Instead of Awk, there is another way of doing this which I often find is easier
because all the calculations stay within GMPL:
In the GMPL program, have
set indices_to_set_to_zero within J default {};
param extra_data_file symbolic := "C:\TEMP\EXTRA.dat";
# ...
# set some x's to 0; note that in the first pass this constraint is not in the
model
# because indices_to_set_to_zero is empty
s.t. SET_SOME_Xs_TO_ZERO {j in indices_to_set_to_zero} :
x[j] = 0;
Then after the "solve" statement:
printf "set indices_to_set_to_zero :=\n" > extra_data_file;
for{ j in J : x[j] <= epsilon}
{
printf "\t%d\n", j >> extra_data_file;
}
printf ";\nend;\n" >> extra_data_file;
Then write a little batch file to execute the GMPL twice with the same "mod"
function. The first time with the normal .mod and .dat, the second time with
the same .mod and .dat, but also include in the glpsol command line the extra
data file.
glpsol -m model.mod -d data.dat
glpsol -m model.mod -d data.dat -d C:\TEMP\EXTRA.dat
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of
Reginald Beardsley
Sent: Sunday, November 10, 2013 1:56 PM
To: Michael Hennebry
Cc: glpk
Subject: Re: [Help-glpk] Applying a threshold to the solution using GMPL?
I've already tested adding a binary weight parameter for the 2nd stage job.
Works great!
I've roughed out the script that will generate the necessary specification in
the data file, but have not implemented and tested. But it's pretty simple to
write an awk script that writes a script that is then executed. Something I've
done many times. The reason for doing it this way is it avoids having to
specify all the weights. By default awk initializes everything to zero, so all
I have to do is specify the few non-zero elements and then print out the array
in GMPL form. With potentially 10-30,000 elements and only a handful of
non-zero elements, this is a big win.
Were it not for your suggestion I'd have wandered off and done something much
harder.
I've got a book on the way describing the mathematics of compressive sensing.
So I'm likely to be pushing a good bit farther with this. There's a huge
range of applications in science and engineering.
A few years ago if asked about doing some of this I'd have given the inquirer a
severe look and said, "You realize that won't work, don't you." Foreman Acton
describes a number of problems he asserts should not be solved with a computer.
But the world has changed. Now you can do it easily. No one has quite figured
out what all the new rules are, but L1 has some amazing properties when solving
inverse problems. We just couldn't afford the compute until a few years ago.
The only down side is lots of different jargon for describing the same thing
because so many disciplines are using the techniques.
--------------------------------------------
On Sun, 11/10/13, Michael Hennebry
<[email protected]<mailto:[email protected]>> wrote:
Subject: Re: [Help-glpk] Applying a threshold to the solution using GMPL?
To: "Reginald Beardsley" <[email protected]<mailto:[email protected]>>
Cc: "glpk" <[email protected]<mailto:[email protected]>>
Date: Sunday, November 10, 2013, 11:54 AM
On Sat, 9 Nov 2013, Reginald
Beardsley wrote:
> I've been hoping it can be done with binary variables in GMPL as I'm still
> trying to refine the problem statement. I'd like to be confident it's a
> good choice before coding it. I'd also like to improve my grasp of
> expressing problems in GMPL. I started out using CPLEX format and
> switching to GMPL has been a huge improvement when trying to explore
> various problem formulations.
I'd recommend against.
You end up with constraints like
x <= U(x)*b
where U(x) is an upper bound on x.
> With a two step solution if i set the weights to 0 or 1 I can probably get
> what I want by light editing of the data file using awk to add the
> weighting array. Not perhaps as elegant as solving in a single step, but
> it would allow using a pure LP solution and avoid the performance hit that
> a MIP formulation implies. Until I read your suggestion I'd been thinking
> along the lines of writing a whole new data file which was pretty painful
> to contemplate.
In the second stage, binaries might be more useful.
You already have a feasible solution and you can substitute smaller numbers
for the U(x)'s.
If you do not mind writing code:
more=false
do {
for each x[j]:
if x[j] != 0:
if changing x[j]
to 0 would not increase L1 too much:
change x[j] to 0
more=true
} while(more)
This would not necessarily be optimal.
The only x's changing are those changed to zero.
You could run the LP again with the new constraints and repeat the process.
Of course, using the API,
each change x[j] to 0 could be followed by a reoptimization.
-- Michael
[email protected]<mailto:[email protected]> "On
Monday, I'm gonna have to tell my kindergarten class, whom I teach not to run
with scissors, that my fiance ran me through with a broadsword."
-- Lily
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