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Re: [Help-glpk] Working with larger numbers

From: Markus Pilz
Subject: Re: [Help-glpk] Working with larger numbers
Date: Tue, 29 Jul 2008 20:10:08 +0200
User-agent: Thunderbird (X11/20080724)


Andrew Makhorin wrote:
> Markus,
> I tried both your instances that you posted me with "glpsol --nopresol
> --noscale --min/--max", and in all four cases the solution reported
> was sufficiently accurate in the sense that KKT optimality conditions
> had zero residual errors.

I was suprised that standard glpsol reports perfect results. Then I
tried "glpsol --exact" and the result changed. For example, using the
attached  mps file:
 (i) "glpsol" reports "objval =   6.750000000e+10"
 (ii) "glpsol --exact" reports "objval =       67500000001.0831"

> Could you demonstrate how "inexactness" looks like? Probably there is
> some misunderstanding.

Yes, this might be a misunderstanding as I'm a LP newbie. Taking a look
at the variables of an other run (similar to the attached file), I have
to deal with values like "12338139601.2095279693603515625" (glp_simplex
+ lpx_exact) instead of "12338139600" (glp_simplex).

The former solution is still a good starting point, but I was surprised
that a "perfect" solution changes after calling lpx_exact.

> (I noticed that to limit arc flows you are using general constraints
> like:
> flow_sum_(3,2),_163800: + x_1 >= 0
>                         + x_1 <= 163800
> It would be better to specify explicit lower and upper bounds of
> corresponding variables; this would allow essentially decreasing the
> number of general constraints.)

Hmm. Can it be that "lpx_write_cpxlp" converts bounds this way?

>> Yes you are right. We already moved to lpx_exact, but it does not help
>> everywhere.
> Does this mean that lpx_exact takes too much time?

No! By default, we call "glp_simplex" followed by "lpx_exact". We did
not experienced a huge increase in runtime.

But now I unsure when to call "lpx_exact". Is it a good advice to call
lpx_exact only, when the KKT check does not report high quality after


Markus Pilz                          University of Bonn
                                     Institute of Computer Science IV
E-Mail: address@hidden          Roemerstrasse 164
Tel.:   +49 228 73-4549              53117 Bonn
Fax.:   +49 228 73-4571              Germany

Attachment: sample.mps
Description: application/mps

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