We use these functions to provide theoretical evidence that traditional GAs use mutation more effectively than crossover, but dispute claims that mutation is a better search mechanism than crossover. To the contrary we show that methods that exploit crossover more effectively can be designed and give evidence that these are powerful search mechanisms. Experimental results using GIGA, the Gene Invariant Genetic Algorithm, and the well known GENESIS program support these theoretical claims.
Finally, this paper provides the initial approach to a different method of analysis of GAs that does not depend on schema analysis or the notions of increased allocations of trials to hyperplanes of above average fitness. Instead it focuses on the search space structure induced by the operators and the effect of a population search using them.