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ID:40137861
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页数:43页
时间:2019-07-23
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1、Chapter6DynamicProgramming(2007)Dynamicprogrammingisausefulmathematicaltechniqueformakingasequenceofinterrelateddecisions.Itprovidesasystematicprocedurefordeterminingtheoptimalcombinationofdecisions.Incontrasttolinearprogramming,theredoesnotexistastandardmathematicalformula
2、tionof"the"dynamicprogrammingproblem.Rather,dynamicprogrammingisageneraltypeofapproachtoproblemsolving,andtheparticularequationsusedmustbedevelopedtofiteachsituation.Therefore,acertaindegreeofingenuityandinsightintothegeneralstructureofdynamicprogrammingproblemsisrequiredto
3、recognizewhenandhowaproblemcanbesolvedbydynamicprogrammingprocedures.Theseabilitiescanbestbedevelopedbyanexposuretoawidevarietyofdynamicprogrammingapplicationsandastudyofthecharacteristicsthatarecommontoallthesesituations.Alargenumberofillustrativeexamplesarepresentedforthi
4、spurpose.6.1APROTOTYPEEXAMPLEFORDYNAMICPROGRAMMINGEXAMPLE1:TheStagecoachProblemTheSTAGECOACHPROBLEMisaproblemspeciallyconstructedtoillustratethefeaturesandtointroducetheterminologyofdynamicprogramming.ItconcernsamythicalfortuneseekerinMissouriwhodecidedtogowesttojointhegold
5、rushinCaliforniaduringthemid-19thcentury.Thejourneywouldrequiretravelingbystagecoachthroughunsettledcountrywheretherewasseriousdangerofattackbymarauders(掠夺者).Althoughhisstartingpointanddestinationwerefixed,hehadconsiderablechoiceastowhichstates(orterritoriesthatsubsequently
6、becamestates)totravelthroughenroute.ThepossibleroutesareshowninFig.6.l,whereeachstateisrepresentedbyacircledletterandthedirectionoftravelisalwaysfromlefttorightinthediagram.Thus,fourstages(stagecoachruns)wererequiredtotravelfromhispointofembarkationinstateA(Missouri)tohisde
7、stinationinstateJ(California).Thisfortuneseekerwasaprudent(谨慎的)manwhowasquiteconcernedabouthissafety.Aftersomethought,hecameupwitharathercleverwayofdeterminingthesafestroute.Lifeinsurancepolicieswereofferedtostagecoachpassengers.Becausethecostofthepolicyfortakinganygivensta
8、gecoachrunwasbasedonacarefulevaluationofthesafetyofthatrun,thesafestrouteshouldbet
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