Evolutionary Computation : A Unified Approach

78 CHAPTER 5. EVOLUTIONARY ALGORITHMS AS PROBLEM SOLVERS
typical ES might be ES(10, 70), a 7:1 ratio, while a typical GA might be GA(50, 50), a 1:1
ratio. Fortunately, EA-based search is not highly sensitive to the particular values chosen
and is frequently performed with default values.
For many problem domains the cpu time required to solve a problem is dominated by the
cost of evaluating the fitness of an individual. If computing the fitness of points in solution
spaces is an independent process, then there is an obvious opportunity for using parallel
computing hardware to speed up the overall search process via parallel fitness evaluation.
In such cases population sizes are often adjusted to take advantage of particular hardware
configurations.
Finally, as we saw in the last chapter, the selection mechanisms used in an EA determine
the “greediness” of the search process: the willingness to focus on short term gains at the
risk of incurring long term losses. Strong selection pressure results in rapid, but possibly
premature, convergence. Weakening the selection pressure slows down the search process,
not unlike the annealing schedule in simulated annealing, but increases the likelihood of
finding global solutions. Finding the appropriate rate of convergence is problem-dependent
and requires some experimentation in practice. If running an EA several times on the same
problem produces substantially different answers each time, the selection pressure is too
strong (premature convergence) and needs to be weakened. An EA with very slowly rising
best-so-far curves suggests the selection pressure is too weak.
5.1.5 Convergence and Stopping Criteria
The terms convergence and stopping criteria have been used fairly loosely up to this point.
In order to implement an effective problem-solving EA we need to be more precise. As
we have seen in the preceding chapters, there are a number of EA properties that one can
potentially use as indicators of convergence and stopping criteria. Ideally, of course, we
want an EA to stop when it “finds the answer”. For some classes of search problems (e.g.,
constraint satisfaction problems) it is easy to detect that an answer has been found. But for
most problems (e.g., global optimization) there is no way of knowing for sure. Rather, the
search process is terminated on the basis of other criteria (e.g., convergence of the algorithm)
and the best solution encountered during the search process is returned as “the answer”.
The most obvious way to detect convergence in an EA is recognizing when an EA has
reached a fixed point in the sense that no further changes in the population will occur. The
difficulty with this is that only the simplest EAs converge to a static fixed point in finite
time. Almost every EA of sufficient complexity to be of use as a problem solver converges
in the limit as the number of generations approaches infinity to a probability distribution
over population states. To the observer, this appears as a sort of “punctuated equilibrium”
in which, as evolution proceeds, an EA will appear to have converged and then exhibit a
sudden improvement in fitness. So, in practice, we need to be able to detect when an EA
has converged in the sense that a “law of diminishing returns” has set in.
As we saw earlier, from a dynamical systems point of view homogeneous populations
are basins of attraction from which it is difficult for EAs to escape. Hence, one useful
measure of convergence is the degree of homogeneity of the population. This provides
direct evidence of how focused the EA search is at any particular time, and allows one to
monitor over time an initially broad and diverse population that, under selection pressure,