Generating All Combinations

GAMS
1

Hello,

I have a column consisting of 13 rows of ones and zeros. I would like to generate all combinations where I have N 1s in the column (where N < 13). What is the fastest way to do that?

Thank you!

2

GAMS does not do matrices so well, but working with subsets will get you there. We use embedded Python to do the actual calculation of the combinations:

set n / 1*13 /; scalar r /4/;
* Calculate n Choose r
$eval nCr fact(card(n))/fact(r)/fact(card(n)-r)
$eval r r
set p 'possible outcomes' / p1*p%nCr% /;
set pn(p,n);
$onembeddedCode Python:
import itertools
pn = []
for t in zip(gams.get('p'),itertools.combinations(gams.get('n'),%r%)):
  for n in t[1]:
    pn.append((t[0],n))
gams.set('pn',pn)
$offembeddedCode pn
display pn;

-Michael

3

Thank you. Works perfectly.