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1、MathematicsLaboratory最優(yōu)化理論與方法阮小娥博士阮小娥教授Spring2011考核方式：考勤：10%作業(yè)：10%+10%綜合報(bào)告：20%閉卷筆試：50%閉卷筆試時(shí)間：地點(diǎn)：2011年春研究生報(bào)告分組編號(hào)組長(zhǎng)組員組員1徐金虎侯江勇梅滋亞2郭仁飛劉維宇趙自新3谷飛飛鐘麗紅孫闖4許金泉王楠李宗欣5許莉莉蔡燕瞿金秀7陳娜王閃閃趙婷婷8蘇曉蕾羅濤洪濤9董襄陽(yáng)杜朝暉呂杭原10張娟娟毛利歡荊菲菲編號(hào)組長(zhǎng)組員組員11崔恒斌劉玉英劉蓓12時(shí)光王超發(fā)郭曉燕13黃杰杰陳成14祁振中孫向志周清保15張輝唐光海陳佳16馮濤刁廣州17王冠榮元華高勇18饒過(guò)彭毅陽(yáng)建19呂海星衛(wèi)瑩20左立
2、云張婷第七章非線性約束最優(yōu)化方法方法特征和評(píng)價(jià)罰函數(shù)方法乘子法可行點(diǎn)法與廣義簡(jiǎn)約梯度法*SQP方法*1非線性約束優(yōu)化模型：NonlinearProgramming（NP）?minfx,??s.t.??cxie???0,i?E??12,,,m?,??cxie???01,i??I?m?,,m.?其中，cx????R,i1,,m,i中至少有一個(gè)為非線性函數(shù)。D??xcxii???00,i?E,cx???,i?I?-約束集、約束域或可行域?k?1??k??k?優(yōu)化策略：構(gòu)造迭代序列x??x?d.k?k??k??k??kk???滿足（1）fx????kd?fx??.（2）x???kdD.
3、21、方法特征與評(píng)價(jià)（1）消去法若cxi???0yii?lncx??無(wú)約束??x1??cx11?mn?,,x???cx,in?1,x??0,????????????i?12,,,m.??x??c?x,,x???m??mm?1n則minfx??minFx???無(wú)約束優(yōu)化問(wèn)題xD??xR?nm?評(píng)價(jià)：期望指數(shù)：可行性：3（2）網(wǎng)格法、隨機(jī)實(shí)驗(yàn)法和復(fù)形法按照某種方式產(chǎn)生測(cè)試點(diǎn)，然后比較目標(biāo)函數(shù)值，驗(yàn)證約束條件。z評(píng)價(jià)：可行性：z?fx,y??精確性：0y算法收斂性：x4MotivationalProblem:“Maximizethefollowing“peaks”function”z
4、?fx,y??2?22???11?22??x35??221?????xyxyxy?31??xe??10???x?ye?e??535Derivativesofthe“peaks”function?dz/dx=-6*(1-x)*exp(-x^2-(y+1)^2)-6*(1-x)^2*x*exp(-x^2-(y+1)^2)-10*(1/5-3*x^2)*exp(-x^2-y^2)+20*(1/5*x-x^3-y^5)*x*exp(-x^2-y^2)-1/3*(-2*x-2)*exp(-(x+1)^2-y^2)?dz/dy=3*(1-x)^2*(-2*y-2)*exp(-x^2-(y+
5、1)^2)+50*y^4*exp(-x^2-y^2)+20*(1/5*x-x^3-y^5)*y*exp(-x^2-y^2)+2/3*y*exp(-(x+1)^2-y^2)?d(dz/dx)/dx=36*x*exp(-x^2-(y+1)^2)-18*x^2*exp(-x^2-(y+1)^2)-24*x^3*exp(-x^2-(y+1)^2)+12*x^4*exp(-x^2-(y+1)^2)+72*x*exp(-x^2-y^2)-148*x^3*exp(-x^2-y^2)-20*y^5*exp(-x^2-y^2)+40*x^5*exp(-x^2-y^2)+40*x^2*exp(-x
6、^2-y^2)*y^5-2/3*exp(-(x+1)^2-y^2)-4/3*exp(-(x+1)^2-y^2)*x^2-8/3*exp(-(x+1)^2-y^2)*x?d(dz/dy)/dy=-6*(1-x)^2*exp(-x^2-(y+1)^2)+3*(1-x)^2*(-2*y-2)^2*exp(-x^2-(y+1)^2)+200*y^3*exp(-x^2-y^2)-200*y^5*exp(-x^2-y^2)+20*(1/5*x-x^3-y^5)*exp(-x^2-y^2)-40*(1/5*x-x^3-y^5)*y^2*exp(-x^2-y^2)+2/3*exp(-(x+1)
7、^2-y^2)-4/3*y^2*exp(-(x+1)^2-y^2)?Ananalyticsolutionisnoteasilyfoundinareasonabletimespan.6GeneticAlgorithms07GA:OperatorsExample8ApplyaGeneticAlgorithmGAprocess:StartwithmultiplefeasiblesolutionsandapplyGArepeatedlytoobtainasolution.10thgeneration
