- author = "David White",
- title = "An Overview of Schema Theory",
- howpublished = "arXiv",
- year = "2014",
- month = "12 " # jan,
- keywords = "genetic algorithms, genetic programming",
- volume = "abs/1401.2651",
- eprint = "1401.2651",
-
URL = "
http://arxiv.org/abs/1401.2651",
- timestamp = "Wed, 07 Jun 2017 14:41:41 +0200",
-
biburl = "https://dblp.org/rec/bib/journals/corr/White14",
- bibsource = "dblp computer science bibliography, https://dblp.org",
- size = "27 pages",
-
abstract = "The purpose of this paper is to give an introduction
to the field of Schema Theory written by a
mathematician and for mathematicians. In particular, we
endeavor to to highlight areas of the field which might
be of interest to a mathematician, to point out some
related open problems, and to suggest some large-scale
projects. Schema theory seeks to give a theoretical
justification for the efficacy of the field of genetic
algorithms, so readers who have studied genetic
algorithms stand to gain the most from this paper.
However, nothing beyond basic probability theory is
assumed of the reader, and for this reason we write in
a fairly style.
Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy. Many of these results have been proven elsewhere, so this paper is designed to serve a primarily expository role. We attempt to cast known results in a new light, which makes the suggested future directions natural. This involves devoting a substantial amount of time to the history of the field.
We hope that this exposition will entice some mathematicians to do research in this area, that it will serve as a road map for researchers new to the field, and that it will help explain how schema theory developed. Furthermore, we hope that the results collected in this document will serve as a useful reference. Finally, as far as the author knows, the questions raised in the final section are new.",
- notes = "Some GP theory",
