多目标线性规划的若干解法及Lingo实现

[1]。。。,。。lingo。。、。maxz1=a11x1+a12x2+…+a1nxnz2=a21x1+a22x2+…+a2nxn………zr=ar1x1+ar2x2+…+arnxn1c11x1+c12x2+…+c1nxn≤b1c21x1+c22x2+…+c2nxn≤b2………cm1x1+cm2x2+…+cmnxn≤bmx1x2…xn≥02A=aijk×nB=b1b2…bmTX=x1x2…xnTZ=z1z2…zkTC=cijm×nmaxZ=AXCX≤BX≥≥03、LingoLingoLINDOLindo。[2]Lingo。LINGO9.0LINGOMAINMODEL。LINGO10.0LINGOLingo350007。、、Lingo。。LingoLingo：O221：A：1671-914X（2011）06－0020-03：2011-10-10：（1979-），，。，：。doi:10.3969/j.issn.1671-914X.2011.06.0201062011112020SUBMODEL。LINGO。“MOD－EL:”、“END”。[2]@SUBMODELmymodel+ENDSUBMODELmymodel“@SOLVEsubmodel”。、Lingo[3]3Xrzizizi*。x0∈Xzi*=zix0xrzixzi*。minx∈DfZx=ri=1ΣZix-Zi*2姨x*3。1maxf1x=-3x1+2x2maxf2x=4x1+3x2s.t2x1+3x2≤182x1+x2≤10x1x2≥0LingoMODELSUBMODELOBJ1MAX=z1z1=2*x2-3*x1@freez1ENDSUBMODELSUBMODELOBJ2:max=z2z2=4*x1+3*x2@freez2ENDSUBMODELSUBMODELCON1:2*x1+3*x2=182*x1+x2=10x1=0x2=0ENDSUBMODELCALC@write‘z1’@newline1;@solveOBJ1CON1@write‘z2’@newline1@solveOBJ2CON1ENDCALCEndz1=12z2=241224.submodelcon2:min=@sqr2*x2-3*x1-12+@sqr4*x1+3*x2-24f1=2*x2-3*x1f2=4*x1+3*x2endsubmodelCALC@write‘’@newline1@solvecon2CON1x1=0.5268x2=5.6488f1x=9.7172f2x=19.0536。minx∈DfZx=ri=1ΣωiZixωi。21。ω1=0.5ω2=0.5min{0.5×3x1-2x2+0.5×-4x1-3x2}。submodelcon3:min=0.5*3*x1-2*x2+0.5*-4*x1-3*x2f1=2*x2-3*x1f2=4*x1+3*x2endsubmodelCALC@write‘’@newline1@solvecon3CON1f1x=12f2x=18。。。[4]Lingo21211Zii=12…rZi*Zi-。2Zi*Zi-≤Zi≤Zi*。Δi=Zi*-Zi-i=12…rdi=ΔiΔ1d1Δ1≠0i≥23min{d1}zi+di=zi*nj=1Σckj≤bkk=12…mdi≥0xi≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥≥044。4x1*…xn*T.LingoSUBMODELobj3:max=4*x1+3*x2ENDSUBMODELSUBMODELobj4:min=4*x1+3*x2ENDSUBMODEL1Z*=1224Z-=-150.Δi=2724d2=2427d1。min{d1}s.t-3x1+2x2+d1=244x1+3x2+2427d1=272x1+3x2≤182x1+x2≤10x1x2d1≥0SUBMODELCON4:min=d12*x2-3*x1+d1=124*x1+3*x2+24/27*d1=24d1=0f1=2*x2-3*x1f2=4*x1+3*x2ENDSUBMODEL@solvecon4CON1f1=7.5570f2=20.0506x1=1.0253x2=5.3165。、。Lingo。、、。［1］.[M].：，2005.［2］，.LINDO/LINGO[M].：，2005.［3］.[J]．，2008，23（3）：14-16．［4］，.[J].（），2007，25（5）：67-69.SomeSolutionsofMulti-objectiveLinearProgrammingandrealizedbyLINGOLIULinFujianChuanzhenCommunicationVocationalCollege,FujianFuzhou350007,ChinaAbstractMulti-objectivelinearprogrammingisoneoftheoptimalproblems.ThebasicideastosolveMulti-objectivelinearprogrammingaretransformingthemulti-objectiveproblemintosingle-objectiveplanning.Thispaperintroducestheidealpointmethod,linearweightedandtheamountofdeviationFuzzymathematicsmethod,finallygiveexamplesofeachmethodandusedtheSubmodelinLingosoftwaretoachieve.ItiseasytowritethisLingoprogram,andsuitableforusinginmodelingcontest．KeywordsMulti-objectiveLinearProgramming;Lingo;single-objective（：：）2222