Evolutionary Computation : A Unified Approach

58 CHAPTER 4. A UNIFIED VIEW OF SIMPLE EAS
lation in less than 20 generations. The reason is straightforward: with a finite population,
any stochastic selection method is likely to result in a loss of diversity simply because of
sampling error. This is a well-understood phenomenon in biology and results in populations
exhibiting “genetic drift”. In our example, having disabled reproductive variation, this effect
is magnified and its compounding effects result in a loss of all but one genotype in less
than 20 generations.
There are two other commonly used selection techniques, tournament selection and
fitness-proportional selection, that can be characterized in a similar manner. Tournament
selection involves randomly selecting k individuals using a uniform probability distribution,
and then selecting the best (or worst) individual from the k competitors as the winner (or
loser). If n individuals need to be selected, n such tournaments are performed (with replacement)
on the selection pool. The effect is to implicitly impose a probability distribution on
the selection pool without explicit calculation and assignment of probabilities. In the case
of binary tournaments (k = 2), the implicit distribution can be shown to be equivalent (in
expectation) to linear ranking, and produces curves identical to the linear ranking curve in
figure 4.6. If we increase the tournament size to k = 3, the implicit probability distribution
changes from linear ranking to quadratic ranking with more probability mass shifted toward
the best. With each increase in the tournament size k, selection becomes more elitist.
More difficult to characterize is fitness-proportional selection, in which each individual
in the selection pool is assigned the probability f i /f sum ,wheref i is the fitness of individual
i, andf sum is the total fitness of all the individuals in the current selection pool. The result
is a dynamically changing probability distribution that can be quite elitist in the early
generations when there is a wide range of fitness values, and typically evolves to a nearly
flat uniform distribution in the later stages, as the population becomes more homogeneous
and the range of fitness values is quite narrow.
As we will see in chapter 6, it can be shown formally that the various selection schemes
can be ranked according to selection pressure strength. Of the ones we have discussed so
far, the ranking from weakest to strongest is:
• uniform
• fitness-proportional
• linear ranking and binary tournament
• nonlinear ranking and tournaments with k>2
• truncation
4.3.1 Choosing Selection Mechanisms
How do we use this knowledge about selection mechanisms when designing an EA There
are two places in simple EAs where selection occurs: when choosing parents to produce
offspring, and when choosing which individuals will survive. The cumulative effect is to
control the focus of search in future generations. If the combined selection pressure is too
strong, an EA is likely to converge too quickly to a suboptimal region of the space. As we
saw in the previous section, even an EA with uniform parent selection and linear ranking