关键词: 萤火虫算法, 收敛分析, 局部收敛

Abstract: The purpose of this paper is to analyze the firefly algorithm (FA) systematically. Firstly, two general convergence conditions are obtained by analyzing the convergence process of FA. One is that mathematical expectation of random disturbance term is equal to 0, the other is that maximum attractiveness value β₀ belongs to (0,2), and usually belongs to (0,1], and the more β₀ value, the faster convergence speed. Nextly, according to the criterion of convergence of random algorithm, this paper proves that the FA is not a globally convergent algorithm. Then, this paper theoretically proves that the FA converges to the local optimal solution by using mathematical induction, sandwich theorem and apagoge. Finally, the convergence processes of FA under different conditions are simulated. The experimental results agree well with the theoretical results and prove the correctness of the theory analysis.

Key words: firefly algorithm, convergence analysis, local convergence