An analysis on convergence and convergence rate estimate of elitist genetic algorithms in noisy environments

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 and convergence speed 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, its convergence rate was analyzed, and its upper and lower bounds for the iteration number expectation were derived when EGA-NE first gets a globally optimal solution.