The global convergence is one of the important features of an intelligent algorithm. In this paper

we take the initiative to handle the convergence of Grey Wolf Optimization (GWO) with Markov chain. Firstly

a Markov chain model of the GWO algorithm is established through defining the state transition sequence of a gray wolf population. Analyzing the properties of the Markov chain proves that it is homogeneous finite. Secondly

based on the convergence criteria of random search algorithms

the global convergence of the GWO algorithm is verified via analyzing the final state transition sequence of the grey wolf population. Finally

simulation studies on typical testing functions

shifting functions and rotating functions are carried out comparing with a few typical swarm intelligent algorithms. The experimental results show that the GWO algorithm has excellent performance on the global convergence

the computational time and precision of optimization.