---------- Forwarded message ---------
De:
Antti Lehtila <antti.lehtila@vtt.fi>Date: qui., 4 de mar. de 2021 às 12:44
Subject: Re: Solver delivers wrong answer when 2 constraints are close
To: <
help-glpk@gnu.org>
Hi,
I think it works fully as documented, and so *per design*. Singleton
rows are treated as column bounds by the preprocessor. See documentation
for *npp_implied_lower*:
*---------------
* Processing implied column lower bound l'[q] includes the following
* cases:
*
* 1) if l'[q] < l[q] + eps, implied lower bound is redundant;
*
* 2) if l[q] + eps <= l[q] <= u[q] + eps, current column lower bound
* l[q] can be strengthened by replacing it with l'[q]. If in this
* case new column lower bound becomes close to current column upper
* bound u[q], the column can be fixed on its upper bound;
*
* 3) if l'[q] > u[q] + eps, implied lower bound violates current
* column upper bound u[q], in which case the problem has no primal
* feasible solution. */
*---------------
The lower bound can have only a single value, but if you define multiple
values for a column lower bound, they must of course be processed in
some order. In this case, the lower bound is first defined l(q)=0, then
l'(q)=1, and finally l'(q)=1.0001. The third value for the bound is thus
considered *redundant*, as per design, and so the second value l(q)=1
remains in effect. This is because *eps* is defined as 1e-3 + 1e-6 *
fabs(q->lb)).
I guess it may be a considered a design flaw, but I think it should not
be called a bug, as it is working as designed and documented. Besides,
I think one should use the Bounds section for bounds, instead of using
multiple constraints for defining a single lower bound.
Best,
Antti
_______________________
On 04.03.2021 11:38, Domingo Alvarez Duarte wrote:
>
> Testing this problem I discover that if we change the order of
> constraint declarations it seems to give the expected answer as stated
> by Thiago (what I think could be another bug).
>
> ====
>
> /param min_bound default 0;/
> /var x >= 0;
>
> minimize y: x;/
> *
> */*s.t. PART_MIN_X: x >= 1 + min_bound;*
> /
> /*s.t. LIM_INF_X: x >= 1;
> *
> /
> /solve;
> display min_bound;
> display x; # EXPECTED RESULT: X == 1.0001
>
> data;
> param min_bound := 1e-4;
> end;/
>
> ====
>
> Output:
>
> ====
>
> x.val = 1.0001
>
> ====
>
> On 3/3/21 19:19, Thiago Neves wrote:
>> Hi.
>> I've found a strange behaviour in glpk which I don't know how to fix
>> nor how to contour it. It seems like GLPK can't distinguish
>> constraints that differs from about 1e-4.
>>
>> Follows simple examples that explain and reproduce the problem.**
>> *
>> *
>> *The first model gives the desired answer (x = 1.0001):*
>> /
>> param min_bound default 0;/
>> /var x >= 0;
>>
>> minimize y: x;/
>> /*
>> s.t. PART_MIN_X: x >= 1 + min_bound;*
>>
>> solve;
>> display min_bound;
>> display x; # EXPECTED RESULT: X == 1.0001
>>
>> data;
>> param min_bound := 1e-4;
>> end;
>> /
>> /_____________________________________/
>> /OUTPUT:/
>> /x.val = 1.0001/
>> /_____________________________________ /
>>
>> *Now, if I add a second constraint "close" to the first one, the
>> solver will deliver an answer that is actually infeasible:*
>>
>> /param min_bound default 0;/
>> /var x >= 0;
>>
>> minimize y: x;/
>>
>> *s.t. LIM_INF_X: x >= 1;
>>
>> */*s.t. PART_MIN_X: x >= 1 + min_bound;*
>>
>> solve;
>> display min_bound;
>> display x; # EXPECTED RESULT: X == 1.0001
>>
>> data;
>> param min_bound := 1e-4;
>> end;/
>> /_____________________________________/
>> /OUTPUT:/
>> x.val = 1
>> /_____________________________________ /
>>
>> *If I change the "min_bound" parameter to 1e-2, the second model
>> works as expected (x = 1.01):*
>>
>> /param min_bound default 0;/
>> /
>> /
>> /var x >= 0;
>>
>> minimize y: x;/
>> *
>> *
>> *s.t. LIM_INF_X: x >= 1;
>>
>> */*s.t. PART_MIN_X: x >= 1 + min_bound;*
>>
>> solve;/
>> /
>> display x; # EXPECTED RESULT: X == 1.01
>>
>> data;
>> param min_bound := 1e-2;
>> end;/
>> /_____________________________________/
>> /OUTPUT:/
>> x.val = 1.01
>> /_____________________________________ /
>> /
>> /
>>
>> Att,
>>
>> *Thiago H. Neves*
>> (31) 98608-0666
>>