Already Moderate Population Sizes Provably Yield Strong Robustness to Noise
arxiv(2024)
摘要
Experience shows that typical evolutionary algorithms can cope well with
stochastic disturbances such as noisy function evaluations.
In this first mathematical runtime analysis of the (1+λ) and
(1,λ) evolutionary algorithms in the presence of prior bit-wise noise,
we show that both algorithms can tolerate constant noise probabilities without
increasing the asymptotic runtime on the OneMax benchmark. For this, a
population size λ suffices that is at least logarithmic in the problem
size n. The only previous result in this direction regarded the less
realistic one-bit noise model, required a population size super-linear in the
problem size, and proved a runtime guarantee roughly cubic in the noiseless
runtime for the OneMax benchmark. Our significantly stronger results are based
on the novel proof argument that the noiseless offspring can be seen as a
biased uniform crossover between the parent and the noisy offspring. We are
optimistic that the technical lemmas resulting from this insight will find
applications also in future mathematical runtime analyses of evolutionary
algorithms.
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