Self-Adaptation - Self-Adaptive Heuristics for Evolutionary Computation - page 37

σ =0 . 1. For the self-adaptive algorithm we use the standard settings. Table 3.1
shows the outcome of the three experiments. 2
The accuracy that can be achieved with the fixed mutation strengths is lim-
ited. The probability to approximate the optimum decreases as small mutations
are not likely when the distance of the individuals to the optimum reach the
degree of the step sizes. Figure 3.5 approves that the approximation capabilities
with a fixed mutation strength are limited. Furthermore, the figure shows that
the ES with σ =0 . 1 is able to take bigger steps at the beginning whereas the ES
with σ =0 . 001 is rather slow. Otherwise, the latter is able to achieve a slightly
better approximation as the mutation strength allows smaller mutations close
to the optimum at the end of the search. The fitness with a fixed step size is
fluctuating when reaching the area of the optimum within the range of the step
size.

3.5 Self-Adaptation of Global Parameters

Eiben, Schut and Wilde [35] propose a method to control the population size and
the selection pressure using tournament selection of an EA self-adaptively. The
problem of such an adaptation is that the parameters population size and tour-
nament size are global while self-adaptation is an approach for the individual
or the component level. The idea of the approach is to derive the global pa-
rameters via aggregation of local information on individual or component level.
The local information is still part of the individual's genome and participates in
recombination and mutation. They introduce an aggregation mechanism which
simply sums up all votes of the individuals for the global parameter. To the best
of our knowledge this has been the only attempt to control global parameters
self-adaptively.

3.6 Theoretical Approaches Toward Self-Adaptation

Only few theoretical work on self-adaptation exists. Most of it concerns the
continuous search domain, i.e. the analysis of the ES mutation strength self-
adaptation. As Beyer and Schwefel [18] state, the analysis of EAs including the
mutation control part is a dicult task. In the following we give an overview
over the main results.

Dynamical Systems

Beyer [16] gives a detailed analysis of the (1 ,λ ) self-adaptation on the sphere

function in terms of progress rate and self-adaptation response also consider-
ing the dynamics with fluctuations. The analysis reveals various characteristics

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2 We present the experimental results in this work by stating the best, the worst, the
average, sometimes also the median result and the standard deviation (dev) of all
runs. A result of a run is the best fitness within a population in the last generation.
Graphical presentations like plots show either typical or average runs.