用软件包求解线性规划问题.doc

用lingo软件包求解规划问题线性规划例min 4x1+x2+x3S,t 2x1+x2+2x3=4 3x1+3x2+x3=3 X1=0,x2=0,x3=0 Model: !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Min S,t Ax=b x=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(j):A(I,j)*x(j)=b(i);Data:C=4,1,1b=4,3A=2,1,2 3,3,1EnddataEnd灵敏度分析(略)有界线性规划例 max x1+2x2S,t -2x1+x2=8 -x1+x2=3X1-x2=30=x1=3,0=x2 Model: !有界线性规划问题Sets:Row/1.3/:b;Col/1.2/:c,x,l,u;Matrix(row,col):A;EndsetsMax=sum(col:c*x);for(col:bnd(l,x,u);for(row(i): sum(col(j):A(I,j)*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max x1+x2 s,t 2x1+x2=6 4x1+5x2=0且为整数model: !整数规划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,j)*x(j)=0 -2x1+4x2+2x3+4x4=4 x1+x2-x3+x4=1 x1,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取0或1for(row(i): sum(col(j):A(I,j)*x(j)=b(i)datac=2,5,3,4b=0,4,1A=-4,1,1,1 -2,4,2,4 1,1,-1,1enddataend无约束最优化问题例题min 1 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max x1x2x3s,t -x1-2x2-2x3=0 x1+2x2+2x3=72 x1=20 x2=11modelsetsvar/1.3/:xendsetsmax=x(1)*x(2)*x(3)-x1-2*x2-2*x3=0x(1)+2*x(2)+2*x3=72x1=20x2=11for(var:free(x); 说明变量x无非负限制end二次规划min f(x)= s,t Ax=b例mins,t x1+x2=1 -x1=0 -x2=0modelsetsvar/1.2/:c,xstr/1.3/:bmatrix(var,var):Hconstr(str,var):Aendsetsfor(var:free(x); 说明变量x无非负限制min=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)=0model setsvar/1.3/:x;endsetsmax=4*x(1)2-x(2)2+2*x(3)2+12; 3*x(1)+2x(2)+x(3)=9;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件物品装件max C1X1+C2X2+.+CnXns.t a1x1+a2x2+.+anxn=0,且xi取整数例max 8X1+5X2+12x3s.t 3x1+2x2+5x3=0,且xi取整数modelsets var/1.3/:a,c,x !说明变量是三