Re: [Help-glpk] Emulating the AMPL ord() function

[Heinrich Schuchardt]

Hello Jason,

any of the following two models should do. If you want an other order 
but the lexical one just provide ord in the data section.

You write that you are using a generator program to create the exclude 
matrix. Why don't you directly write the allowed pairs instead of the 
matrix?

set P;
param exclude{P, P};
set ALLOWED_PAIRS, dimen 2 := setof{i in P, j in P : exclude[i,j] == 0 
&& exclude[j,i] == 0 && i < j} (i,j);
display ALLOWED_PAIRS;
data;
set P := person01 person02 person03 person04;
param   exclude:        person01 person02 person03 person04 :=  
        person01        0       1       0       0
        person02        1       0       0       1
        person03        1       0       0       1
        person04        0       1       1       0
;
end;

====

set P;
param exclude{P, P};
param ord{i in P} := sum{j in P: i > j} 1;
set ALLOWED_PAIRS, dimen 2 := setof{i in P, j in P : exclude[i,j] == 0 
&& exclude[j,i] == 0 && ord[i] < ord[j]} (i,j);
display ord;
display ALLOWED_PAIRS;
data;
set P := person01 person02 person03 person04;
param   exclude:        person01 person02 person03 person04 :=  
        person01        0       1       0       0
        person02        1       0       0       1
        person03        1       0       0       1
        person04        0       1       1       0
;
end;

Best regards

Heinrich Schuchardt

On 27.12.2014 20:13, Jason Foster wrote:
> As part of shifting my group towards open source tools I've been working on 
> converting some AMPL models to GMPL.  So far it's been working really well 
> (thanks for some great work!) and I've just run into my first multi-hour snag.  
> I've searched online and near as I can tell:
>
> 1) GMPL doesn't implement "ordered sets" (because "ordered" implies a 
> mathematical ordering vs. the lexical ordering of the input text)
> 2) it is possible to work around some of these issues using a variety of 
> techniques that require a reasonably deep understanding of GMPL
>
> Regarding (2) there is a construct documented at 
> http://lists.gnu.org/archive/html/help-glpk/2006-11/msg00059.html that I can't 
> get to work as written:
>
> set S;
> param ref{i in 1..card(S)}, symbolic, in S; # ref[i] refers to i-th element of 
> S;
> param a{S};
> a[ref[i]] # means a[i-th element of S]
>
> The error I get is that ref[i] is empty.
>
> There is also a fairly involved discussion at 
> http://en.wikibooks.org/wiki/GLPK/GMPL_Workarounds that addresses sorted 
> output.  I poked at that for a bit and ran into some difficulties because I am 
> looking for the lexical position within the set, not the result of a 
> calculation.
>
> The problem I am trying to solve is that I have the following data:
>
> set PEOPLE := person01 person02 person03 person04;
>
> param   exclude:        person01 person02 person03 person04 :=  
>         person01        0       1       0       0
>         person02        1       0       0       1
>         person03        1       0       0       1
>         person04        0       1       1       0
> ;
>
> exclude is "guaranteed" to be a symmetric matrix (assuming the generation code 
> is working properly).  The AMPL code I have is trying to create:
>
> set ALLOWED_PAIRS := {i in PEOPLE, k in PEOPLE: ( exclude[i, k] = 0 and exclude[k, 
> i] = 0 ) and ( ord(i) < ord(k) )};
>
> Of course this code doesn't work in GMPL because of the missing ord() function. 
>  I believe that the goal is to precent the set from including redundant 
> elements which will help keep the number of constraints down to something 
> reasonable.
>
> Based on what I've seen this should be a solvable problem using the tools 
> available within GMPL but my current mental model isn't sufficient to work it 
> out. I'm hoping that someone on the list can show a workaround and as such can 
> help me continue the push to transition to a purely open source toolchain.
>
> Thanks for any help or insights that you can offer!
>
> Jason

Best regards

Heinrich Schuchardt