Mitchell, T. J. (2010) An exploration of evolutionary computation ...

Step-Size Mutation
To ensure that step-sizes remain positive, the individual step lengths of the vector are
mutated by a multiplicative, rather than additive process (as is case for mutation of the
object parameters). The principles derived for the mutation of object-variables also apply
for the mutation of the strategy parameters. For example, mutations to the object
parameters should be ordinal, scalable and unbiased. However, as mutations are applied
multiplicatively they should be drawn from a random number source with expectation 1.0.
For this reason the log-normal update rule is applied to the step-size vector as follows:
with and . Schwefel and Rudolph (1995)
recommend setting the learning parameters and , according to:
The order in which the evolutionary operators are applied to the object and strategy
parameters is also an important factor in the successful application of self-adaptation. The
step-size parameters should be mutated prior to the object parameters, to ensure that any
useful mutative step made in the object space is directly attributed to the accompanying
step-size vector. The intention here is that the useful strategy parameters that led to the
adaptation of strong object parameters are inherited by descendent individuals to deliver
even fitter solutions throughout subsequent generations.
Derandomised Self-Adaptation
Ostermeier et al (1994) presented a derandomised mutative step-size control procedure
designed to improve the performance of the original self-adaptation mechanism. The
traditional mutative self-adaptive mechanism (outlined above) has been shown to break
down when small population sizes are employed (Schwefel, 1987). While these symptoms
can be reduced with the use of intermediate recombination and larger population sizes,
Ostermier et al (1994) set out to tackle the cause of these shortcomings. Two deficiencies
in the traditional self-adaptive process were identified:
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