A new approach to dynamics analysis of genetic algorithms without selection

Theoretical analysis of the dynamics of evolutionary algorithms is believed to be very important to understand the search behavior of evolutionary algorithms and to develop more efficient algorithms. We investigate the dynamics of a canonical genetic algorithm with one-point crossover and mutation theoretically. To this end, a new theoretical framework has been suggested in which the probability of each chromosome in the offspring population can be calculated from the probability distribution of the parent population after crossover and mutation. Empirical studies are conducted to verify the theoretical analysis. The finite population effect is also discussed. Compared to existing approaches to dynamics analysis, our theoretical framework is able to provide richer information on population dynamics and is computationally more efficient