生物免疫遗传算法的几乎处处强收敛性分析及收敛速度估计

The Analysis on Strong Convergence(a.s.) and Convergence Rate Estimate of Immune Genetic Algorithm

本文引入鞅方法和通过对免疫算子的研究,分析了生物免疫遗传算法所形成种群的鞅性质并由此得出了算法本身的几乎处处强收敛性结论.另外,还针对免疫优化算法的收敛速度展开研究,给出了结合算法参数的定量表达式,然后还就不同参数对算法收敛速度的的影响效果展开讨论,为明确如何更好改善算法效能的方向起到了一定的作用.

In this paper,by the introduction of martingale and the study of immune operators,the martingale characteristic of the population related to the Immune Genetic Algorithm （IGA） was analyzed. Then the strong convergence （a. s. ） of IGA is deduced with lemmas.Next,the convergence rate of IGA was studied and the quantitative expression that relates to many parameters in IGA is presented. The discussion about the effect of different parameters on the convergence rate was carried out, which will be helpful to improve the performance of the algorithm.