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(a) Given the following fitness values of points, find the number of local optima (assume minimization) under (a) the standard decimal (base 10) representation, (b) the standard binary, and (c) the binary-reflected Gray representation (using 3 bits, that is a 3-dimensional bit-space for both (b) and (c)). Assume the standard encoding scheme used in class (e.g., integer 3 in decimal encoding = string 010 in 3-bit Gray encoding = string 011 in 3-bit binary encoding). Decimal integers 0 through 7 have the corresponding fitness values 5, 10, 15, 30, 25, 2, 40, 20. (b) Argue which of the three encoding schemes (integer, conventional binary, and Gray) would be likely to make it easier for an EA to succeed on this particular problem.
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