Can the schema theorem make long-term predictions about schema propagation?
David B. Fogel · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
The schema theorem describes the expected proportion of a particular schema at the next generation in an evolutionary algorithm given the current proportion of that schema, its realized fitness, and the mean fitness of all extant solutions (ignoring the effects of variation operators). Simple iterative analysis of this relationship, extrapolated over successive generations, has led to a claim that the use of proportional selection generates an exponentially increasing proportion of schemata that are of above-average fitness. This paper shows that this claim is not correct, and moreover that iterating the expectations derived from the schema theorem leads to erroneous predictions about schemata propagation even in the simplest problems and even when iterated over only two generations.