032807 - Lecture 17 Recall Specialize this to case...

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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 H-representatives exist in P(t), how many on average will exist in P(t+1)? Genetic operators operating on either create or destroy instances of H-or both, or neither. If you have an H- member parent: Prob{at least one of its offspring is an H-member} (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)=(1-p 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| (# H members in P(t+1)): Prob{H member is picked as a parent on any pick}=
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