Using the Markov chain of the best individual to analyze convergence of genetic algorithms

The convergence analyses of genetic algorithms by applying the Markov chains of populations usually depend on the representation of solutions. This paper models the homogeneous finite Markov chain of the best individual in populations, and presents a precise definition of the global convergence of genetic algorithms according to the limit distribution of the chain. Two unified decision theorems about the global convergence are proposed and proved strictly, which are independent of representation and selection mechanism. The results of analysing the convergence of different genetic algorithms illustrate that the unified decision theorems are generally practical.