Evolutionary Computation : A Unified Approach

132 CHAPTER 6. EVOLUTIONARY COMPUTATION THEORY
120
Average Generations to Fixed-Point Convergence
100
80
60
40
20
Uniform stochastic
Fitness-proportional
Binary Tournament
0
0 50 100 150 200 250
Parent=Offspring Population Size
Figure 6.10: Average fixed-point convergence times for various parent selection methods in
a non-overlapping-generation EA with m = n and no reproductive variation.
selection (pure drift) is a bit surprising at first, but easy to understand. With neutral
selection, all of the initial genotypes are equally likely to be lost, so the average fixed-point
fitness is the same as the average fitness of the initial population (approximately 50.0).
As one would expect, when we switch to fitness-biased selection methods, we dramatically
increase the likelihood of converging to high-fitness fixed points. The stronger the fitness
bias, the higher the resulting fixed-point fitness. At the same time, both binary tournament
and fitness-proportional selection are themselves stochastic sampling techniques and are
subject to sampling errors as well (i.e., drift). The effects of this drift can be seen quite
clearly in figure 6.11, in that lower convergence fitness is obtained as the population size m
decreases.
So, is this self-adaptive selection pressure of fitness-proportional selection good or bad
The answer, of course, depends on a number of things, including the application domain. As
we will see in chapter 7, softer and adaptive forms of selection are helpful when the fitness
landscape is itself changing during an EA run. On the other hand, if one is given a fixed
computational budget to find a reasonable solution to an optimization problem, stronger
and more aggressive forms of selection are necessary.
6.3.1.3 Non-overlapping-Generation Models with n ̸=m
Of course, many EAs are run with a parent population size of m and a different offspring
population size n, so it is important to understand how this affects EA dynamics. For
non-overlapping-generation EAs, the only interesting case is n>m. In this case one needs
to specify both a parent selection method and a survival selection method to select the m