优化设计上机

1、优化设计上机一、无约束优化问题例1:minim i?f=已工七4工：+ 4i工金 + 1)建立目标函数M文件：%目标函数mbfun.m function f = mbfun(x)f = exp(x(1)*(4*x(1)八2+2*x(2)八2 + 4*x(1)*x(2)+2*x(2)+1);运行：%优化x0=0,0； options = optimset(LargeScale,off);x,fval,exitflag,output = fminunc(mbfun,x0,options)%运行结果Optimization terminated: relative infinitj-norm of

2、gradient less than options. TolFun.0. 5000-1. 0000fval =8304e-015E output =iterations funcCount st epsize first orderopt algorithm message73312.4568e-008? mediuni-scale: Quasi-Newton line search1, Optimization terminated: relative inf initynorm of gradient less than options. TolFun.（2）例1自己修改并调试运行:改为

3、：minimizef x = exi+x2 4x2 + x2 + 4x1x2 + 2x2 + 1建立目标函数M文件:%目标函数mbfun.mfunction f = mbfun(x)f = exp(x(1)+x(2)*(4*x(1)八2+x(2)八2 + 4*x(1)*x(2)+2*x(2)+1);运行：%优化x0=0,0; options = optimset(LargeScale,off);x,fval,exitflag,output = fminunc(mbfun,x0,options)%运行结果Opt iiriizat ion t eririinated: relative inf i

4、ni t y-no rm of gradient less than options. ToIFwl.0000-3. 0000fval =-1.4715ezitflag =iterations fui_icCoui_Lt stepsize firstorderopt algor itmessageoutput = 93915.2899e-007? inediujTL-scale: Quasi-Nev.H： on line searcl_L? Optiinization terminated: relative infinity-noriTL of gradient less than opti

5、ons. ToIFuil. ?二、有约束优化问题例1:(to within options. TolCon = le-006): ineqlin ineqnonlin12-9. 54741. 0474iniiiLLnize f(x) = e4.ic； + Srtg + 心俨金 +2知 + 1)subject to the constraints _览_ 2 - -L5 弋俨2 -10建立目标函数M文件：%目标函数mbfun.m function f = mbfun(x)f = exp(x(1)*(4*x(1)八2+2*x(2)八2 + 4*x(1)*x(2)+2*x(2)+1);建立非线性约束

6、函数M文件：%非线性约束函数confun.m function c, ceq = confun (x)c = 1.5 + x(1)*x(2) - x(1) - x(2);-x(1)*x(2) - 10;ceq =;运行：%优化x0 = -1,1；options = optimset(LargeScale,off);x, fval = fmincon(mbfun,x0,confun,options)%运行结果Optimization terminated: first-ouder optima.1 ity measure less than opt ions.ToLFun and masimum

7、 const r aint violat ion is less than opt ions. ToLCon.Active inequalitiesupperlowerfval =. 0236(2)例2自己修改并调试运行:修改约束条件为：X1X2+X1 - X2 1X1X2 -5建立目标函数M文件：%目标函数mbfun.m function f = mbfun(x)f = exp(x(1)*(4*x(1)八2+2*x(2)八2 + 4*x(1)*x(2)+2*x(2)+1);建立非线性约束函数M文件：%非线性约束函数confun.m function c, ceq = confun (x)c

8、= -1 + x(1)*x(2) - x(1) - x(2);-x(1)*x(2) -5;ceq =;运行：%优化x0 = -1,1；options = optimset(LargeScale,off);x, fval = fmincon(mbfun,x0,confun,options)%运行结果Optimization terminated: Magnitude of directional derivative in search direction less than 2*options. TolFun and maKimuni constraint violation is less

9、than options. TolCon.Active inequalities (to within options. TolCon = le-006): lower upper ineqlin ineqnonlin21. 8199-2. 7475fval =-1.4629三、自选题目：有约束：已知某机床主轴悬臂梁受到的切削力F=15000N。主轴内经d=30mm。悬臂端许用挠度y =0.05mm。要求主轴两支撑跨度：300mm l 650mm，外径：60mm D 140mm，悬臂端 长度：90mm 0女 E(x4 d4)2即 9.07058挡 W -1 0 x4 3042300 x 650

10、60 x 14090 x3 150则总体模型为：f(X) = 0.7854(x1 + x3)(x; 900)S. t. 9.07058x2(x1+ x3) 1 0 x4 304 2300 x 65060 x 14090 x3 A=;b=;Aeq=;beq=; lb=300,60,90; ub=650,140,150; options=optimset(largescale,off,display,iter); x,fval=fmincon(mbfun,x0,A,b,Aeq,beq,lb,ub,confun,options) %运行结果maxDirectionalFirst-orderIterF

11、-countf (k) const raintSt ep-sizederivat iveoptimality Procedure048270261.851e+007Infeasible st art point19 1.75511e+006011.07e+0065.31e+005214 1.75511e+00601-0. 1244. 99e+004 Hessian modified twice319 1.75327e+00601-1. 84e+0034.99e+004 Hessian modified twice424 1.47657e+00601-2. 67e+0052.7e+004529

12、1.47657e+00601-0. 05024.63e+004 Hessian modified twice3ptimization terininated: Searchi directionless than 2*opt ions. TolXand maximum const raint violat ion is less than opt ions. TolCon.Active inequalities (to within options. TolCon = le-006):lowerupperineqlininequonlinJ300. 000075. 634590. 0000 f

13、val =1.4766e+006（1）无约束：已知梯形截面管道的参数是：底边长。，高度为h，面积A=64516mm2,斜边与底边的 夹角为&管道内液体的流速与管道截面的周长s的倒数成比例关系。试按照使流体流速最 大的要求确定该管道的参数。_ 0:解：（1）建立数学模型: 截面周长：s = c +-sin 9截面面积：A = ch + h2 cot 9 = 64516贝|J： c = 64516 hcot9h则:s=64516h-hcot9 +k = 64516 工+ ksin 9 h tan 9 sin 9取h、0为设计变量:X=x1, x2=h,0为使流体的速度最大，则管道截面周长最小即可。

14、（2）目标函数：2x1sinx264516 x1=x1tanx2（3）编程调试运行: 建立目标函数M文件:%目标函数mbfun.mfunction f=mbfun(x) a=64516;f=a/x(1)-x(1)/tan(x(2)*pi/180)+2*x(1)/sin(x(2)*pi/180);运行：x0=25,45; x,fval=fminunc(mbfun,x0)%运行结果Optimization terminat ed: relative infinity-norm of gradient less than options. TolFun. k =192. 995860. 0005fval =668.5656编制绘制目标函数等值线和曲面的程序 xx1=linspace100,300,25;xx1=linspace(100,300,25); xx2=linspace(30,120,25); x1,x2=meshgrid(xx1,xx2); f1=64516./x1-x1./tan(x2火pi/180)+2*x1./sin(x2火pi/180); subplot(1,2,1); h=contour(x1,x2,f1);h=contour(x1,x2,f1);