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Re: [Help-glpk] memory usage seems very high

From: Andrew Makhorin
Subject: Re: [Help-glpk] memory usage seems very high
Date: Sat, 13 Jun 2009 19:19:08 +0300

> A couple of strange things:

> First, when I run your model on my Windows box, it doesn #8217;t run
> completely.  In particular, it generates a few of your constraints
> (c1 to cc) and then nicely stops.  The output looks like:

> Reading model section from big.mod...
> 7103 lines were read
> Generating z...
> Generating c0...
> Generating c1...
> Generating c2...
> Generating c3...
> Generating c4...
> Generating c5...
> Generating c6...
> Generating c7...
> Generating c8...
> Generating c9...
> Generating ca...
> Generating cb...
> Generating cc...

> So it does not get to the optimization
> piece.  I wonder if that #8217;s a window #8217;s limitation because
> you have very long lines.

Was there any error message? The mathprog translator has no limit to
the line length.

> Second, your model (from your output below) is quite small.  It is fairly
> dense (30% non-zeros) but even if it was 100% dense I would expect it
> would take 10MB, not 2GB.  At full density, my guess the memory formula
> would be something like:  82*5256*12*2 = 10MB: 82=number of rows,
> 5256=number of columns, 12 = size of double plus size of an int,
> 2=doubled the requirements to hold the A matrix to also hold the LU basis
> and other things.  And, with the simplex algorithm, the LU factorization
> tends to be only a bit more dense than the matrix itself, so I would have
> really expected memory usage to be around 3 or 4MB.

The mathprog translator needs extra memory to store attributes of all
model objects, and it does that inefficiently. For example, every scalar
variable (or parameter) is represented as 0-dimensional array, and every
such array has an internal routine (in bytecode) used to compute its
members. Please see:
for some calculations about the memory requirements.

Rather than to use a lot of scalar variables it would be essentially
better to use subscripted variables. For example, instead of

. . .
var HES031008936>=0;
var HES031007598>=0;
var HES031008727>=0;
var HES031005876>=0;
var HES031009338>=0;
var HES031005658>=0;
. . .

we could use only one set and one variable subscripted over it:

set J;
var x{j in J}, >= 0;
. . .
set J := ... HES031008936 HES031007598 HES031008727 HES031005876
         HES031009338 HES031005658 ...

that would significantly reduce the memory used by the translator.

Another, much better way for such plain models is to use cplex lp

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