Abstract: The theoretical investigation to Evolutionary Algorithms, e. g. convergence analysis, runtime analysis, is currently a hot topic, and the related theoretical results arc few despite many experimental results. I}his paper established a homogeneous Markov process model associated with(1+1)ES .It is proved by means of the theory of Markov process with continuous state that the Markov process associated with(1+1) ES has exponential ergodicity in a class of continuous optimization problem,hence the(1+1)ES can finally converge to the optimal solution with probability 1 when solving such a problem. The proposed analytic approach provides a new thought to the theoretical research of evolutionary algorithms.

Key words: Evolutionary computation, Evolution strategy, Convergence, Continuous optimization, Markov process