An Introduction to Genetic Algorithms - Boente

prone to rather arbitrary orderings.
Many−Character and Real−Valued Encodings
For many applications, it is most natural to use an alphabet of many characters or real numbers to form
chromosomes. Examples include Kitano's many−character representation for graph−generation grammars,
Meyer and Packard's real−valued representation for condition sets, Montana and Davis's real−valued
representation for neural−network weights, and Schultz−Kremer's real−valued representation for torsion
angles in proteins.
Holland's schema−counting argument seems to imply that GAs should exhibit worse performance on
multiple−character encodings than on binary encodings. However, this has been questioned by some (see,
e.g., Antonisse 1989). Several empirical comparisons between binary encodings and multiple−character or
real−valued encodings have shown better performance for the latter (see, e.g., Janikow and Michalewicz
1991; Wright 1991). But the performance depends very much on the problem and the details of the GA being
used, and at present there are no rigorous guidelines for predicting which encoding will work best.
Tree Encodings
Chapter 4: Theoretical Foundations of Genetic Algorithms
Tree encoding schemes, such as John Koza's scheme for representing computer programs, have several
advantages, including the fact that they allow the search space to be open−ended (in principle, any size tree
could be formed via crossover and mutation). This open−endedness also leads to some potential pitfalls. The
trees can grow large in uncontrolled ways, preventing the formation of more structured, hierarchical candidate
solutions. (Koza's (1992, 1994) "automatic definition of functions" is one way in which GP can be encouraged
to design hierarchically structured programs.) Also, the resulting trees, being large, can be very difficult to
understand and to simplify. Systematic experiments evaluating the usefulness of tree encodings and
comparing them with other encodings are only just beginning in the genetic programming community.
Likewise, as yet there are only very nascent attempts at extending GA theory to tree encodings (see, e.g.,
Tackett 1994; O'Reilly and Oppacher 1995).
These are only the most common encodings; a survey of the GA literature will turn up experiments on several
others.
How is one to decide on the correct encoding for one's problem? Lawrence Davis, a researcher with much
experience applying GAs to realworld problems, strongly advocates using whatever encoding is the most
natural for your problem, and then devising a GA that can use that encoding (Davis 1991). Until the theory of
GAs and encodings is better formulated, this might be the best philosophy; as can be seen from the examples
presented in this book, most research is currently done by guessing at an appropriate encoding and then trying
out a particular version of the GA on it. This is not much different from other areas of machine learning; for
example, encoding a learning problem for a neural net is typically done by trial and error.
One appealing idea is to have the encoding itself adapt so that the GA can make better use of it.
5.3 ADAPTING THE ENCODING
Choosing a fixed encoding ahead of time presents a paradox to the potential GA user: for any problem that is
hard enough that one would want to use a GA, one doesn't know enough about the problem ahead of time to
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