Firefly algorithm(referred as FA) is an intelligent optimization algorithm developed by Xin-She Yang at Cambridge University in 2007. Nowadays, Firefly algorithm has been a hot research area in intelligent optimization algorithms, and it is used to deal with optimization problems and engineering optimization problems in our real life. But its theoretical research is proved to be lacking. In this paper, the Markov chain model of the Firefly algorithm is established by analyzing the theory of Firefly algorithm, and it is proved that the Firefly algorithm ensures global convergence. Then an improved algorithm of Firefly algorithm has been put forward, and been used to deal with the objective function optimization problem. The researches in this paper are as follows:1ã€The theory of intelligent optimization algorithm, and its development process and the thinking origin of Firefly algorithm are stated, the basic ideas and steps of Firefly algorithm are introduced, and the status of Firefly algorithm research at home and abroad are reviewed.2ã€A deep mathematical analysis is made for Firefly algorithm respectively from macroscopic and microscopic views. First, a strict mathematical descriptions is given for the basic conception of Firefly algorithm,with the definition of Firefly position state, Firefly state space position and so on. Second, the Firefly state transition equation has proved to be a Markov chain process, and the Markov chain model of Firefly algorithm is established. Finally, the convergence of the Firefly algorithm is analyzed using the Markov chain theory. The paper proves the convergence of Firefly algorithm.3ã€Firefly algorithm has some disadvantages that need to be improved, for instance: algorithmâ€™s premature convergence, easy to fall into local optimum. Considering these advantages, Gaussian disturbance is added to the position of the firefly in the iterative process, and a Firefly algorithm based on Gaussian disturbance(referred as GFA) is proposed in the paper. The Firefly algorithm based on Gaussian disturbance and the Firefly algorithm are compared and analyzed by carrying out numerical experiments for 12 test functions. The simulation results show that the Firefly algorithm based on Gaussian disturbance is better than the Firefly algorithm.4ã€The Firefly algorithm based on Gaussian disturbance is applied to deal with the function optimization problem. |