Evolutionary Computation : A Unified Approach

6.5. SELECTION AND REPRODUCTION INTERACTIONS 177
recall that EA-2 uses an overlapping-generation model with truncation survival selection.
As we saw earlier, this means that the average fitness of the population can never decrease,
regardless of how aggressive the reproductive operators are. As a consequence, success rates
cannot be increased by lowering the average fitness of the population as they can with nonoverlapping-generation
models like EA-1. Rather, in overlapping models like EA-2, success
rates decrease as reproductive operators get more aggressive, and increase as the operators
become more conservative.
Figures 6.44 and 6.45 make it clear how important the exploration/exploitation balance
is in improving population fitness. They also point out the difficulty of achieving the proper
balance. Both EA-1 and EA-2 exhibited mutation rate “sweet spots”, but at quite different
levels of mutation strength. Currently our theory is not strong enough to predict these sweet
spots. Rather, they are obtained experimentally. This observation was the motivation for
the ES community to develop early on an adaptive mutation operator that dynamically
increased/decreased its exploratory power in an attempt to maintain a uniform success rate
of approximately 20% (Schwefel, 1981).
6.5.5 Selection and Other Mutation Operators
To keep things simple initially, the focus has been on one of the simplest and most widely
used family of asexual reproduction operators: mutation operators that are designed to
clone a parental genome and add some genetic variability by modifying one or more gene
values. Although the analysis focused on discrete mutation operators, the general results are
the same for real-valued representations with Gaussian mutation, namely, the importance
of finding a balance between selection and the strength of mutation.
Obviously, there are more complex asexual reproduction mechanisms that might change
the genome length, make correlated changes to gene values, move genes around on the
genome, etc. Since these issues are intimately related to representation issues, we will defer
further discussion and revisit these issues in section 6.6.
6.5.6 Selection and Multiple Reproductive Operators
In practice most EAs have more than one reproductive operator active during an evolutionary
run. This means that, in addition to understanding the properties of the individual
operators, the EA designer must also understand how they work in combination with each
other. In the case of the crossover and mutation operators studied in the previous sections,
our understanding of how they work independently suggests that the two reproductive operators
are in many ways complementary to each other and, if properly combined, could
result in better EA performance improvements than by using one or the other alone. For
the discrete reproductive operators, the constant level of genotype diversity produced by
mutation provides a means by which crossover-generated diversity can now be maintained
indefinitely (if desired). For the real-valued reproductive operators, Gaussian mutation can
compensate for the loss of phenotype diversity due to blending recombination. In each case,
the key is finding the balance between the exploitation of selection and the exploration of
reproduction.
If we focus on the offspring population, one could imagine finding some individuals that