A new Markov chain analysis for a GA using symbolic representation

A new Markov chain model for a GA using symbolic representation (SymGA) is proposed. Based on the newly proposed Markov chain model, the search behavior of the SymGA is explained. As long as the mutation operator is employed, our Markov chain for the SymGA is regular. Using this model, we show that the stochastic search behavior of the SymGA is independent of the initial population, and the SymGA converges to the optimal state with a certain probability as the number of trials increases