Theoretical Investigation on the Generalized Crossover Operator

As described in [Col 96], classical single point crossover (SPC) can be implemented through a sequence of mathematical operations; generalization of such a mathematical description originates the generalized crossover (GC). In this paper, after a brief recall to GC, we perform either a theoretical or experimental investigation of its properties. The first theoretical result we present is an expression which describes, as a function of the string length and of a parameter characteristic of GC (the GC base), the relation between GC and SPC. The second result, obtained through extensive computer simulations, describes the distribution of the sons generated by GC. Such a result is useful to explain the good behavior of GC. Finally, some comparative results between GC and BLX-a crossover [Esh 92] are presented.