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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 fitnessproportional 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 randomnumber 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 roulettewheel 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
 DELCHAMPS
 Algorithms

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