基于萤火虫算法的Markov模型及收敛性分析

摘要

为完善萤火虫算法（FA ）的收敛性理论，本文就萤火虫算法（FA ）建立了M arkov链数学分析模型。通过分析该M arkov 链的性质，证明萤火虫位置的群体状态序列是有限齐次 M arkov链；通过分析萤火虫位置的群体状态转移过程，得到群体状态序列必将进入最优状态集的结论；然后证明萤火虫算法满足随机优化算法全局收敛的两个条件 C1和 C2，从而保证萤火虫算法全局收敛。在此基础上，通过几个典型测试函数对萤火虫算法的全局收敛性进行数值实验，验证了萤火虫算法的全局收敛性。%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 homoge‐neous 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 op‐timal 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 experi‐ments w ere used to demonstrate that firefly algorithm can indeed achieve global optimality efficiently , and the global convergence is ensured .