Evolutionary Computation : A Unified Approach

5.2. EA-BASED OPTIMIZATION 93
particular application better. Rather than choosing among a small set of historically developed
EAs, the OPT-EA designer thinks in terms of a parameterized family of algorithms
that can be effectively tuned by making adjustments to parameters such as:
• parent population size
• offspring population size
• parent selection pressure
• survival selection pressure
• representation
• reproductive operators
For example, one can generally obtain improvements in an OPT-ES on problems like
BBF2 by switching to non-overlapping generations and/or adopting a weaker form of survival
selection such as linear ranking. Similarly, one can frequently obtain OPT-GA improvements
by introducing some degree of generational overlap and/or a stronger form of parental
selection pressure such as linear ranking.
Having a tunable optimization procedure can also be viewed as a disadvantage in that
considerable time might have to be spent finding the right parameter settings for our OPT-
EA, a parameter optimization problem in its own right! Fortunately, the situation is not
as bad as it sounds. Most OPT-EAs have a fairly large “sweet spot” for their parameter
settings, in the sense that robust and effective performance is obtained with “in the ballpark”
parameter settings, and come with appropriately chosen defaults. In addition, as we will
see in chapter 7, progress continues to be made on developing EAs that are capable of
self-adapting their parameters.
5.2.2.5 Integer-Valued Parameter Optimization
Less frequently encountered, but equally difficult, are parameter optimization problems in
which the parameters are integer-valued. One strategy for solving such problems that immediately
comes to mind is to consider them as a special case of real-valued problems. This
can be done in several ways, the simplest of which is to embed the discrete integer solution
space in a real-valued solution space and treat it as a real-valued parameter optimization
problem. In order for this to work, the function to be optimized must be extendable, in
some reasonably natural way, to the larger real-valued solution space. Having done so,
the optima found using a real-valued optimization technique are likely to be associated with
non-integral parameter values. Hence, an additional procedure is required to find the nearest
integer-valued solutions.
Such strategies are often possible if the function is available in closed form, but do not
make much sense when the function is defined implicitly (e.g., via a simulation) and only
integer arguments make sense (e.g., the number of crew members assigned to a plane).
In such cases one needs an effective way to search integer-valued solution spaces directly.
Adapting techniques that were designed to search real-valued spaces is often difficult since