Self-Adaptation - Self-Adaptive Heuristics for Evolutionary Computation - page 31

number of generations, also see figure 3.5. The step sizes have to be adapted in
order to speed up the optimization process. In the approach of the 1/5th-rule
the whole populations makes use of the same σ for all individuals. It states that
the ratio of successful mutations should be 1/5th. If the ratio is greater than
1/5th the step size should be increased, if it is less than 1/5th the step size
should be decreased. This rule is applied every g generations. Figure 3.3 shows
the pseudocode of Rechenberg's adaptation method. It must hold 0 <λ< 1. The

1. Perform the (1+1)-ES for a number g of generations:

• Keep σ constant during this period,

• Count the number s of successful mutations during this period

2. Estimate success rate p s by

p s := s/g (3.2)

3. Change σ according to

⎨
⎩

σ/λ, if p s > 1 / 5

σ := σ · λ, if p s < 1 / 5 (3.3)

σ, if p s =1 / 5

4. Go to step 1.

Fig. 3.3. Pseudocode of the 1/5th rule of Rechenberg

aim of this approach is to stay in the so called evolution window guaranteeing
nearly optimal progress. Of course, the 1/5th rule is not the proper heuristic for
every problem and is outperformed by self-adaptive step size approaches. The
optimal value for the factor a depends on several factors such as the number of
generations g and the dimension of the problem N .

Self-Adaptive

The concept of self-adaptation is a step into the direction of parameter indepen-
dent EC. Self-adaptation is usually associated with the step size control of ES.
It was originally introduced by Rechenberg and Schwefel [132], later by Fogel
for EP. Self-adaptive algorithms are characterized by the integration of strategy
parameters which influence the genetic operators into the individuals' chromo-
somes. These parameters undergo genetic variation and are therefore involved
into the evolutionary optimization process

Hybridization

The hybridization of different parameter control techniques is a source for many
interesting variants. An example is the DSES, a heuristic for constraint handling,
see chapter 7.4. The self-adaptive mutation strength control of ES fails in the