A Free Lunch Proof for Gray versus Binary Encodings

A measure of complexity is proposed that counts the number of local minima in any given problem representation. A special class of functions with the maximum possible number of optima is also deened. A proof is given showing that reeected Gray code induce more optima than Binary over this special class of functions; by the No Free Lunch principle, reeected Gray codes therefore induces fewer optima over all other remaining functions.

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