基于遗传算法的多目标问题求解方法

20037SHUILIXUEBAO7:2002206226:(50099624);(2001ABB042);(50209011):(1977-),,,,:055929350(2003)07200642061,2,2(11,100044;21,430072):,,,,,:;;;:TV697:A,,(GeneticAlgorithm,GA),,,[1-3][4-6][7],,,,,(Multi2ObjectiveGeneticAlgorithm,MOGA),1111,,,n,,:fi(x3)fi(xt)i=1,2,,n(1)(1)ix3[8]46,,,,,,,,:(1),,()(2),,,,,112NObj(1)X11X12X1NX1Obj(2)X21X22X2NX2Obj(n)Xn1Xn2XnNXn11211211,,(,)1:,Obj(i)(i=1,,n),n;N,i,Xi,,:Ei(Xj)=(N-Ri(Xj))2Ri(Xj)1;kN2Ri(Xj)=1;i=1,2,,n(2)E(Xj)=ni=1Ei(Xj)j=1,2,,N;:n;N;Xjj;Rii;Ei(Xj)Xji,E(Xj)Xj;k(1,2),,,,11212PcPm,[9]:Pc=k1(fmax-f)(fmax-favg)ffavgk2ffavg(3)Pm=k3(fmax-f)(fmax-favg)ffavgk4ffavg(4):fmax;favg;f2;f;k1,k2,k3,k4[0,1]PcPm,PcPmk1,k3,k1=k2,k3=k456Pc,Pm,,1,,,;,,k1,k3,PcPm1k1k301,k1(015018),k3(0105012),k,,,PcPm,k11213n(n),,5%15%(1),,2,,n,B,n,66PPB,22[10]:maxZ1(x)=15x1+15x2+10x3maxZ2(x)=16x1+1715x2+20x3(5)stg1(x)=x1+x2+x330g2(x)=x1+2x2+x340g3(x)=x2+4x360,13,200,Pc=016,Pm=011,200(2),2X1X2X3Z1Z2X1X2X3Z1Z22010045049513107415523191014454991210841052718102440503129940552915171034355071010104005351794430509159101139553917854255129912390541151596420517153F,170m(313m3),205m(1319m3),19815m(11113m3),410kW,918kW,715106m3P,6107m3P:max{E(ƒq,Q),F(ƒq,Qg)}(6):E(ƒq,Q)=Nn=1En(qn,Qn);F(ƒq,Qg)=Nn=1Fn(qn,Qgn);qnQnQgnn();WnFnn:(1):Zmin(n)ZnZmax(n)Zmin(n)Zmax(n)()(,);(2):qout(n)qminqmin(3):Wgmin(n)Wg(n)Wgmax(n)76Wgmin(n)Wgmax(n)()(4):NminNNmaxNminNmax(3)1,190m3(:m3Ps)4566677788491575884951128915081266908679712899910111212369254243338031630524721734836634P108m3P108kWhP104kWh1310222131121124175221291214351922119211144617121163101857149211251111681372017610147817120123101389147191591014910111191191013101018018157918,(),,,,(),():V(t+1)-V(t)Win(t)-(Wgmin(t)+Wxmin(t))(7)(7),Wgmin(t)Wxmin(t)t,(),,500,017,011,10,5004,324,,,,424,:(1),(2),,(3)86,,,,,,,,,:[1],.[J].,1996,2:22-25.[2],,.[J].,1998,10:20-22.[3],,.[J].,1999,12:31-37.[4],,.FP[J].,1996,1:1-4.[5],.[J].,1997,3:275-280.[6],.[J].,1999,3:31-34.[7]RobinWardlaw,MohdSharif.EvaluationofGeneticAlgorithmsforOptimalReservoirResources[J].JournalofWaterResourcePlanningandManagement,1999,125(1):25-33.[8].[M].:,1990.[9],.[J].,1997,(1):40-47.[10][],.[M].:,2000.Newmethodforsolvingmulti2objectiveproblembasedongeneticalgorithmYOUJin2jun1,JIChang2ming2,FUXiang2(11ChinaInstituteofWaterResourcesandHydropowerresearch,Beijing100044,China;21WuhanUniversity,Wuhan430072,China)Abstract:Anewmulti2objectivegeneticalgorithmbasedonthevarietyofplentifulsolutionineverygen2erationoftheevolutionisproposed,bywhichtheParetosetcanbesearchedbycalculationofonlyonetimeinterchange.Theappraisingfunctioninthismethodranksthegenebycomparingtheirperformanceineachobjectivefunctionthroughthesortingmatrixcreatedbytheobjectivefunction.Inordertoelevatetheefficiencyofthismethod,theparameterscalibrationisimprovedandtheParetosolutionsselectioniscontrolledeffectively.Theapplicationinamulti2objectivereservoirslong2termoptimaloperationforpowergenerationandwatersupplyisgivenasanexampletodemonstratethefeasibilityofthismethod.Keywords:multi2objectiveprogramming;geneticalgorithm;optimization;reservoiroperation96