Re: Solver delivers wrong answer when 2 constraints are close

[Heinrich Schuchardt]

On 3/4/21 4:44 PM, Antti Lehtila wrote:
> 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

In this line an apostrophe is missing.

  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;

It is this strengthening that fails:

src/npp/npp3.c:567
eps = (q->is_int ? 1e-3 : 1e-3 + 1e-8 * fabs(q->lb));

Set eps to 1E-5 and you are fine.

Or run with --nopresol.

@Andrew:
Shouldn't 1E-5 be good enough?
Why do we need eps > 0?

Best regards.

Heinrich

> *
> *  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