关于遗传规划收敛性的一个定理

遗传规划是一种通过进化程序来得到问题近似或精确的方法，讨论遗传规划的收敛性质，证明在采用生长法变异算子的条件下遗传规划搜索有限的文法树空间的收敛性的一个 并证明如果不采用最优个体保留策略则遗传规划是不收敛的，最后指出在遗传规划中使用变异算子的理论的实际意义。

A Theorem on the Convergence of Genetic Programming

Genetic Programming is a method for evolving functions that find approximate or exact solutions to problems. Although it has been successfully applied in many practical domains, its theoretical foundation is very weak. In this paper ,the authors discuss the convergence property of genetic programming ,and prove that, under adopting some mutation operations called growing method mutation , the genetic programming will converge when it searches a finite parse tree space, and then ,the authors prove that without the best individual preservation strategy the genetic programming will not converge. Finally, it is pointed out that there is great significance in theory and practice for some type of mutation operators.