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

there are few theoretical studies for the convergence and the convergence speed of genetic algorithms in noisy environments (GA-NE).In this study

Objective functions are assumed to be perturbed by additive random noise.We construct a Markov chain that models elitist-worst genetic algorithms in noisy environments (EWGA-NE).Then the convergence of EWGA-NE is deduced based on the absorbing state Markov chain.Next

the convergence rate of EWGA-NE was studied.The upper and lower bounds for the number of iterations that EWGA-NE selects a globally optimal solution were derived.