[AMPL 1864] Strange results from AMPL

[Eric-105]

Hi there,

I solved a mixed integer problem, say, A (minimization problem), I got
following results:

CPLEX 11.0.0: optimal integer solution; objective 15043258.48
324295 MIP simplex iterations
34 branch-and-bound nodes
1 cover cut
412 flow-cover cuts
1 Gomory cut
7314 implied-bound cuts

Therefore, this objective value 15043258.48 should be the overall
optimal value for this model. However, when I inserted another
bounding constraint and resolve the problem, the objective value is
even smaller than that value within a integer solution gap.  The
reuslts are as follows:

CPLEX 11.0.0: optimal integer solution within mipgap or absmipgap;
objective 14621338.27
84000 MIP simplex iterations
1 branch-and-bound nodes
absmipgap = 234.119, relmipgap = 1.60121e-05
398 flow-cover cuts
1 Gomory cut
5176 implied-bound cuts

Can anyone help me understand this observation? Thank you!

Eric
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[Paul A. Rubin]

Eric wrote:

> I solved a mixed integer problem, say, A (minimization problem), I got
> following results:
>
> CPLEX 11.0.0: optimal integer solution; objective 15043258.48
> 324295 MIP simplex iterations
> 34 branch-and-bound nodes
> 1 cover cut
> 412 flow-cover cuts
> 1 Gomory cut
> 7314 implied-bound cuts
>
> Therefore, this objective value 15043258.48 should be the overall
> optimal value for this model. However, when I inserted another
> bounding constraint and resolve the problem, the objective value is
> even smaller than that value within a integer solution gap.  The
> reuslts are as follows:
>
> CPLEX 11.0.0: optimal integer solution within mipgap or absmipgap;
> objective 14621338.27
> 84000 MIP simplex iterations
> 1 branch-and-bound nodes
> absmipgap = 234.119, relmipgap = 1.60121e-05
> 398 flow-cover cuts
> 1 Gomory cut
> 5176 implied-bound cuts
>
> Can anyone help me understand this observation? Thank you!

In my experience, this sort of anomaly usually traces back to a
mixture of poor scaling in the original problem and/or rounding errors
and/or the particular tolerances being used.  The fact that you only
needed one b-&-b node after you added the extra bounding constraint
makes me wonder if either of the presolvers is a factor here.  Try
doing this again with AMPL's presolver off (CPLEX's presolver will
still be on) and see if the same or similar happens.  If so, also turn
off CPLEX's presolver and see what shakes.

/Paul

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[Eric-105]

Thank you Paul for your suggestions. I will try and see.

On Jul 8, 7:09 am, Paul <ru...@...> wrote:

> Eric wrote:
> > I solved a mixed integer problem, say, A (minimization problem), I got
> > following results:
>
> > CPLEX 11.0.0: optimal integer solution; objective 15043258.48
> > 324295 MIP simplex iterations
> > 34 branch-and-bound nodes
> > 1 cover cut
> > 412 flow-cover cuts
> > 1 Gomory cut
> > 7314 implied-bound cuts
>
> > Therefore, this objective value 15043258.48 should be the overall
> > optimal value for this model. However, when I inserted another
> > bounding constraint and resolve the problem, the objective value is
> > even smaller than that value within a integer solution gap.  The
> > reuslts are as follows:
>
> > CPLEX 11.0.0: optimal integer solution within mipgap or absmipgap;
> > objective 14621338.27
> > 84000 MIP simplex iterations
> > 1 branch-and-bound nodes
> > absmipgap = 234.119, relmipgap = 1.60121e-05
> > 398 flow-cover cuts
> > 1 Gomory cut
> > 5176 implied-bound cuts
>
> > Can anyone help me understand this observation? Thank you!
>
> In my experience, this sort of anomaly usually traces back to a
> mixture of poor scaling in the original problem and/or rounding errors
> and/or the particular tolerances being used.  The fact that you only
> needed one b-&-b node after you added the extra bounding constraint
> makes me wonder if either of the presolvers is a factor here.  Try
> doing this again with AMPL's presolver off (CPLEX's presolver will
> still be on) and see if the same or similar happens.  If so, also turn
> off CPLEX's presolver and see what shakes.
>
> /Paul- Hide quoted text -
>
> - Show quoted text -

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[Hans Mittelmann]

The first problem was solved the second not really.

On Jul 7, 4:28 pm, Eric <erichuan...@...> wrote:

> Hi there,
>
> I solved a mixed integer problem, say, A (minimization problem), I got
> following results:
>
> CPLEX 11.0.0: optimal integer solution; objective 15043258.48
> 324295 MIP simplex iterations
> 34 branch-and-bound nodes
> 1 cover cut
> 412 flow-cover cuts
> 1 Gomory cut
> 7314 implied-bound cuts
>
> Therefore, this objective value 15043258.48 should be the overall
> optimal value for this model. However, when I inserted another
> bounding constraint and resolve the problem, the objective value is
> even smaller than that value within a integer solution gap.  The
> reuslts are as follows:
>
> CPLEX 11.0.0: optimal integer solution within mipgap or absmipgap;
> objective 14621338.27
> 84000 MIP simplex iterations
> 1 branch-and-bound nodes
> absmipgap = 234.119, relmipgap = 1.60121e-05
> 398 flow-cover cuts
> 1 Gomory cut
> 5176 implied-bound cuts
>
> Can anyone help me understand this observation? Thank you!
>
> Eric

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