simplifying algebraic expressions
DavidM
nospam at nowhere.com
Tue Jun 26 23:56:38 CEST 2007
On Tue, 26 Jun 2007 04:22:23 -0700, Mark Westwood wrote:
> I'm with Robin Becker on this one, if GP is good enough for your
> problem, then the answers it produces should be good enough. Set the
> fitness criteria in favour of shorter rather than longer expressions
> and let you system run a little longer.
Thanks for your comments.
I tried this and came up with some very interesting results.
In the fitness function, I added a multiplier:
badness *= numnodes
Where 'badness' is the calculated fitness (always >0, lower is better),
and 'numnodes' is the number of nodes in the program tree.
Result? The population never evolved past a certain point, and problem
never got solved.
So I tried to make the multiplier more gentle:
badness *= math.log(1 + numnodes)
Same result.
Tried even more gentle:
badness *= math.pow(numnodes, 1.0/12)
That is, multiply badness by the twelfth root of the number of nodes.
Population evolved better, but still didn't breed a winning organism.
Finally, I set a threshold, and only punished organisms if they exceeded
this complexity threshold:
if numnodes > threshold:
badness *= math.pow(numnodes - threshold, 1.0/12)
That worked.
Seems that I have to allow a 'punishment free' threshold of complexity,
otherwise the population stagnates.
Cheers
David
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