1、2实验1 单纯形法求解线性规划实验1 单纯形法求解线性规划成绩专业班级学号 姓名 报告日期2012.4.5 实验类型:验证性实验 综合性实验 设计性实验实验目的:进一步熟练掌握单纯形法求解线性规划。实验内容:单纯形法求解线性规划4个 实验原理 线性规划单纯形法(线性规划解有四种情形,唯一最优解,无穷多个最解,无界解,无可行解)实验步骤1 要求上机实验前先编写出程序代码 2 编辑录入程序3 调试程序并记录调试过程中出现的问题及修改程序的过程4 经反复调试后,运行程序并验证程序运行是否正确。5 记录运行时的输入和输出。 预习编写程序代码:实验报告:根据实验情况和结果撰写并递交实验报告。参考程序(1
2、) 实验原理 (a) 当所有sgma=0,并且基变量中没有人工变量,非基变量的sgnm均不为0,此时方程对应的唯一解 (b) 当所有的sgma=0,并且基变量中没有人工变量,非基变量中有sgma=0的,此时方程对应的无穷多解 (c)当所有的sgma0,并且p0 h=1; endend vv=0; while h0 msg,mk=max(sgma); for i=1:m if A(i,mk)0 sta(i)=b(i)/A(i,mk); else sta(i)=10000; end end mst,mr=min(sta); if mst=10000 flg=unbounded solution;
3、fm=inf; xx=; b=; h=-1; vv=1; AA=; else zy=A(mr,mk) for i=1:m if i=mr for j=1:n A(i,j)=A(i,j)/zy; end b(i)=b(i)/zy; else end end for i=1:m if i=mr amk=A(i,mk); b(i)=b(i)-amk*b(mr); for j=1:n A(i,j)=A(i,j)-amk*A(mr,j); end else end A; B1=A(:,1:m); % B1 新基的逆矩阵; cb(mr)=c(mk); xx(mr)=mk; sgma=c-cb*A; h=-
4、1; for i=1:n if sgma(i)0 h=1; end end end cb b fm=sum(cb*b); if (h=-1)&(vv=1) vv=0; for i=1:m if xx(i)=2; flg=nofeasibel; xx=; fm=; b=; vv=1; AA=; end if vv=1 AA=A; ss=size(find(sgma) ww=ss(2) if ww=n-m flg=There is only one solution; else flg=There are many solutions; end end end end end end(1) m1=
5、0m1 = 0 m=3m = 3 n=5n = 5 A=1 0 0 1 2;0 1 0 4 0;0 0 1 0 4A = 1 0 0 1 2 0 1 0 4 0 0 0 1 0 4 b=8;16;12b = 8 16 12 c=0 0 0 2 3c = 0 0 0 2 3 xx,b,fm,sgma,AA,flg=myprgmh(m1,m,n,A,b,c)zy = 4cb = 0 0 3b = 2 16 3zy = 1cb = 2 0 3b = 2 8 3zy = 2cb = 2 0 3b = 4 4 2ss = 1 2ww = 2xx = 4 3 5b = 4 4 2fm = 14sgma =
6、 -1.5000 -0.1250 0 0 0AA = 0 0.2500 0 1.0000 0 -2.0000 0.5000 1.0000 0 0 0.5000 -0.1250 0 0 1.0000flg =There is only one solution 有唯一解 m1=0m1 = 0 m=2m = 2 n=4n = 4 A=1 0 -1 1;0 1 -0.5 1A = 1.0000 0 -1.0000 1.0000 0 1.0000 -0.5000 1.0000 b=1;2b = 1 2 c=0 0 2 2c = 0 0 2 2 xx,b,fm,sgma,AA,flg=myprgmh(m
7、1,m,n,A,b,c)xx = b = fm = Infsgma = 0 0 2 2AA = flg =unbounded solution 无界解 m1=2m1 = 2 m=2m = 2 n=6n = 6 A=1 0 1 -1 -1 0;0 1 -3 1 0 -1A = 1 0 1 -1 -1 0 0 1 -3 1 0 -1 b=0;3b = 0 3 c=-1000 -1000 1 1 0 0c = -1000 -1000 1 1 0 0 xx,b,fm,sgma,AA,flg=myprgmh(m1,m,n,A,b,c)zy = 1cb = -1000 1b = 3 3xx = b = f
8、m = sgma = 0 -1 -1996 0 -1000 -999AA = flg =nofeasibel 无可行解 m1=0m1 = 0 m=2m = 2 n=5n = 5 A=1 0 -1 1 3;0 1 12 4 10A = 1 0 -1 1 3 0 1 12 4 10 b=20;90b =20 90 c=0 0 -5 5 13c = 0 0 -5 5 13 xx,b,fm,sgma,AA,flg=myprgmh(m1,m,n,A,b,c)zy = 3cb = 13 0b = 6.6667 23.3333zy = 0.3333cb = 5 0b = 20.0000 10.0000ss = 1 2ww = 2xx = 4 2b = 20.0000 10.0000fm = 100.0000sgma = -5 0 0 0 -2AA = 1.0000 0 -1.0000 1.0000 3.0000 -4.0000 1.0000 16.0000 0 -2.0000flg =There are many solutions 有无穷解
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