基于随机泛函的免疫进化算法收敛性及性能分析  

The convergence and performance analyses of immune evolutionary algorithm based on stochastic functional theory

作　　者：徐雪松[1,2] 杨胜杰[1] 陈荣元[1] 梁伟 蒋伟进[1] XU Xue-song;YANG Sheng-jie;CHEN Rong-yuan;LIANG Wei;JIANG Wei-jin(Key Laboratory of Hu,nan Province for New Retail Virtual Reality Technology, Hu＇nan University of Commerce, Changsha 410205, China;Mobile E-business Collaborative Innovation Center of Hu＇nan Province, Hu＇nan University of Commerce, Changsha410205, China)

机构地区：[1]湖南商学院新零售虚拟现实技术湖南省重点实验室,长沙410205 [2]湖南商学院湖南省移动电子商务协同创新中心,长沙410205

出　　处：《控制与决策》2018年第6期1100-1106,共7页Control and Decision

基　　金：国家自然科学基金项目(61772196);国家社会科学基金项目(14BJY066);湖南省自然科学基金项目(2016JJ2069)

摘　　要：分析基于免疫响应原理的免疫进化算法流程和运行机制.根据免疫抗体群的状态转移过程,研究免疫进化算法的马尔科夫随机过程,并采用随机泛函分析算法的收敛性,突破传统马尔可夫链方法对解空间较大问题分析的局限性.根据免疫进化算法参数构成和抗体种群达到吸收态的转换特性,采用泛函理论论证算法收敛速度估计、时间复杂度计算和参数选择原则.通过实验总结影响免疫进化算法收敛性的关键因素,为解空间较大及高维优化问题的免疫进化算法收敛性和性能分析提供可行方法.Based on the immune response principle and operation mechanism, an immune evolutionary algorithm is discussed. According to the state transfer process of immune antibodies and Markov stochastic process, the immune evolutional algorithm convergence is analyzed by using the stochastic functional theory, which breaks the flaw of the traditional Markov chain method. The key factors that influencing the convergence rate and parameter selection principle are introduced by using functional theory and immune population state transformation process. Then the operation time complexity and the parameters are discussed through experiment comparison. The conclusion and theory developed in this paper shew new light on various practices and ideas employed by researches for larger and higher-dimensional optimization problem.

关 键 词：随机泛函 免疫响应 进化算法 收敛性 收敛速率 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]