Syntactic Analysis of Convergence in Genetic Algorithms

We use the average hamming distance of a population as a syntactic metric to obtain probabilistic bounds on the time convergence of genetic algorithms. Analysis of a flat function provides worst case time complexity for static functions and gives a theoretical basis to the problem of premature convergence. We suggest simple changes that mitigate this problem and help fight deception. Further, employing linearly computable syntactic information, we can provide upper limits on the time beyond which progress is unlikely on an arbitrary function. Preliminary results support our analysis.