数学季刊 ›› 2003, Vol. 18 ›› Issue (2): 213-220.
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摘要： There has been a growing interest in mathematical models to character the evolutionary algo- rithms.The best-known one of such models is the axiomatic model colled the abstract evolutionary al- gorithm.In this paper,we first introduce the definitions of the abhstract selection and evolution opera- tors,and that of the abstract evolutionary algorithm,which describes the evolution as an abstract sto- chastic 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.
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