Rigorous Hitting Times for Binary Mutations

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Rigorous Hitting Times for Binary Mutations (1999)

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by Josselin Garnier , Leila Kallel , Marc Schoenauer

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@MISC{Garnier99rigoroushitting,
    author = {Josselin Garnier and Leila Kallel and Marc Schoenauer},
    title = {Rigorous Hitting Times for Binary Mutations},
    year = {1999}
}

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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. Keywords Evolutionary algorithms, stochastic analysis, binary mutations, Markov chains, hitting times. 1 Introduction One known drawback of Evolutionary Algorithms as function optimizers is the amount of computational efforts they re...

Keyphrases

binary mutation rigorous hitting time computational effort multiple independent optimizers distinct situation keywords evolutionary algorithm e selection statistical distribution mutation operator function optimizers 1-bit-flip mutation onemax problem standard mutation binary evolutionary optimization framework 1-bit-flip mutation convergence time evolutionary algorithm markov chain stochastic analysis multiplicative factor

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