Theoretical Bounds for Genetic Algorithms

Abstract

We investigate various properties of Genetic Algorithms. We present 1) a result which highlights the potential existence of long-run crossover and mutation bias in a GA, together with a partial avoidance strategy based on mutation operators, 2) an analysis of GA premature convergence, which indicates the advantage of larger populations, 3) an application of the theory of metric spaces which describes an intrinsic smoothness property of GA populations and highlights the safety in numbers principle and 4) a lower bound on the convergence rate of a mutation-crossover GA. The models presented are generally independent of solution encoding and are thus applicable to a wide range of Genetic Algorithms.