Markov model and convergence analysis based on firefly algorithm
HU Ting-tin · Basic Sciences Journal of Textile Universities · 2014
In order to perfect the convergence theory of firefly algorithm(FA),the Markov chain model of the firefly algorithm is established.It was shown that the firefly group state sequence containing both the firefly states,the current local and the global optimal firefly states constructs a limited and homogeneous Markov chain by analyzing the property of the Markov chain.The transition process of the firefly group state sequence was analyzed,and the conclusion that sequence will eventually converges to the optimal state set was drawn;and it was proved that the firefly algorithm ensures global convergence as it meets the global convergence criterions of random search algorithms.Furthermore,numerical experiments were used to demonstrate that firefly algorithm can indeed achieve global optimality efficiently,and the global convergence is ensured.