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5
Numerical Constants
and the GEP-RNC Algorithm
Numerical constants are an integral part of most mathematical models and,
therefore, it is important to allow their integration in the models designed by
evolutionary techniques.
We know already that evolutionary algorithms handle functional building
blocks somewhat unconventionally. So, it is not surprising that the simplest
of all mathematical building blocks - numerical constants - can also be han-
dled somewhat unconventionally.
In this chapter we are going to discuss different methods of handling nu-
merical constants in evolutionary computation, using gene expression pro-
gramming as a framework. We will start by introducing the simpler forms of
handling numerical constants, followed by a detailed description of the GEP-
RNC algorithm (GEP with the facility for handling random numerical con-
stants) and all its components. The chapter finishes with a case study in
which three different approaches to the problem of constants' creation are
compared on four different problems: two simple computer generated prob-
lems and two real-world problems from two different fields (disease diagno-
sis and analog circuit design).
5.1 Handling Constants in Automatic Programming
It is assumed that the creation of floating-point constants is necessary to
design mathematical models using evolutionary techniques (see, e.g., Koza
1992 and Banzhaf 1994). Most of these techniques, however, use the simple
approach of using a fixed set of numerical constants that are then added to
the terminal set, as no special facilities for handling random numerical con-
stants were developed. But Koza also implemented a special facility for han-
dling random numerical constants in genetic programming (Koza 1992). For
