE-mail:suilusi@163.comAbstract:Asacomb

3、inatorialoptimizationproblem,vehicleroutingproblem(VRP)isatypicalNP-hardproblem;anassumptionthatthedemandofcustomerscannotbesplitisgiventothetraditionalVRPformulation.However,thetransportationcostcanbereducedbymeansofsplittingthedemandofcustomersinpracticallogisticsoperation.Thispapersolvedthesplitd

4、eliveryvehicleroutingproblem(SDVRP)bymeansoftheantcolonyalgorithm.Theintegerprogrammingmodeloftheproblemisgiveninthispaper,andacorrespondingimprovedantcolonyoptimizationalgorithm(ACO)basedoncharacteristicoftheproblemisdesignedtosolvetheproblem.Somesimulationexperimentsonthisalgorithmandincomparisonw

5、iththetraditionalVRPareconducted,whichshowthattheproposedACOalgorithmiseffectiveandtheSDVRPcanreducemoretotalcoststhantraditionalVRP.KeyWords:thesplitdeliveryvehicleroutingproblem(SDVRP)antcolonyalgorithm(ACO)logistic⿟᳔ⷁǃ䌍⫼᳔ᇥǃᯊ䯈ሑ䞣ᇥǃՓ⫼䔺䕚ሑ䞣ᇥ1ˊᓩ㿔˄˄INTRODUCTION˅[2]ㄝ˅DŽ䔺䕚䇗ᑺᰃ⠽⌕ㅵ⧚Ё᳔䞡㽕ⱘ䚼ߚDŽ䱣ⴔ⼒Ⳃࠡ䔺䕚䏃ᕘ䯂乬ⱘⷨおЏ㽕ߚЎϸ

6、⾡˖䴲⒵Ӯⱘথሩҹঞ⍜䌍㗙ᇍ᳡ࡵ䋼䞣㽕∖ⱘϡᮁᦤ催ˈ䕑੠⒵䕑DŽ䖭ϸ⾡ᰃḍ᥂䳔∖䞣੠䔺䕚䕑䞡䞣ᴹߦ催ᬜⱘ䔺䕚䇗ᑺᇏᡒߎϔᴵ᳔Ӭⱘ䔺䕚㸠偊䏃㒓ˈߚⱘˈ㗠ϨⳂࠡ໻໮᭄Ҏⷨおⱘᰃ䴲⒵䕑ⱘᚙމDŽϡԚ᳝߽Ѣ䰡Ԣ⠽⌕Ё䋻⠽ᑧᄬⱘ䌍⫼ˈ㓽ⷁଚક䴲⒵䕑ⱘ䔺䕚䏃ᕘ䯂乬ⷨおⱘᰃ↣Ͼᅶ᠋⚍ⱘ䳔∖ϞᏖ਼ᳳˈ㗠Ϩ䗤⏤៤Ў⠽⌕៤䋹ⱘ݇䬂DŽⷨお䔺䞣ҙ⬅ϔ䕚䔺ᴹᅠ៤ˈгህᰃ䇈䳔∖ᰃϡৃᢚߚⱘDŽ䕚䏃ᕘ䯂乬ˈ䖯㸠䔺䕚䏃㒓Ӭ࣪ˈᦤ催⠽⌕ᬜ⥛ǃԚᰃ೼ᅲ䰙ᚙމЁˈᕔᕔӮߎ⦄䚼ߚӏࡵ៪㗙ܼ䚼䰡Ԣ⠽⌕៤ᴀ੠ᦤ催᳡ࡵ䋼䞣ᇍѢ䖯㒣⌢عᒋ〇ӏࡵⱘ䳔∖䞣䛑䕗໻ⱘᚙމˈℸᯊབᵰҡ✊㽕ϔ䕚ᅮⱘথሩ݋᳝䞡㽕ᛣНDŽ䔺ᴹᅠ៤ӏࡵⱘ䆱ᖙ✊ӮՓ䔺䕚ⱘぎ䕑⥛ᦤ催ˈ

7、ҢӴ㒳ⱘ䔺䕚䏃ᕘ䯂乬˄VehicleRoutingProblemˈ㗠䗴៤䔺䕚䌘⑤ⱘ⌾䌍DŽ಴ℸˈⷨお䳔∖ৃᢚߚⱘ[1]ㅔ⿄VRP˅᳔ᮽѢ1959ᑈ⬅Dantig੠Ramserᦤ䔺䕚䏃ᕘ䯂乬᳝ᕜདⱘ⦄ᅲᛣНˈ㗠Ϩ䍞ᴹ䍞໮ⱘߎˈᑊϔⳈᰃ㔥㒰᳔Ӭ࣪䯂乬Ё᳔෎ᴀⱘ䯂乬Пϔˈᄺ㗙ᓔྟⷨお䖭Ͼ䯂乬DŽ⬅Ѣ݊ᑨ⫼ⱘᑓ⊯ᗻ੠㒣⌢Ϟⱘ䞡໻Ӌؐˈ໮ᑈҹ2ˊSDVRP䯂乬ⱘᭈ᭄㾘ߦ῵ൟ˄INTEGERᴹྟ㒜ফࠄ೑ݙ໪ᄺ㗙ⱘ