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1、MathematicalModelandGeneticOptimizationforHybridFlowShopSchedulingProblemBasedonEnergyConsumptionXiangLiu1,FengxingZou1,XiangpingZhang11.DepartmentofAutomaticControl,CollegeofMechatronicsEngineeringandAutomationNationalUniversityofDefenseTechnology,Hunan,Changsha410073,ChinaE-mai

2、l:liuxiangfang@tom.comAbstract:Hybrid?owshopschedulingproblem(HFSP)ischaracterizedastheschedulingofjobsina?owshopenvironmentwhere,atanystage,theremayexistmultiplemachines.Besidesthe?nishingtimeofthelastjob,energyconsumptionisanotherimportantfactoraffectingeconomybene?tofhybrid?ow

3、shop.Amixed-integernonlinearprogrammingmodelisestablishedfortheHFSPwithminimizingtheenergyconsumption,accordingtothecharacteristicofHFSPinpractice.ItisatypicalNP-hardcombinatorialoptimizationproblem.Forsolvingitef?ciently,animprovedgeneticalgorithmispresented.The?tnessbasedonther

4、ankingoftheenergyconsumptionofeveryindividualandtheself-adaptivemutationoperationbasedonthe?tnessareadopted.Thenumericalexperimentiscarriedoutonthethree-two-threeHFSP,andtheresultindicatesthatthemodelisrightandtheimprovedalgorithmisef?cient.KeyWords:HybridFlowShopScheduling,Energ

5、yConsumption,Mixed-integerNonlinearProgrammingModel,Im-provedGeneticAlgorithm1INTRODUCTIONHybrid?owshopschedulingproblem(HFSP)isoneofthemostwell-knownproductionschedulingproblemsandatypicalNP-hardcombinatorialoptimizationproblemwithstrongengineeringbackgrounds.Itgenerallyexitsinm

6、anyindustrialdomains,suchasindustryofmetallurgy,pack-inghouse,chemicalindustry,pharmacyandsoon.Soithasreceivedmuchinterestsandmanyfruitsareobtained[1],[2],[3].Hybrid?owshopschedulingproblemcanbepresentedasFig.1[4].TherearenjobswhichwillFigure1:TheSchematicDiagramofHybridFlowShopb

7、eprocessed.Eachjobmustexperiencesstageswiththesamedirection.ThereareMjmachinesandeachjobcanbeassignedtoanyoneoftheMjmachinesatstagej,(j=1,2,···,s).Itispresumedthatalltheparametersing,themakespanisanimportantconstraint.Accordingtoareknown.Onthiscondition,jobswillbeassignedtotheset

8、heconstraintsinthehybrid?owshopandtheobj