用软件包求解线性规划问题

《用软件包求解线性规划问题》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、用lingo软件包求解规划问题线性规划例min4x1+x2+x3S,t2x1+x2+2x3=43x1+3x2+x3=3X1>=0,x2>=0,x3>=0Model :!求解线性规划问题Min=4*x1+x2+x3 ;2*x1+x2+2*x3=4;3*x1+3*x2+x3=3;End例大型问题,考虑用矩阵MinS,tAx=bx>=0model:!求解线性规划问题sets:row/1..2/:b;col/1..3/:c,x;matrix(row,col):A;endsetsmin=@sum(col:c*x);@for(row(i):@sum(col

2、(j):A(I,j)*x(j)=b(i);Data:C=4,1,1b=4,3A=2,1,23,3,1EnddataEnd灵敏度分析(略)-7-有界线性规划例maxx1+2x2S,t-2x1+x2<=8-x1+x2<=3X1-x2<=30<=x1<=3,0<=x2

3、)*x(j)<=b(i));Data:c=1,2b=8,3,3;A=-2,1,-1,1,1,-1;l=0,0u=3,100000000000000;enddataend整数规划例maxx1+x2s,t2x1+x2<=64x1+5x2<=20x1,x2>=0且为整数model:!整数规划-7-sets:row/1..2/;b;col/1..2/:c,x;matrix(row,col):A;endsetsmax=@sum(col:c*x);@for(col:@gin(x));!说明变量x取整数@for(row(i);@sum(col(j):A(I,

4、j)*x(j))<=b(i);data:c=1,1;b=6,20A=2,1,4,5;enddataend0---1规划0----1规划格式为:@bin(x)例min2x1+5x2+3x3+4x4s,t-4x1+x2+x3+x4>=0-2x1+4x2+2x3+4x4>=4x 1+x2-x3+x4>=1x1,x2,x3.x4=0或1model:!0---1规划setsrow/1..3/ :bcol/1..4/ :c,xmatrix(row,col):A;endsetsmin=@sum(col:c*x)@for(col:@bin(x));!说明变量x

5、取0或1@for(row(i):@sum(col(j):A(I,j)*x(j)>=b(i))datac=2,5,3,4b=0,4,1-7-A=-4,1,1,1-2,4,2,41,1,-1,1enddataend无约束最优化问题例题min1]model:!无约束最优化问题2]sets3]var/1..2/:x4]endsets5]@for(var:@free(x))说明变量x无非负限制6]目标函数7]end一般约束最优化问题例题maxx1x2x3s,t-x1-2x2-2x3<=0x1+2x2+2x3<=72x1<=20x2<=11modelset

6、svar/1..3/:xendsetsmax=x(1)*x(2)*x(3)-7--x1-2*x2-2*x3<=0x(1)+2*x(2)+2*x3<=72x1<=20x2<=11@for(var:@free(x));说明变量x无非负限制end二次规划minf(x)=s,tAx<=b例mins,tx1+x2<=1-x1<=0-x2<=0modelsetsvar/1..2/:c,xstr/1..3/:bmatrix(var,var):Hconstr(str,var):Aendsets@for(var:@free(x));说明变量x无非负限制min=@

7、sun(matrix(i,j):0.5*H(I,j)*x(i)*x(j)+@sum(var(i):c(i)*x(i));@for(str(i):@sum(var(j):A(I,j)*x(j)<=b(i));dataH=2,0,0,2c=-2,-4A=1,1,-1,0,0,-1-7-b=1,0,0enddataend求解非线性规化问题maxst3x1+2x2+x3=9x1,x2,x3>=0modelsetsvar/1..3/:x;endsetsmax=4*x(1)^2-x(2)^2+2*x(3)^2+12;3*x(1)+2x(2)+x(3)=9;

8、end1)背包问题设有n件物品,且第i件物品的重量为,其价值为,而背包能承受的总重量是b,问应如何选择这些物品,使背包中所装物品的价值最大?解:设第i