0001, 0100,0011,1100
0000
1101, 0111, 1111, 0101
1011, 1110, 1001, 0110
1010
0010, 1000
Lecture 17: 03/28/2007
Recall:
<Missed>
Specialize this to case where
Q={representative in P(t) of some schema H}
=
∩ ( )
H P t
True that Prob{some element of Q slected as a parent on any one pick}=
∈
( )
x Qpsel x
Question
: given that Hrepresentatives exist in P(t), how many on average will exist in P(t+1)?
Genetic
operators operating on either create or destroy
instances of Hor both, or neither.
If you have an H
member parent:
Prob{at least one of its offspring is an Hmember}
≥
(Prob(crossover doesn’t damage))(Prob(mutation
doesn’t damage))
Prob(no crossover damage)
≥
Prob(crossover point doesn’t fall in defining length) =

( ) 
1 pcd H L 1
where d(H) = defining length of H.
Prob(no mutation damage) = prob(no fixed bits in H flipped)=(1p
m
)
o(H)
where o(H)=order
of H
=#(fixed bits in H)
Hence, prob that any given parent in
∩ ( )
H P t
will have at least one offspring in
∩ ( )
H P t
will have at least
one offspring in H is
≥ 
 ( 
) ( )
1 pcdHL 1 1 pm o H
Use this to calculate a lower bound
on 
∩
+
H Pt 1
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 Spring '07
 DELCHAMPS
 Algorithms, Holland, PROB, phenotype space

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