Self-Adaptation - Self-Adaptive Heuristics for Evolutionary Computation - page 34

3.4 The Concept of Self-Adaptation

Self-adaptation is usually associated with the step size control of ES. It was orig-
inally introduced by Rechenberg and Schwefel [132], later by Fogel [43] for EP.
Self-adaptive algorithms are characterized by the integration of strategy para-
meters, which influence the genetic operators or other parameters of the EA,
into the individuals' chromosomes. Typical is the influence of strategy parame-
ters on mutation rates, crossover probabilities and recently population sizes. The
chromosome of each individual a =( O, Σ ) contains a set of solutions encoding
objective variables O and a set of strategy variables Σ . The strategy parameters
σ i ∈

Σ are bound to the objective variables and evolved by means of the genetic
operators recombination, mutation and selection. We summarize the concept of
self-adaptation in the following definition.

Definition 3.1 (Self-Adaptation of EA Parameters)
Self-adaptation is the evolutionary control of strategy parameters Σ,boundto
each individual a and used to control parameters of the EA.

Appropriate parameter settings have a positive effect on the individual's fit-
ness and are consequently more likely inherited to the offspring. Hence, self-
adaptation means an implicit control of the strategy parameters. Self-adaptation
can be seen as a dynamical optimization process optimizing the strategy param-
eters during the walk through the search space. The convergence of the strategy
parameters is a sign for a good working self-adaptive process, but it is no neces-
sary condition.
In ES and EP the self-adaptive strategy variables are usually parameteriza-
tions of the mutation distributions. For example, an individual a of a ( μ + ,λ )-ES
with objective variable vector x is mutated in the following way:

x := x + z (3.4)

and

z := ( σ 1 N 1 (0 , 1) ,...,σ N N N (0 , 1)) (3.5)

The strategy parameter vector undergoes mutation

σ 1 e ( τ 1 N 1 (0 , 1) ,...,σ N e ( τ 1 N N (0 , 1) .

σ := e ( τ 0 N 0 (0 , 1)) · (3.6)

As the mutation step size has an important impact on the quality of the mu-
tations and undergoes mutation itself, the evolutionary search controls the step
size implicitly. Of course, self-adaptation is not restricted to steps sizes. Self-
adaptive parameters also control the skewness of mutation probability functions,
see chapter 4 or the probabilities of crossover.
Figure 3.4 illustrates the concept of self-adaptation. The individual performs
the search in two subspaces: the objective and the strategy parameter search