Exact computation of the expectation curves of the bit-flip mutation using landscapes theory

Authors:
Francisco Chicano;Enrique Alba
Affiliations:
University of Málaga, Málaga, Spain;University of Málaga, Málaga, Spain
Venue:
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Year:
2011

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Abstract

Bit-flip mutation is a common operation when a genetic algorithm is applied to solve a problem with binary representation. We use in this paper some results of landscapes theory and Krawtchouk polynomials to exactly compute the expected value of the fitness of a mutated solution. We prove that this expectation is a polynomial in p, the probability of flipping a single bit. We analyze these polynomials and propose some applications of the obtained theoretical results.