About the convergence rates of a class of gene expression programming  

作　　者：DU Xin DING LiXin 

机构地区：[1]State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430072, China [2]Department of Information Engineering, Shijiazhuang University of Economics, Shijiazhuang 050031, China

出　　处：《Science China(Information Sciences)》2010年第4期715-728,共14页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 60975050);the Research Fund for the Doctoral Program of Higher Education (Grant No. 20070486081); Advanced Interdisciplinary Studies Foundation of Wuhan University (Grant No. 6081014)

摘　　要：This paper studies the convergence rates of gene expression programming based on maintaining elitist （ME-GEP） by means of Markov chain and spectrum analysis. We obtain the following results： （1） MEGEP algorithm converges to the global optimum in probability. （2） The convergence rates of ME-GEP algorithm depend on the revised spectral radius of transition matrix of Markov chain corresponding to the algorithm. （3） The upper bounds of revised spectral radius are estimated, which are determined by the parameters of ME- GEP algorithm. （4） As an application of the theoretical results acquired in the papers the convergence rates of ME-GEP for the polynomial function modeling problem are also analyzed, which verifies the relations between the convergence rates and the algorithm parameters.This paper studies the convergence rates of gene expression programming based on maintaining elitist （ME-GEP） by means of Markov chain and spectrum analysis. We obtain the following results： （1） MEGEP algorithm converges to the global optimum in probability. （2） The convergence rates of ME-GEP algorithm depend on the revised spectral radius of transition matrix of Markov chain corresponding to the algorithm. （3） The upper bounds of revised spectral radius are estimated, which are determined by the parameters of ME- GEP algorithm. （4） As an application of the theoretical results acquired in the papers the convergence rates of ME-GEP for the polynomial function modeling problem are also analyzed, which verifies the relations between the convergence rates and the algorithm parameters.

关 键 词：GEP ME-GEP convergence rates Markov chain revised spectral radius 

分 类 号：O212.1[理学—概率论与数理统计] TP311[理学—数学]