<br><font size=2 face="sans-serif">Philip,</font>
<br>
<br><font size=2 face="sans-serif">I said I would play about with your
problem and report on what I did and how I went about it :</font>
<br>
<br><font size=2 face="sans-serif">All these experiments were with stand
alone solver - SOS is a bit trickier and I will get to that later. Also
symmetry breaking would help but I would need help in CglPreProcess and/or
pointers to relevant papers.</font>
<br>
<br><font size=2 face="sans-serif">The first thing to do is solve the problem
however slowly and look at log and solution. Using defaults this
took 1148 seconds and 150K nodes. Looking at the log file it looked
as if strong branching was not buying very much. What was more interesting
was that all variables took integer values although only half were declared
integer. Assuming this would always be true I tried setting them
all integer. This time strong branching was kicking in and it took
5K nodes and 413 seconds. I also saw that cuts and heuristics were
not doing much good so switched them off. </font>
<br>
<br><font size=2 face="sans-serif">Again looking at log I saw that Cbc
could work out that valid objective values had to be a multiple of 0.1
so any solution has to be 0.1 better than previous. Going back to
original formulation and setting that value of 0.1 gave 31K nodes
but 305 seconds. Finally in this phase of tuning I tried switching
off strong branching as my hunch was that it might cost too much for the
effect gave an increase in nodes to 38K but the time dropped to 233 seconds.</font>
<br>
<br><font size=2 face="sans-serif">Further ideas such as just having some
(but not the original set) variables integer gave various perturbations
on time and nodes but no significant improvement.</font>
<br>
<br><font size=2 face="sans-serif">I have started looking at SOS possibilities
but am not far along. </font>
<br>
<br><font size=2 face="sans-serif">Basically I use multiple runs and an
editor and grep to try and get a feel for problem.</font>
<br>
<br><font size=2 face="sans-serif">John Forrest</font>