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Rigorous hitting times for binary mutations

Abstract : In the binary evolutionary optimization framework, two mutation operators are theoretically investigated. For both the standard mutation, in which all bits are flipped independently with the same probability, and the 1-bit-flip mutation, which flips exactly one bit per bitstring, the statistical distribution of the first hitting times of the target are thoroughly computed (expectation and variance) up to terms of order l (the size of the bitstrings) in two distinct situations: without any selection, or with the deterministic (1+1)-ES selection on the OneMax problem. In both cases, the 1-bit-flip mutation convergence time is smaller by a constant (in terms of l) multiplicative factor. These results extend to the case of multiple independent optimizers.
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https://hal.inria.fr/inria-00001277
Contributor : Marc Schoenauer <>
Submitted on : Thursday, May 4, 2006 - 4:39:33 PM
Last modification on : Thursday, March 5, 2020 - 6:27:17 PM
Long-term archiving on: : Saturday, April 3, 2010 - 11:18:06 PM

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Josselin Garnier, L. Kallel, Marc Schoenauer. Rigorous hitting times for binary mutations. Evolutionary Computation, Massachusetts Institute of Technology Press (MIT Press), 1999, 7 (2), pp.167-203. ⟨inria-00001277⟩

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