The Isomorphism Theorem of Partheno-genetic Algorithm and Traditional Ggenetic Algorithm

Partheno-Genetic Algorithm (PGA) repeals crossover operators of Traditional Genetic Algorithm (TGA) while uses the reproduction manner with only parent. Comparing with TGA, the genetic operation of PGA is simpler; the initial population of PGA need not be varied; there is no "immature convergence" during using PGA; the searching efficiency of PGA is higher. As PGA uses the reproduction manner with only parent while no using the reproduction manner with double parents as such most of the biology, most of the scholar thinks that PGA does not belong to the category of genetic algorithms. In this paper, based on concept of abstract system, two abstract systems, PGA and TGA are constructed and it is proved that the two abstract systems are isomorphic, so PGA has the same computing mechanism as TGA, that is to say, PGA belongs to the category of genetic algorithms as TGA.