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J. Garnier
L. Kallel
M. Schoenauer
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 {em 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 {em 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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