Abstract: There has been a growing interest in mathematical models to character the evo- lutionary algorithms.The best-known one of such models is the axiomatic model called the abstract evolutionary algorithm(AEA),which unifies most of the  currently known evolu- tionary algorithms and describes the evolution as an abstract stochastic process composed of two fundamental abstract operators:abstract  selection  and  evolution  operators.In this paper,we first introduce the definitions of the generalized abstract selection and evolution operators.Then we discuss the characterizatlon of some parameters related to generalized abstract  selection  and  evolution  operators.Based  on  these  operators,we  finally  give  the strong convergence of the generalized abstract evolutionary algorithm. The present work provides a big step toward the establishment of a unified theory of evolutionary computa- tion.

Key words: selection , operators;evolution , operators;evolutionary , algorithm;strong , con-
vergence