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Define the fitness f of bit string x with length m = 4, to be the...

Define the fitness f of bit string x with length m = 4, to be the integer represented by the binary number x,( eg. f(0011)=3, f(1111)=15). What is the average times of the schema **1* under f? What is the average fitness of schema *0** under f?

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Answer #1

Thr average times of the schema **1* under f = 8 / 16 =0.5 # the f(**1*) = 2,3,6,7,10,11,14,15 - total 8 numbers

# the total bit strings with length 4 is 16

# so answer is f(**1*) / 16

For the schema (*0**) the instances have the fitness values 0,1,2,3,8,9,10,11

which yield an average fitness of f (0 * * *) = (0+1+2+3+8+9+10+11) / 8 = 5.5

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