- author = "Lee Altenberg",
- year = "1994",
- title = "The {Schema} {Theorem} and {Price}'s {Theorem}",
- booktitle = "Foundations of Genetic Algorithms 3",
- editor = "L. Darrell Whitley and Michael D. Vose",
- publisher = "Morgan Kaufmann",
- publisher_address = "San Francisco, CA, USA",
- address = "Estes Park, Colorado, USA",
- pages = "23--49",
- month = "31 " # jul # "--2 " # aug,
- organisation = "International Society for Genetic Algorithms",
- note = "Published 1995",
- keywords = "genetic algorithms, genetic programming",
- ISBN = "1-55860-356-5",
-
URL = "
http://dynamics.org/~altenber/PAPERS/STPT/",
-
URL = "
http://dynamics.org/Altenberg/FILES/LeeSTPT.pdf",
-
DOI = "
doi:10.1016/B978-1-55860-356-1.50006-6",
-
abstract = "Holland's Schema Theorem is widely taken to be the
foundation for explanations of the power of genetic
algorithms (GAs). Yet some dissent has been expressed
as to its implications. Here, dissenting arguments are
reviewed and elaborated upon, explaining why the Schema
Theorem has no implications for how well a GA is
performing. Interpretations of the Schema Theorem have
implicitly assumed that a correlation exists between
parent and offspring fitnesses, and this assumption is
made explicit in results based on Price's Covariance
and Selection Theorem. Schemata do not play a part in
the performance theorems derived for representations
and operators in general. However, schemata re-emerge
when recombination operators are used. Using
Geiringer's recombination distribution representation
of recombination operators, a ``missing'' schema
theorem is derived which makes explicit the intuition
for when a GA should perform well. Finally, the method
of ``adaptive landscape'' analysis is examined and
counterexamples offered to the commonly used
correlation statistic. Instead, an alternative
statistic---the transmission function in the fitness
domain--- is proposed as the optimal statistic for
estimating GA performance from limited
samples.
Copyright 1996 Lee Altenberg",
-
notes = "FOGA-3
Deals with GAs as a whole, not specifically GP.",
