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1、1、一维函数一维单峰函数一维多峰单全局最优解函数一维多峰多局部最优解函数2、二维函数2.1二维单峰函数2.2二维多峰单全局最优解函数2.2.1SHUBERTFUNCTION最新可编辑word文档Description:Dimensions:2TheShubertfunctionhasseverallocalminimaandmanyglobalminima.Thesecondplotshowsthethefunctiononasmallerinputdomain,toallowforeasierviewing.InputDomain:Thefunctionisus
2、uallyevaluatedonthesquarexi∈[-10,10],foralli=1,2,althoughthismayberestrictedtothesquarexi∈[-5.12,5.12],foralli=1,2.GlobalMinimum:最新可编辑word文档SchwefelFunction2.2.2EGGHOLDERFUNCTION最新可编辑word文档Description:Dimensions:2TheEggholderfunctionisadifficultfunctiontooptimize,becauseofthelargenumb
3、eroflocalminima.InputDomain:Thefunctionisusuallyevaluatedonthesquarexi∈[-512,512],foralli=1,2.GlobalMinimum:最新可编辑word文档2.2.3Levy5testobjectivefunction.ThisclassdefinestheLevy5globaloptimizationproblem.Thisisamultimodalminimizationproblemdefinedasfollows:Here,representsthenumberofdimen
4、sionsandfor.Two-dimensionalLevy5functionGlobaloptimum:for.2.2.4LANGERMANNFUNCTION最新可编辑word文档Description:Dimensions:dTheLangermannfunctionismultimodal,withmanyunevenlydistributedlocalminima.Therecommendedvaluesofm,candA,asgivenbyMolga&Smutnicki(2005)are(ford=2):m=5,c=(1,2,5,2,3)and:Inp
5、utDomain:Thefunctionisusuallyevaluatedonthehypercubexi∈[0,10],foralli=1,…,d.Globaloptimum:forclassgo_benchmark.XinSheYang01(dimensions=2)最新可编辑word文档2.2.5Xin-SheYang1testobjectivefunction.ThisclassdefinestheXin-SheYang1globaloptimizationproblem.Thisisamultimodalminimizationproblemdefin
6、edasfollows:Thevariableisarandomvariableuniformlydistributedin.Here,representsthenumberofdimensionsandfor.Two-dimensionalXin-SheYang1functionGlobaloptimum:forfor2.2.6XinSheYang02(dimensions=2)Xin-SheYang2testobjectivefunction.ThisclassdefinestheXin-SheYang2globaloptimizationproblem.Th
7、isisamultimodalminimizationproblemdefinedasfollows:Here,representsthenumberofdimensionsandfor.最新可编辑word文档Two-dimensionalXin-SheYang2functionGlobaloptimum:forfor2.2.7XinSheYang03(dimensions=2)Xin-SheYang3testobjectivefunction.ThisclassdefinestheXin-SheYang3globaloptimizationproblem.Thi
8、sisam
