Self-Adaptation - Self-Adaptive Heuristics for Evolutionary Computation - page 33

which decreases the mutation strength depending on the number of generations.
Back [7] decreases the mutation rate according to the distance to the optimum.
The most famous example is the step size of the ES Gaussian mutations, see
chapters 2.2, 3.4 and 4.1. Back [7], [6] introduced a self-adaptive control mech-
anism for GA bit-string representations. But other deterministic and adaptive
control mechanisms exist as well. For example the 1/5th rule of Rechenberg
[114]. Behind mutation strength control lies the notion of exploring the search
space with big mutations at the beginning of the search and afterwards exploit-
ing the vicinity of the optimum in the exploitation phase with smaller variations.
Chapter 4 gives a brief outline of self-adaptive mutation operators, e.g. Gaussian
mutation of ES, correlated mutation or the control of parameters that bias the
mutation into beneficial directions.
Crossover Operators
Davis [30] adapts the crossover rates of his GA by rewarding crossover operators
which created successful offspring. The approach makes use of different kinds of
crossover operators. A reward increases the relative application probability of a
successful crossover in comparison to the others. Schaffer and Morishima [128]
introduced the punctuated crossover which adapts the crossover points for bit
string representations. In chapter 6 various self-adaptive extensions of frequently
used crossover operators are introduced.
Selection
Most selection algorithms exhibit parameters which tune the selection pressure,
e.g. the Boltzmann or ranking selection. Consequently, also these parameters can
be subject to control mechanisms. The tournament size of tournament selection
is another example for a tunable selection parameter. In the past, the control
of the selection pressure has not been considered very often and is subject to
current research. Eiben [35] introduced the self-adaptive control for tournament
selection, also see section 3.5.
Population
The population sizes of EAs influence the exploration and exploitation aspect
of the evolutionary search. Many research activities have been investigated into
appropriate populations sizes [37]. E.g. Smith [145] adjusts the population size
according to the probability of a defined selection error. The approach of Hinterd-
ing et al. [56] controls the population sizes of three in parallel evolved populations
according to heuristic rules. Arabas et al. [2] adjust the population size indirectly
by assigning each individual with a maximum lifetime depending on its fitness.
Furthermore, the expected number of offspring is proportional to the number of
survived generations. Recently, Eiben [35] proposed an approach to control pop-
ulation sizes and selection pressure self-adaptively, as already mentioned. This
approach is described in section 3.5.