An Introduction to Genetic Algorithms - Boente

these random effects, Bedau and Packard subtracted u0 from u. They showed that, in general, the only genes
that take part in activity waves are those with usage greater than u0
Next, Bedau and Packard defined P (t,u), the "net persistence," as the proportion of genes in the population at
time t that have usage u or greater. As can be seen in figure 3.13, an activity wave is occurring at time t' and
usage value u' if P (t, u) is changing in the neighborhood around (t',u'). Right before time t' there will be a
sharp increase in P (t, u), and right above usage value u' there will be a sharp decrease in P(t,u). Bedau and
Packard thus quantified activity waves by measuring the rate of change of P(t,u) with respect to u. They
measured the creation of activity waves by evaluating this rate of change right at the baseline u0. This is how
they defined A(t):
That is, the evolutionary activity is the rate at which net persistence is dropping at u = u0. In other words, A (t)
will be positive if new activity waves continue to be produced.
Bedau and Packard denned "evolution" in terms of A (t): if A(t) is positive, then evolution is occurring at time
t, and the magnitude of A(t) gives the "amount" of evolution that is occurring at that time. The bottom plot of
figure 3.13 gives the value of A(t) versus time in the given run. Peaks in A(t) correspond to the formation of
new activity waves. Claiming that life is a property of populations and not of individual organisms, Bedau and
Packard ambitiously proposed A(t) as a test for life in a system—if A(t) is positive, then the system is
exhibiting life at time t.
The important contribution of Bedau and Packard's 1992 paper is the attempt to define a macroscopic quantity
such as evolutionary activity. In subsequent (as yet unpublished) work, they propose a macroscopic law
relating mutation rate to evolutionary activity and speculate that this relation will have the same form in every
evolving system (Mark Bedau and Norman Packard, personal communication). They have also used
evolutionary activity to characterize differences between simulations run with different parameters (e.g.,
different degrees of selective pressure), and they are attempting to formulate general laws along these lines. A
large part of their current work is determining the best way to measure evolutionary activity in other models
of evolution—for example, they have done some preliminary work on measuring evolutionary activity in
Echo (Mark Bedau, personal communication). It is clear that the notion of gene usage in the Strategic Bugs
model, in which the relationship between genes and behavior is completely straightforward, is too simple. In
more realistic models it will be considerably harder to define such quantities. However, the formulation of
macroscopic measures of evolution and adaptation, as well as descriptions of the microscopic mechanisms by
which the macroscopic quantities emerge, is, in my opinion, essential if evolutionary computation is to be
made into an explanatory science and if it is to contribute significantly to real evolutionary biology.
Thought Exercises
1.
2.
Chapter 3: Genetic Algorithms in Scientific Models
Assume that in Hinton and Nowlan's model the correct setting is the string of 20 ones. Define a
"potential winner" (Belew 1990) as a string that contains only ones and question marks (i.e., that has
the potential to guess the correct answer), (a) In a randomly generated population of 1000 strings, how
many strings do you expect to be potential winners? (b) What is the probability that a potential winner
with m ones will guess the correct string during its lifetime of 1000 guesses?
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