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Evolutionary Computation

Summer 2015, Vol. 23, No. 2, Pages 217-248
(doi: 10.1162/EVCO_a_00130)
© 2015 Massachusetts Institute of Technology
Fitness Probability Distribution of Bit-Flip Mutation
Article PDF (398.66 KB)

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.