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Unformatted text preview: ECE 493 HOMEWORK ASSIGNMENT IV Spring 2007 1. Reconcile the two formulas for the expected number of times a specific string x from the current population P ( t ) is picked to be a parent for the “next generation.” Recall that | P ( t ) | = n and that we pick n parents using n independent draws from A where we do the draws according to fitness-proportional selection. That is, for each of the n draws, the probability that we select x that draws is given by p sel ( x ) = f ( x ) P y ∈ A f ( y ) , where f is the fitness function. The two formulas to reconcile for the expected number of times x gets picked are • np sel ( x ) • P n k =0 ` n k ´ kp k sel ( x )(1- p sel ( x )) n- k You might want to use k n ` n k ´ = ` n- 1 k- 1 ´ (please show this to be true) and also P m r =0 ` m r ´ a r b m- r = ( a + b ) m . 2. Suppose you have a random-number generator that gives you random numbers dis- tributed uniformly on the interval [0 , 1]. (Note: MATLAB has one of those built in.) Design a way to implement roulette-wheel selection using it. (Suggestion: suppose you have a population of three strings with fitnesses 3, 7, and 11. Their respective probabilities of being selected as parents are 1...
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This note was uploaded on 02/01/2010 for the course ECE 496 taught by Professor Delchamps during the Spring '07 term at Cornell University (Engineering School).
- Spring '07