Evolutionary Computation : A Unified Approach

130 CHAPTER 6. EVOLUTIONARY COMPUTATION THEORY
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Average Population Fitness at Fixed-Point Convergence
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Binary tournament
Linear ranking
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Parent=Offspring Population Size
Figure 6.8: Average fixed point fitness for linear ranking and tournament selection.
Understanding this relationship also allows the EA designer to fill in the rather large
gap we saw in figure 6.5 between the selection pressures induced by truncation and linear
ranking. This is easily accomplished by increasing q as illustrated in figure 6.9.
The combination of these two features, the implementation simplicity and the ability
to control selection pressure easily, has made tournament selection the preferred choice of
many EA practitioners.
Fitness-Proportional Selection
The three selection methods that we have studied so far can be summarized as providing a
wide range of selection pressures, from very strong (truncation) to moderate (tournament)
to weak (linear ranking). Each method has a parameter that allows an EA designer to
fine tune the selection pressure within these general categories. However, having chosen a
particular selection method, the induced selection pressure is then constant for the entire
evolutionary run. A natural question to ask is whether it is possible and useful to adapt the
selection pressure during an evolutionary run. It is clearly possible and in fact rather easy
to do so with the three selection methods we have studied so far by designing a procedure
for dynamically modifying the method’s tuning parameter. Whether this will be useful will
depend on both the application domain and the particular update procedure chosen.
However, there is another selection method, fitness-proportional selection, that selfadapts
the selection pressure without requiring the designer to write additional code. This
is accomplished by defining the probability of selecting individual i at generation t to be
fitness(i)/total fitness(t). If we sample this distribution m times, the expected number of
times individual i is chosen is simply fitness(i)/ave fitness(t). In particular, if we focus