a branch-and-cut algorithm for the undirected selective traveling salesman problem

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1、ABran h-and-CutAlgorithmfortheUndire tedTravelingur haserroblemyyGilbertaporteorgeRiera-edesmauan-oseSalazar-Gonzalezontreal,September2000Abstra tThepurposeofthisarti leistopresentabran h-and- utalgorithmfortheundire tedTravelingur haserroblemwhi h onsistsofdetermini

2、ngaminimum- ostroutethroughasubsetofmarkets,wherethe ostisthesumoftravelandpur hase osts.Theproblemisformulatedasanintegerlinearprogramandseveralfamiliesofvalidinequalitiesarederivedtostrengthenthelinearrelaxation.Thepolyhedralstru tureoftheformulationisanalyzedandseveral lasseso

3、fvalidinequalitiesareprovedtobefa et-dening.Abran h-and- utpro edureisdevelopedandtestedoverseveral lassesofrandomlygeneratedinstan es.Resultsshowthattheproposedalgorithmoutperformallpreviousapproa hesand ansolveoptimallyinstan es ontainingupto200markets.eywords:Travelingur ha

4、serroblem,TravelingSalesmanroblem,Bran h-and- ut,Heuristi .1
ntrodu tionThepurposeofthisarti leistopresentabran h-and- utalgorithmfortheundire tedTravel-ingur haserroblem(T)denedasfollows.Consideradepotv,asetofmarkets:=0E oledesHautesEtudesCommer ialesandCentreforResea

5、r honTransportation,3000hemindelaC^ote-Sainte-Catherine,ontreal,CanadaH3T2A7.yDE
C,Fa ultaddeatemati as,Universidaddeaaguna,38271aaguna,Tenerife,Spain.1fv;:::;vg,andasetofprodu ts:=fp;:::;pg.etG=(V;E)beanundire tedgraph1n1mwhereV:=fvg[isthevertexsetandE:=f[v;v℄:v;v2V;i

6、

7、vel ostbetweenvandvisequaltothe ostoftheedgeiijkkie=[v;v℄denotedby.TheT onsistsofdeterminingasimple y leinGpassingthroughijethedepotandasubsetofmarketssothatallprodu tsarepur hasedatatotalminimum ostobtainedbyaddingtherouting ostandthepur hasepri e.ThisdenitionoftheTgenerali

8、zesthe lassi al asewithunlimitedsupplies