The Convergence of the Abstract Evolutionary Algorithm Based on a Special Selection Mechanism  

作　　者：BIYong-qing XUEMing-zhi 

机构地区：[1]DepartmentofMathematics,ShangqiuNormalCollege,Shangqiu47600,China [2]KeyLabforRadarSignalProcessing,XidianUniversity,Xi‘an710071,China

出　　处：《Chinese Quarterly Journal of Mathematics》2003年第2期213-220,共8页数学季刊（英文版）

基　　金：Supported by the National Science Foundation of China(60133010);Supported by the Science Foundation of Henan Province(2000110019)

摘　　要：There has been a growing interest in mathematical models to character the evolutionary algorithms. The best-known one of such models is the axiomatic model colled the abstract evolutionary algorithm. In this paper, we first introduce the definitions of the abhstract selection and evolution operators, and that of the abstract evolutionary algorithm, which describes the evolution as an abstract stochastic process composed of these two fundamental abstract operators. In particular, a kind of abstract evolutionary algorithms based on a special selection mechansim is discussed. According to the sorting for the state space, the properties of the single step transition matrix for the algorithm are anaylzed. In the end, we prove that the limit probability distribution of the Markov chains exists. The present work provides a big step toward the establishment of a unified theory of evolutionary computation.

关 键 词：abstract evolutionary algorithm a transition matrix CONVERGENCE 

分 类 号：O242.23[理学—计算数学]