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1、MathematicalModelandGeneticOptimizationforHybridFlowShopSchedulingProblemBasedonEnergyConsumptionXiangLiu1,FengxingZou1,XiangpingZhang11.DepartmentofAutomaticControl,CollegeofMechatronicsEngineeringandAutomationNationalUniversityofDefenseTechnology,Hunan,Changsha410073,ChinaE-mai
2、l:liuxiangfang@tom.comAbstract:Hybridflowshopschedulingproblem(HFSP)ischaracterizedastheschedulingofjobsinaflowshopenvironmentwhere,atanystage,theremayexistmultiplemachines.Besidesthefinishingtimeofthelastjob,energyconsumptionisanotherimportantfactoraffectingeconomybenefitofhybridflow
3、shop.Amixed-integernonlinearprogrammingmodelisestablishedfortheHFSPwithminimizingtheenergyconsumption,accordingtothecharacteristicofHFSPinpractice.ItisatypicalNP-hardcombinatorialoptimizationproblem.Forsolvingitefficiently,animprovedgeneticalgorithmispresented.Thefitnessbasedonther
4、ankingoftheenergyconsumptionofeveryindividualandtheself-adaptivemutationoperationbasedonthefitnessareadopted.Thenumericalexperimentiscarriedoutonthethree-two-threeHFSP,andtheresultindicatesthatthemodelisrightandtheimprovedalgorithmisefficient.KeyWords:HybridFlowShopScheduling,Energ
5、yConsumption,Mixed-integerNonlinearProgrammingModel,Im-provedGeneticAlgorithm1INTRODUCTIONHybridflowshopschedulingproblem(HFSP)isoneofthemostwell-knownproductionschedulingproblemsandatypicalNP-hardcombinatorialoptimizationproblemwithstrongengineeringbackgrounds.Itgenerallyexitsinm
6、anyindustrialdomains,suchasindustryofmetallurgy,pack-inghouse,chemicalindustry,pharmacyandsoon.Soithasreceivedmuchinterestsandmanyfruitsareobtained[1],[2],[3].HybridflowshopschedulingproblemcanbepresentedasFig.1[4].TherearenjobswhichwillFigure1:TheSchematicDiagramofHybridFlowShopb
7、eprocessed.Eachjobmustexperiencesstageswiththesamedirection.ThereareMjmachinesandeachjobcanbeassignedtoanyoneoftheMjmachinesatstagej,(j=1,2,···,s).Itispresumedthatalltheparametersing,themakespanisanimportantconstraint.Accordingtoareknown.Onthiscondition,jobswillbeassignedtotheset
8、heconstraintsinthehybridflowshopandtheobj
