GLPK - 上限约束不能正常工作

编程问答 2022-04-24

问题描述

我正在使用 GLPK，我正在努力理解为什么不遵守上限约束。 我有这样的事情：

param n0;
param n1;
param n2;
param start_0{i in 0..n0};
param end_0{i in 0..n0};
param start_1{i in 0..n1};
param end_1{i in 0..n1};
param start_2{i in 0..n2};
param end_2{i in 0..n2};

var y0 {k in 0..n0} binary; 
var y1 {k in 0..n1} binary;
var y2 {k in 0..n2} binary;

[...]

minimize obj: (sum{k in 0..n2}(end_2[k]*y2[k] + 600*y2[k])  - (sum{k in 0..n0} (start_0[k]*y0[k])));

[...]

s.t. c1: (sum{k in 0..n2} (end_2[k]*y2[k] ) - (sum{k in 0..n0} (start_0[k]*y0[k] ))) <= 7000;

s.t. c2_1: sum{k in 0..n0} y0[k] = 1 ;
s.t. c2_2: sum{k in 0..n1} y1[k] = 1 ;
s.t. c2_3: sum{k in 0..n2} y2[k] = 1 ;

[...]
solve;

[...]

printf (sum{k in 0..n2} (end_2[k]*y2[k] ) - (sum{k in 0..n0} (start_0[k]*y0[k] )));

最后一个 printf 给了我 7200。但是上面的约束 c1 应该保证差值不大于 7000。

求解器输出如下：

GLPK Integer Optimizer,v4.65
7 rows,353 columns,1332 non-zeros
353 integer variables,all of which are binary
Preprocessing...
6 rows,1059 non-zeros
353 integer variables,all of which are binary
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.625e+09  ratio =  1.625e+09
GM: min|aij| =  9.998e-01  max|aij| =  1.000e+00  ratio =  1.000e+00
EQ: min|aij| =  9.996e-01  max|aij| =  1.000e+00  ratio =  1.000e+00
2N: min|aij| =  7.561e-01  max|aij| =  1.000e+00  ratio =  1.323e+00
Constructing initial basis...
Size of triangular part is 6
Solving LP relaxation...
GLPK Simplex Optimizer,v4.65
6 rows,1059 non-zeros
      0: obj =  -2.232000000e+05 inf =   1.329e-04 (2)
      2: obj =   6.210000000e+04 inf =   0.000e+00 (0)
*     5: obj =   7.097321429e+03 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Integer optimization begins...
Long-step dual simplex will be used
+     5: mip =     not found yet >=              -inf        (1; 0)
+   272: >>>>>   1.320000000e+04 >=   1.140000000e+04  13.6% (237; 2)
+   304: mip =   1.320000000e+04 >=     tree is empty   0.0% (0; 477)
INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.8 Mb (851464 bytes)
display statement at line 22
[...]
Model has been successfully processed

我做错了什么？ 非常感谢您的帮助，

解决方法

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glpklinear-programmingsimplexupperbound