The convergence of artificial bee colony algorithm is analyzed theoretically by using the stochastic process theory.
Some mathematical definitions of artificial bee colony algorithm and one step transition probability of nectar source position
are given and the Markov chain model of the algorithm is established. Some properties of the Markov chain are analyzed,
and the conclusions that the artificial bee colony state sequence is a finite homogeneous of Markov chain and the state space
of artificial bee colony is irreducible are obtained. It is proved that the artificial bee colony algorithm ensures the global
convergence as the algorithm meets two assumptions of the random search algorithm for the global convergence.