Question

我有一个242线性不等式的系统，有9个变量（x1，...，x9），如下所示：

0 <= f1(x1,...,x9) <= 20
0 <= f2(x1,...,x9) <= 20
...
0 <= f242(x1,...,x9) <= 20

使用约束：

0 <= x1,...,x9 <= 30

如何使用MATLAB代码处理此问题？

提前谢谢。

Answer 1

这不是直接回答你的问题。您可以下载GNU GLPK和Gusek Editor并尝试建模您的需求。

如果MATLAB也支持MathProg，GAMS等数学编程语言，那么你可以对线性方程进行建模并在没有任何目标函数的情况下求解（如@sascha所评论）。

/* MathProg Example : With trivial inequalities  */

param m, integer, > 0, default 242;
param n, integer, > 0, default 9;
set INEQUALITIES := 1..m;
set VARS := 1..n;
var x{j in VARS}, >= 0, <= 30;

s.t. phi{i in INEQUALITIES}: i - sum{j in VARS} x[j]  <= 20;

solve;

for{j in VARS} {
        printf"x[%2d] = %2d\n", j, x[j];
}

end;

内部生成的方程式如下：

Minimize
 obj: 0 x(1)

Subject To
 phi(1): - x(1) - x(2) - x(3) - x(4) - x(5) - x(6) - x(7) - x(8) - x(9)
 <= 19
 phi(2): - x(1) - x(2) - x(3) - x(4) - x(5) - x(6) - x(7) - x(8) - x(9)
 <= 18
 phi(3): - x(1) - x(2) - x(3) - x(4) - x(5) - x(6) - x(7) - x(8) - x(9)
 phi(242): - x(1) - x(2) - x(3) - x(4) - x(5) - x(6) - x(7) - x(8)
 - x(9) <= -222

Bounds
 0 <= x(1) <= 30
 0 <= x(2) <= 30
 0 <= x(3) <= 30
 0 <= x(4) <= 30
 0 <= x(5) <= 30
 0 <= x(6) <= 30
 0 <= x(7) <= 30
 0 <= x(8) <= 30
 0 <= x(9) <= 30

End

在解决模型时，解决方案看起来像：

>C:\gusek\glpsol.exe --cover --clique --gomory --mir -m "vijay.mod"    
GLPSOL: GLPK LP/MIP Solver, v4.64
Parameter(s) specified in the command line:
 --cover --clique --gomory --mir -m vijay.mod
Reading model section from vijay.mod...
vijay.mod:17: warning: final NL missing before end of file
17 lines were read
Generating phi...
Model has been successfully generated
GLPK Simplex Optimizer, v4.64
242 rows, 9 columns, 2178 non-zeros
Preprocessing...
222 rows, 9 columns, 1998 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 222
      0: obj =   0.000000000e+00 inf =   2.475e+04 (222)
    222: obj =   0.000000000e+00 inf =   0.000e+00 (0) 2
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.5 Mb (538071 bytes)
x[ 1] = 30
x[ 2] = 30
x[ 3] = 30
x[ 4] = 30
x[ 5] = 30
x[ 6] = 30
x[ 7] = 30
x[ 8] = 12
x[ 9] =  0
Model has been successfully processed
>Exit code: 0    Time: 0.212

用MATLAB求解一个包含9个变量的242个线性不等式的系统

1 个答案: