Program Component Schema Theories

Since John Holland’s work in the mid-1970s and his well known schema theorem [Holland, 1975, Goldberg, 1989b], schemata are often used to explain why genetic algorithms work. Schemata are similarity templates representing entire groups of chromosomes. The schema theorem describes how schemata are expected to propagate generation after generation under the effects of selection, crossover and mutation. The usefulness of schemata has been recently criticised (see for example [Altenberg, 1995, Macready and Wolpert, 1996, Kargupta, 1995, Kargupta and Goldberg, 1994]) and many researchers nowadays believe that Holland’s schema theorem is nothing more than a trivial tautology of no use whatsoever (see for example [Vose, 1999, preface]). However, as stated in [Radcliffe, 1997], the problem with Holland’s schema theorem is not the theorem itself, rather its over-interpretation.