解决后 GLPK 变量似乎发生了变化

Question

我遇到了一个 glpsol 的奇怪行为，更准确地说是它的一个变量。我运行命令使用 glpsol -m sol.mod

输入，在文件sol.mod中：

set Points := (1..3);
var a{i in Points}, >= 0;
var x1{i in Points};
var x2{i in Points};
maximize obj: sum{i in Points} a[i];
px1: x1[1] = 0;
py1: x2[1] = 0;
px2: x1[2] = 2;
py2: x2[2] = 1;
px3: x1[3] = 3;
py3: x2[3] = 3;
p1x2: x1[1] + a[1] <= x1[2] - a[2];
p1x3: x1[1] + a[1] <= x1[3] - a[3];
p2x3: x2[2] + a[2] <= x2[3] - a[3];
solve;
printf "#OUTPUT:\n";
#printf{i in Points} "a_%d = %d\n", i, a[i];
printf "a[1]: %d\n", a[1];
printf "-a[1]: %d\n", -a[1];
printf "a[3]: %d\n", a[3];
printf "#OUTPUT END:\n";
end;

输出：

    GLPSOL: GLPK LP/MIP Solver, v4.52
Parameter(s) specified in the command line:
 -m sol.mod
Reading model section from sol.mod...
22 lines were read
Generating obj...
Generating px1...
Generating py1...
Generating px2...
Generating py2...
Generating px3...
Generating py3...
Generating p1x2...
Generating p1x3...
Generating p2x3...
Model has been successfully generated
GLPK Simplex Optimizer, v4.52
10 rows, 9 columns, 21 non-zeros
Preprocessing...
3 rows, 3 columns, 6 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 3
*     0: obj =   0.000000000e+00  infeas =  0.000e+00 (0)
*     3: obj =   3.500000000e+00  infeas =  0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (126476 bytes)
#OUTPUT:
a[1]: 2
-a[1]: -1
a[3]: 2
#OUTPUT END:
Model has been successfully processed

问题似乎是 a[1] 被评估为 2，而 -a[1] 被评估为 -1。另外 a[3] 也等于 2，所以约束 p1x3 不满足。

目前我不知道如何解决这个问题，甚至不知道是什么原因造成的。

Answer 1

将 %d 格式说明符更改为 %g，看看会发生什么。请注意，a{i} 是可能具有分数值的连续变量。

解决后 GLPK 变量似乎发生了变化

GLPK Variable seems to change after solve

glpk

mathprog