Lecture ??+1: 04/11/2007
Recall:
No Free Lunch theorems.
Two views (with warning that it’s not totally settled how
they apply to evolutionary alogirthms.)
Warning to exercise caution when applying these
theorems.
Bottom Line:
the behavior of GAs, etc. behaves in a complicated way on the interplay
between encoding, genetic operators, fitness function.
Need to “make sense” together for
the problem.
Price’s Theorem:
One theoretical attempt (promising but not “finished) at isolationg “makesense” idea:
Price’s Theorem
from population genetics.
Essentially if you have a “numerical
observable” on a population (like fitness, etc.) if it exhibits high positive (or negative)
correlation between the value on a set of parents and value on a set of offspring, then
evolution will show a marked tendency to increase
(decrease) value of observable as it
proceeds.
“correlation” in Price’s Theorem <==> interplay between encoding, fitness, genetic operators
D’champs Idea
: might try to design encodings to make the “Price correlation” large.
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 Spring '07
 DELCHAMPS
 Algorithms, Evolution, Game Theory, Fitness landscape, Free Lunch theorems, genetic operators

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