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Journal Articles Evolutionary Computation Year : 1999

Rigorous hitting times for binary mutations

Josselin Garnier
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Marc Schoenauer


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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Dates and versions

inria-00001277 , version 1 (04-05-2006)


  • HAL Id : inria-00001277 , version 1


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