关于生物免疫遗传算法收敛性的一般讨论研究

General discussion on convergence of immune genetic algorithm

针对免疫遗传算法收敛性质的研究非常缺乏,提出了利用随机过程理论和引入遗传吸收率、散射率参数进行分析的方法.通过数学建模证明了免疫遗传算法所形成的种群序列的强马尔可夫性,利用遗传吸收率和散射率的计算,证明了在时间趋于无穷的情况下,该免疫遗传算法的概率弱收敛性.采用遗传吸收率、散射率和小生境技术对于防治早熟概率的详细计算和对混沌算子的分析,得到了该免疫遗传算法实际收敛效果的量化表示.研究结果表明,该方法能简化分析计算过程,对于算法效果的改善、算法运行时的参数选择具有较好的指向作用.

Aimed at the lack of research on the convergence of immune genetic algorithm （IGA）, two methods using the stochastic process theory and introducing the genetic absorptivity and genetic scattering rate were proposed. The strong Markovian property attributed to the population sequence was deduced by mathematical modelling. By calculating the genetic absorptivity and the genetic scattering rate, the weak convergence in probability of the immune genetic algorithm was proved on the condition that the time tended to infinity. By analyzing the chaos operator and deducing genetic absorptivity, genetic scattering rate and the probability on the prevention to premature by niche the quantitative convergence effect of the immune genetic algorithm was obtained. The results show that the methods can simplify the analysis computation process and are helpful for directing choice of better IGA parameters and improving the performance of the algorithm.