The genetic algorithm is a kind of searching method which simulates the natural evolution. It is simple and easy to implement, especially it do not need the special field knowledge, so it has been using in very broad fields. Now the genetic algorithm has got a lot of fruits and more scholars begin to pay attention to it.The genetic algorithm is still a new technology being in the development. Despite its success in so many domains, its theoretical groundwork is weak. There are still lots of problems to study and develop.This paper has done some work in the researching of theory and application of the genetic algorithm. Fist, the schemata theorem is studied and the effort of enlarging the applied scope of the theorem is done. Second, based on the study of the basic structure of the genetic algorithm, some improvement is given: two new concept, reproducing population and competing population, are put forward and the relative evolution strategies are given. All above done, the paper gives a new framework of the genetic algorithm. A current genetic algorithm which is called TNGA is also given in the paper. Subsequently, the paper proves the convergenceof TNGA using the functional analysis. Finally, the paper use TNGA to solve the CTSP problem. At the same time, the paper also uses the genetic algorithm to solve the DCPM problem.
