Texas College Mathematics Journal

Vol. 3 (2006), pp. 10-26.

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*A Genetic Algorithm for Drawing Ordered Sets*

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Brian Loft and John Snow

**MSC (1991):** Primary 68W20; Secondary 06A06

**Key words**: genetic algorithm, ordered set

**Abstract**: An order relation is a binary relation which is reflexive,
antisymmetric, and transitive. Order relations occur naturally in many areas of
mathematics (two basic examples are the ordering of the real numbers and the
subset relation). The structure of a small set with an order relation can often
be completely described by drawing a diagram called a Hasse diagram.

A
genetic algorithm is a problem solving technique which treats potential
solutions to a problem as biological lifeforms which compete and reproduce in a
process similar to natural selection in hopes of generating an acceptable
solution.

In this manuscript, we introduce the basics of genetic
algorithms and develop a genetic algorithm for drawing Hasse diagrams of ordered
sets.

Department of Mathematics and Statistics, Sam Houston State University,
Huntsville, Texas 77341-2206

E-mail address: loft@shsu.edu , jsnow@shsu.edu

Received by Editor: August 22, 2005 and in revised form January 31,
2006.

Posted: February 3, 2006.

© Copyright 2006