Hierarchical Crossover and Probability Landscapes of Genetic Operators

The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point crossover operations. This model is solved analytically in the flat fitness case. Numerical simulations compare the way of phase space exploration of different genetic operators. In the case of a non-flat fitness landscape, numerical solutions of the evolution equations point out ways to estimate premature convergence.