Information Technology Reference
In-Depth Information
of a vector of objective and strategy variables. In real-valued search spaces the
objective variables are real values
x
1
,...,x
N
representing the assignment of
the variables of an
N
-dimensional optimization problem. The strategy variables
contain additional information, usually parameters for the Gaussian mutation
operator. There are three main principles for the design of mutation operators
proposed by Beyer [16]:
•
reachability,
•
unbiasedness, and
•
scalability.
The first principle
reachability
ensures that the whole objective and strategy
parameter search space can be reached within a finite number of generations.
This is also a necessary condition for proving global convergence, also see our
convergence proof for inversion mutation in section 5.3. The
scalability
condi-
tion ensures that the mutation strength can adapt to values, which guarantee
improvements during the optimization process. The condition of
unbiasedness
is appropriate to many unconstrained real search spaces. But for constrained
problems EAs with a self-adaptive step size mechanism often suffer from a dis-
advantageous success probability at the boundary of the feasible search space
[75], also see chapter 7. For this problem class biased mutation is an appropriate
technique, see section 4.5.3 of the this chapter.
Various mutation operators for ES exist. For the basic (
μ
+
,λ
)-ES uncorre-
lated isotropic mutation was introduced by Rechenberg [113] and Schwefel [131]
as well as correlated mutation by Schwefel [132]. Many extensions and variations
Taxonomy of ES mutation operators
mutation
randomized
derandomized
unbiased
biased
CSA
CMA
standard
correlated asymmetric
BMO/GMO
Fig. 4.1.
A small taxonomy of mutation operators for ES. Mutation operators can
be classified into randomized and derandomized mutation of the mutation strength.
Within the category of randomized operators we distinguish between unbiased and
biased mutation.
Search WWH ::
Custom Search