Though cultural algorithms have been applied to many optimization problems in various fields, there lakes
the theory analysis related to the convergence performance of these algorithms. Therefore, aiming at traditional cultural
algorithms, the search process of cultural algorithm is analyzed by means of finite Markov chains. Furthermore, the
probability distribution of population in decision spaces is deeply studied by making use of the axiomatic model. It is proved
that cultural algorithms quasi-converge to the optimal solution in probability under the guidance of normative knowledge,
topographical knowledge and situational knowledge in belief space.