Cognitive Science, Hampshire College
David M. Clark
Mathematics, SUNY New Paltz
This page contains material related to "Genetic Programming for
Finite Algebras," a paper in
the Proceedings of
the Genetic and Evolutionary Computation Conference (GECCO-2008),
published by The Association of Computing Machinery.
The work reported in this paper was
awarded the gold medal in the Human Competitive Results contest at the
2008 Genetic and Evolutionary Computation Conference (press release).
We describe the application of genetic programming (GP) to a problem in pure mathematics, in the study of finite algebras. We document the production of human-competitive results in the discovery of particular algebraic terms, namely discriminator, Pixley, majority and Mal'cev terms, showing that GP can exceed the performance of every prior method of finding these terms in either time or size by several orders of magnitude. Our terms were produced using the ECJ and PushGP genetic programming systems in a variety of configurations. We compare the results of GP to those of exhaustive search, random search, and algebraic methods.
Spector, L., D. M. Clark, I. Lindsay, B. Barr, and J. Klein. 2008, in press. Genetic Programming for Finite Algebras. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2008). ACM Press.
Full paper in PDF format: http://hampshire.edu/lspector/pubs/gpfa-gecco-2008.pdf (192KB).
Prepared for the GECCO 2008 conference: http://hampshire.edu/lspector/gpfa-gecco-2008/slides.pdf (1.3MB).
We thank our anonymous reviewers for thorough and constructive criticism. This material is based upon work supported by the National Science Foundation under Grant No. 0308540. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.