Evolutionary Computation : A Unified Approach

188 CHAPTER 6. EVOLUTIONARY COMPUTATION THEORY
Frequently, finding useful subcomponents is part of the problem being posed by an
application domain. In such cases one is given (or has a good sense of) the lowest-level
building blocks (primitive elements) and the goal is to discover how best to group (link)
these elements into higher-level subcomponents. This means that the representation and the
reproductive operators must facilitate the discovery and preservation of important linkages.
Here again, we understand how this can be accomplished in particular cases such as representing
executable code as Lisp parse trees or representing graph structures as adjacency
lists. However, an overarching theory remains out of reach.
6.7 Landscape Analysis
The final piece of the puzzle in defining effective EAs is the fitness landscape used to bias
the evolutionary search. Intuitively, we want fitness landscapes that are “evolution friendly”
in the sense that they facilitate the evolutionary discovery of individuals with high fitness.
In order for this to be true, the landscape must have several desirable properties. First,
landscapes must provide hints as to where individuals with high fitness might be found.
This sounds intuitively obvious, but care must be taken since there are many applications
in which the simplest, most natural notions of fitness do not have this property. Boolean
satisfiability problems are a good example of such a situation, in which the goal is to
find truth assignments to a set of Boolean variables that will make a complicated Boolean
expression involving those variables true. For any particular assignment, either you win
or you lose, and for difficult problems there are very few winning combinations. If we use
winning/losing as our fitness landscape, we have presented our EA with a binary-valued
fitness landscape the value of which is zero almost everywhere. By providing no hints as
to where winning combinations might be found, EAs (and all other search techniques) can
do no better than random search. Suppose, however, that the fitness landscape could be
redefined to appear more like a bed sheet draped over this spiky landscape. Then, losing
combinations provide hints (in the form of gradients) as to where one might find winning
combinations (see, for example, Spears (1990)).
A more subtle difficulty arises when a fitness landscape provides insufficient or misleading
information. For example, if the landscape consists of a large number of independently
distributed local optima, following local optima information will not improve the chances of
finding a global optimum. This situation is made worse if the landscape is deceptive, in the
sense that the hints it provides draw an EA away from the best solutions rather than toward
them. If something is known about the nature of such landscapes, EAs can be designed to
deal with them (see, for example, Goldberg (2002)).
Even when a landscape is evolution friendly, it still remains the job of the EA designer
to choose an internal representation and reproductive operators to take advantage of the information
provided. Theoretical guidance for this comes in the form of Price’s theorem that
was introduced and discussed in section 6.5. Recall that Price’s theorem had two terms: one
corresponding to improvements in fitness due to selection, and a second term corresponding
to improvements in fitness due to reproductive variation. If we think of this from a landscape
viewpoint, it means exploiting the information provided by the current population via
parent selection, and leveraging that information via reproductive variation. If we assume