A Note on the Escape Probabilities for Two Alternative Methods of Selection Under Gaussian Mutation

All methods of evolutionary computation employ a mechanism for selecting which solutions in a population should be retained to serve as the basis for generating further samples. A variety of selection procedures have been offered: proportional selection (Holland, 1975), tournament selection (Fogel, 1988; Goldberg 1990), the so-called "plus" and "comma" methods of evolution strategies (Bäck and Schwefel, 1993), and so forth. The choice of which selection mechanism to employ has traditionally been based on empirical trial-and-error or mathematical analysis of the time required for a single solution to dominate a population (takeover time) (Goldberg and Deb, 1991; Bäck, 1994; Fogel and Fogel, 1995). Although this latter analysis provides a framework for studying the stringency of different selection procedures, it does not in general provide information concerning the probability of discovering improved solutions because it omits the interaction between variation and selection (it focuses only on selection). In attempting to gain insight into the choice of selection operator, it may be more productive to move toward an analysis that explicitly incorporates the interaction of these two fundamental facets of evolutionary computation.