Random noise perturbs objective functions in many practical problems,and genetic algorithms (GAs) have been widely proposed as an effective optimization tool for dealing with noisy objective functions.However,little papers for convergence of genetic algorithms in noisy environments (GA-NE) have been published.In this paper,a Markov chain that models elitist genetic algorithms in noisy environments (EGA-NE) was constructed under the circumstance that objective function is perturbed only by additive random noise,and it was proved to be an absorbing state Markov chain.The convergence of EGA-NE was proved on the basis of the character of the absorbing state Markov chain.
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