Re: Non dominating queens problem

TS wrote:

Place N Queens on an N*N board leaving a maximum number of unattacked
cells.

any idea? 

I have implemented it, but nothing fancy, so I am a bit unwilling to
post code. The problem is that apart from some obvious and general
improvements to generate&test, I can't find anything more intelligent
to solve this problem. Still, here are the results (so far):

N  max #unattacked fields     msecs
1            0
2            0
3            0
4            1                   20
5            2                   20
6            4                  140
7            6                 1990
8           11                 8000
9           18                23200
10          20               537110
11          30              1137280
12          36             10241570
13
14
15
16        >= 82           (still running)

My attempt was purely Prolog - if someone tried a CLP formulation,
please tell us about it and your experience.
If someone has some (proven) insights in how to reduce the search space
drastically, please let us know !

BTW, I tried 16 early on because I thought I had a good lower bound for
values of N that are of the form i^2 - but I was quite wrong, as for
N=16, my lower bound was 64 ... way off the already attained 82 :-(

Cheers

Bart Demoen
.