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Re: [Help-glpk] Operand following / has invalid type

From: Michael Hennebry
Subject: Re: [Help-glpk] Operand following / has invalid type
Date: Thu, 10 Sep 2020 10:38:58 -0500 (CDT)
User-agent: Alpine 2.20 (DEB 67 2015-01-07)

On Thu, 10 Sep 2020, Andrew Makhorin wrote:

On Wed, 2020-09-09 at 18:17 -0300, wrote:

I'm trying to make a program that populates a binary matrix keeping
many blank lines as possible, e.g.

Add another variable for each row in the binary matrix:
z[row]>=m[row, col]
minimize its sum.
The z's need not be binary.

It can be done with a single z,
but I expect user-defined cuts would be necessary.
Note that GLPK assumes cuts are not mathematically necessary.
GLPK might return a solution you deem infeasible.
In that case, you would neeed to add a cut and rerun.
Keeping the previously discovered cuts would not be automatic.

Since I know the sum of the lines won't be too big I decided to use
approach based on division, but I'm getting a "operand following /
invalid type" error.

/* binary matrix */
var m{x in X, y in Y} binary;
/* minimizes total (sum of line)^-1, a full line is better than two 
half-full lines*/
minimize maxEmpty: sum{x in X} 1/(1 + sum{y in Y} m[x,y]);

This can be done, sort of.
Again you would need an auxillary variable for each matrix row.
I expect the additional constraints
could be inserted with the original set.

Again it coulod be done with a single z
and the same complications are before.

In constraints and objectives you can divide only by a constant
expression. In your case you divide by a linear form that leads to a
non-linear objective function, which is not allowed. Probably you need
to reformulate your model.

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