The Markov chain model for the shuffled frog leaping algorithm (SFLA) was established.It was shown that the frog memeplex state sequence containing both the frog states and the current local and the global optimal frog states constructs a homogeneous Markov chain.The transition process of the frog memeplex state sequence was analyzed

and the conclusion that sequence will eventually converges to the optimal state set was drawn.Furthermore

it was proved that the shuffled frog leaping algorithm ensures global convergence as it meets the global convergence criterions of random search algorithms.