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:2008-06-16:(60474029,60404007,60334030));(08JJ3126):(1968),,,,:(E-mail:doveyyw@126.com):1003-6199(2008)03-0007-05(,528000):,,,,Jbuilder9,,:;;;;(VRP):TP181:AANewAlgorithmforVehicleRoutingProblemswithCapacityLimitedBasedontheMinimumSpanningTreeYANGYue2wu(CollegeofElectromechanics&InformationEngineering,FoshanUniversity,Foshan528000,China)Abstract:Anoptimizedstrategyisproposedtoinvestigatedthevehicleroutingproblems.Webuildhereadescrtionoftheroutingnetwithminimumspanningtreesanddecisiontosearchthenearestapproach.Analgorithmisdevelopedtoobtainmin-spanningfromspanningtrees.Bydottingthemin-spanningtree,weobtaintheoptimizedroutesuchthatthecyclecapacitykeepminimum.ThecorrespondingalgorithmisrealizedwithJbuild9,whichshowsthatouralgorithmproposedhereisvalidandcon2cise,andsimplfiesthecomplexcityofpreviousresults.Keywords:distributiondelivers;theminimumspanningtree;distributionnode;distributionrouting;vehicleroutingproblem(VRP)1,[1],,,,,(LocationProblem)(VehicleRoutingProblemVRP)(InventoryControlProblem)(VRP),G.Dantzig[2]1959,,,,VRPNP,VRP[3,4][5,6],VPRVRP[7,8][9,10],27320089ComputingTechnologyandAutomationVol127,No13Sep.2008,,,,;,,[11,12]VRP,VRP,,,,,,2,,VRP,(SingleDepotVRP),SD2VRP,VRP,(ClosedVRP)CVRP,,OVRP(OpenVRP),CSDVRPG=(V,E)n+1,V,EV={v1,v1,,vn},v0,v1vnn,qi(1in),E={vi,vj(vi,vjV,ij}C,m,Li,Wi(i=1,2,,m),k(1km)Rk,Nk,RikRkivi(xi,yi),vi,vjdij=vij,()EuclideCSDVRP:minF=mk=1Nk-1i=1(drikri+1k+drNkk0+d0rik)(1)subjecttoni=1qiC(2)Nk-1i=1(drikrj+1k+drNk0k+d0rjk)Lk(3)Nki=1qiWk,(k=1,2,,m)(4)ni=1Nk=n(5)(Ri\v0)(Rj\v0)=(6),(5)(6)3311v0,vivj(ij)v0vivjdoidoj,vivjvij,,1(a)1(b)1(a)2voi+2voj;(b)voi+voj+vij;,(b)(a)voi+voj-vij0,n,,,,312v0,v1,v2,v3,v4,v5,v6,v7,v8,v9,2(a),()(),820089:231211(1)v0,TRN(TreeRootNode);(2),CN(CurrentNode),CN:aTRN;(3)CN(NeighborNodeNumberNNN),NNN0,(4);NNN=0(6);(4)CN(DistanceShortestNeighborNode,DSNN),(ShortestDistance,SD)CN,CN,DSNN,SD;,(5);,CN,DSNN,CN,DSNN,SD,(5);,CN,DSNN,SD,DSNN;DSNNCN,(3);(5),CN,(3);,(7);(6),CN,CN,,,(5);(7),CN,CN,,,,2(b)31212,:(1)2(b),,SubTreeNumber;(2)SubTreeNumber2,Sub2TreeNumber2,(9)(3)(3)For(I=1;I(SubTreeNumber-1);I++)(4)I;(5)For(Num=I+1;NumSubTreeNum2ber;Num++)(6)Num,I,(5),,IkNumm,I.node[k],Num.node[m],SD;(5);(7)Num,I,,(3);(8)I,,,,SubTreeNumber=Sub2TreeNumber-1,(2)(9),2(c)313,,,,2(c),V4v7,v4v7v0,v4(v7),v0,v7(v4),9273:v0,,2vo4+2vo7=23(1+2+2+5)+23(3+4+3)=40,,,v4v6,v4,v0,v6,v6v7,v0,2vo4+2vo7+6+3=(1+2+2+5)+6+3+(3+4+3)=29,:(1)2(c),,v0,;3(a),v1v5,v9v7,v4v6(2),v1,v5;vo1=3;vo5=6;vo1+vo5=9,v15=11;vo1+vo5,v1v5,,v1,v5;,v1,v5,3(b);(3)3(b)(v0),v0,3(c)3314(root)(vi),,,,A*(Floyd)(Dijkstra)OSDVRP,,,OSDVR::(1)(root),;(2),,InitSet;(3)InitSet,Name,InitSet;(4)Name,,;(5)Set,(3),;:,,(3(c)v2,v8,v3),,:(root),,;:(1),n,n1,(4),n=1,(2),n=0,(6);(2),,,,;(3),,(2);(4),;0120089(5),2(a),3.13.23.3,1(b);(6),,,4,,,,,Jbuilder9,,,,[1]ArchW.S.SomeproblemsinMarketDisdtibution:IllustratingtheApplicationofaBasicPhilosphyofBusiness[J].HarvardU2niversityPressJan.,1915.[2]DantzigG.,RamserJ.Thetruckdispatchingproblem[J].ManagementScience,1959(6):80-91.[3]TorthP.,VigoD.Models,relaxationsandexactapproachesforthecapacitatedvehicleroutingproblem[J].DiscreteAppliedMathematics,2002(123):487-512.[4]LeeC.G.,MarinaA.CheslseaC.etal.Ashortestpathap2proachtothemultiple-vehecleroutingproblemwithsplitpick-ups[J].TransportationResearch,2006PartB(40):265-284.[5]FisherM.L.,JaikumarR.A.GernerlizedAssigmentHeuris2ticforVehicleRouting[J].Networks,1981(11):109-124.[6]TalliardE.D.ParallelIterativeSearchMethodsforVehicleRoutingProblems[J].Networks,1993(23):661-673.[7],.3-optvrp[J].:,vol.20,1992(3):254-256.[8],..[J].,2003,18(4):418-422.[9]Tavakkoli-MoghaddamR.,SafaeiN,GholipourY.Ahybridsimulatedannealingforcapacitatedvehicleroutingproblemswiththeindependentroutelength[J].AppliedMathematicsandComputation,2006(176):445-454.[10],.VRP[J].,vol.25,2003(1):39-44.[11]BentR.,HentenryckP.V.Atwo-stagehybridalgorithmforpickupanddeliveryvehicleroutingproblemswithtimewindows[J].Computers&OperationResearch,vol.33,2006:875-893.[12]BrandaoJ.Anewtabusearchalgorithmforvehicleroutingproblemwithbackhauls[J].EuropeanJournalofOperationalResearch,vol.173,2006:540-555.[13],.JBuilder[M].:,2004-01-01.11273: