An Introduction to Genetic Algorithms - Boente

the best possible solution has been found, whereas a GA might converge on a local optimum rather than on
the globally best solution. If the space is smooth or unimodal, a gradient−ascent algorithm such as
steepest−ascent hill climbing will be much more efficient than a GA in exploiting the space's smoothness. If
the space is well understood (as is the space for the well−known Traveling Salesman problem, for example),
search methods using domain−specific heuristics can often be designed to outperform any general−purpose
method such as a GA. If the fitness function is noisy (e.g., if it involves taking error−prone measurements
from a real−world process such as the vision system of a robot), a one−candidate−solution−at−a−time search
method such as simple hill climbing might be irrecoverably led astray by the noise, but GAs, since they work
by accumulating fitness statistics over many generations, are thought to perform robustly in the presence of
small amounts of noise.
These intuitions, of course, do not rigorously predict when a GA will be an effective search procedure
competitive with other procedures. A GA's performance will depend very much on details such as the method
for encoding candidate solutions, the operators, the parameter settings, and the particular criterion for success.
The theoretical work described in the previous chapter has not yet provided very useful predictions. In this
chapter I survey a number of different practical approaches to using GAs without giving theoretical
justifications.
5.2 ENCODING A PROBLEM FOR A GENETIC ALGORITHM
As for any search and learning method, the way in which candidate solutions are encoded is a central, if not
the central, factor in the success of a genetic algorithm. Most GA applications use fixed−length, fixed−order
bit strings to encode candidate solutions. However, in recent years, there have been many experiments with
other kinds of encodings, several of which were described in previous chapters.
Binary Encodings
Chapter 4: Theoretical Foundations of Genetic Algorithms
Binary encodings (i.e., bit strings) are the most common encodings for a number of reasons. One is historical:
in their earlier work, Holland and his students concentrated on such encodings and GA practice has tended to
follow this lead. Much of the existing GA theory is based on the assumption of fixed−length, fixed−order
binary encodings. Much of that theory can be extended to apply to nonbinary encodings, but such extensions
are not as well developed as the original theory. In addition, heuristics about appropriate parameter settings
(e.g., for crossover and mutation rates) have generally been developed in the context of binary encodings.
There have been many extensions to the basic binary encoding schema, such as gray coding (Bethke 1980;
Caruana and Schaffer 1988) and Hillis's diploid binary encoding scheme. (Diploid encodings were actually
first proposed in Holland 1975, and are also discussed in Goldberg 1989a.)
Holland (1975) gave a theoretical justification for using binary encodings. He compared two encodings with
roughly the same information−carrying capacity, one with a small number of alleles and long strings (e.g., bit
strings of length 100) and the other with a large number of alleles and short strings (e.g., decimal strings of
length 30). He argued that the former allows for a higher degree of implicit parallelism than the latter, since an
instance of the former contains more schemas than an instance of the latter (2 100 versus 2 30 ). (This
schema−counting argument is relevant to GA behavior only insofar as schema analysis is relevant, which, as I
have mentioned, has been disputed.)
In spite of these advantages, binary encodings are unnatural and unwieldy for many problems (e.g., evolving
weights for neural networks or evolving condition sets in the manner of Meyer and Packard), and they are
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