Parametric Regression Through Genetic Programming

Short Description
netic programming (GP) to rediscover the well-known brachistochrone solution. The. 1. See [1] for an excellent tutorial introduction to genetic programming. …

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Content
Parametric Regression Through Genetic Programming
Edwin Roger Banks, James Hayes, and Edwin Nunez
COLSA Corporation, 6726 Odyssey Drive, Huntsville, AL 35806
{rbanks, jhayes, enunez}@colsa.com
Abstract. Parametric regression in genetic programming can substantially
speed up the search for solutions. Paradoxically, the same technique has difficulty
finding a true optimum solution. The parametric formulation of a problem
results in a fitness landscape that looks like an inverted brush with many bristles
of almost equal length (individuals of high fitness), but with only one bristle
that is very slightly longer than the rest, the optimum solution. As such it is
easy to find very good, even outstanding solutions, but very difficult to locate
the optimum solution. In this paper parametric regression is applied to a minimum-
time-to-target problem. The solution is equivalent to the classical brachistochrone.
Two formulations were tried: a parametric regression and the classical
symbolic regression formulation. The parametric approach was superior without
exception. We speculate the parametric approach is more generally applicable
to other problems and suggest areas for more research.
1 Introduction
Mathematicians sometimes use parametric formulations of expressions. Rather than
write y(x), for example, they would write y(t) and x(…