deceptive - 2 Example s Let f (x) = x 2 be the objective...

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1 Problem 2: Deceptive Deceptive Function: Due to the nature of the objective function, very bad strings are generated when good building blocks are combined together. Example: Consider the a 2-bit string whose optimal solution is (1, 1) . The problem arises when the conditions: The lower schemata (0, *) or (*, 0) does not contain the optimal string (1, 1) as an instance and leads the GA away from (1, 1) . ,*) 1 ( ,*) 0 ( or , ) 1 (*, ) 0 (*, ) 0 , 1 ( ) 1 , 1 ( ) 1 , 0 ( ) 1 , 1 ( ) 0 , 0 ( ) 1 , 1 ( f f f f f f f f f f > > > > > s Let’s consider the case with order-1 schema only s The average fitness of a “bad” schema is better than the average fitness of a “good” schema deceptive problem s This will lead GA away from the global objective as the “bad” schema will more likely be selected. One bit deceptive
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Unformatted text preview: 2 Example s Let f (x) = x 2 be the objective function, and we want to find x such that f(x) is maximized. s x is in 3-bit string (L=3) s Obviously, 111 is optimal s If it is an one-bit deceptive problem, one of the following cases is to be fulfiled: ( ) ( ) ( ) ( ) ( ) ( )      < < < * * * * 1 * * * 1 * * * 1 * * f f f f f f (any one condition) Example s It can be computed that (according to the objective function): s f(**0) = [f(000)+f(010)+f(100)+f(110)]/4=14 s f(**1) = [f(001)+f(011)+f(101)+f(111)]/4=21 s Similarly, we have s f(*0*)=10.5 s f(*1*)=24.5 s f(0**)=3.5 s f(1**)=31.5 s Hence, the problem is not deceptive....
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This note was uploaded on 05/01/2011 for the course ELECTRICAL EE5602 taught by Professor Xuequan during the Spring '11 term at City University of Hong Kong.

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deceptive - 2 Example s Let f (x) = x 2 be the objective...

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