An Introduction to Genetic Algorithms - Boente

Chapter 3: Genetic Algorithms in Scientific Models
time the gene was used—that is, every time the specified input situation arose for the bug and the specified
action was taken by the bug. When a parent passed on a gene to a child through asexual reproduction or
through crossover, the value of the counter was passed on as well and remained with the gene. The only time a
counter was initialized to zero was when a new gene was created through mutation. In this way, a gene's
counter value reflected the usage of that gene over many generations. When a bug died, its genes (and their
counters) died with it.
For each time step during a run, Bedau and Packard (1992) plotted a histogram of the number of genes in the
population displaying a given usage value u (i.e., a given counter value). One such plot is shown here at the
top of figure 3.13. The x axis in this plot is time steps, and the y axis gives usage values u. A vertical slice
along the y axis gives the distribution of usage values over the counters in the population at a given time step,
with the frequency of each usage value indicated by the grayscale. For example, the leftmost vertical column
(representing the initial population) has a black region near zero, indicating that usage values near zero are
most common (genes cannot have high usage after so little time). All other usage values are white, indicating
that no genes had yet reached that level of usage. As time goes on, gray areas creep up the page, indicating
that certain genes persisted in being used. These genes presumably were the ones that helped the bugs to
survive and reproduce—the ones
Figure 3.13: Plots of usage statistics for one run of the Strategic Bugs model. Top plot: Each vertical column
is a histogram over u (usage values), with frequencies of different u values represented on a gray scale. On
this scale, white represents frequency 0 and black represents the maximum frequency. These histograms are
plotted over time. Bottom plot: Evolutionary activity A(t) is plotted versus t for this run. Peaks in A(t)
correspond to the formation of new activity waves. (Reprinted from Christopher G. Langton et al. (eds.).
Artificial Life: Volume II, ©1992 by Addison−Wesley Publishing Company, Inc. Reprinted by permission of
the publisher.)
that encoded traits being selected. Bedau and Packard referred to these gray streaks as "waves of activity."
New waves of activity indicated the discovery of some new set of genes that proved to be useful.
According to Bedau and Packard, the continual appearance of new waves of activity in an evolving population
indicates that the population is continually finding and exploiting new genetic innovations. Bedau and
Packard defined a single number, the evolutionary activity A(t),that roughly measures the degree to which the
population is acquiring new and useful genetic material at time t.
In mathematical terms, Bedau and Packard defined u0 as the "baseline usage"—roughly the usage that genes
would obtain if selection were random rather than based on fitness. As an initial attempt to compensate for
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