Local convergence of general genetic algorithms using dynamical method

Beyond analyzing the detail proved in bypast job, the theorem, the existence of local peak in general form of genetic algorithm, is proved. It is pointed out that a lot of selection and crossover operators can satisfy the conditions in this proof. For other familiar selection strategies, such as, linear ranking, exponential ranking and tournament, the model is constructed under finite population. So, the formula of operator effect under infinite population can be calculated by the limiting of finite model. The existence and convergence of local peak with these selection strategies are proved. Simultaneously, it is proved that the linear ranking selection strategy is irrelevant to strategy parameter. This strategy is equivalent to tournament selection which size is 2.