Looking Beyond Selection Probabilities: Adaptation of the χ² Measure for the Performance Analysis of Selection Methods in GAs

Viewing the selection process in a genetic algorithm as a two-step procedure consisting of the assignment of selection probabilities and the sampling according to this distribution, we employ the χ² measure as a tool for the analysis of the stochastic properties of the sampling. We are thereby able to compare different selection schemes even in the case that their probability distributions coincide. Introducing a new sampling algorithm with adjustable accuracy and employing two-level test designs enables us to further reveal the intrinsic correlation structures of well-known sampling algorithms. Our methods apply well to integral methods like tournament selection and can be automated.