Self-Adaptation - Self-Adaptive Heuristics for Evolutionary Computation - page 35

objective variable search space strategy variable search space

2

optimum

x 2

optimal strategy
parameters for x 1

x 1

1

15

10

fitness landscape

5

0

-5

150

100

50

0

-50

-150

-100

-100 -50

0

50

100

-150

150

Fig. 3.4. The principle of self-adaptation. The figure illustrates the concept of search-
ing in the objective and the strategy variable search space. We consider step sizes in
a continuous search domain as an example. The strategy variable search space is dis-
played in double scale for better readability. For x 1 the yellow rectangular represents
the optimal step sizes.

space. Strategy parameters influence the genetic operators of the objective vari-
able space. The optimal settings vary depending on the location of the solu-
tion in the fitness landscape. Only the objective variables define the solution
and have an impact on the fitness. The genetic operators for strategy and
objective variables may vary, e.g. some paper propose dominant recombina-
tion and log-normal mutation for the strategy variables and intermediate and
meta-EP mutation for the objective variables [18]. We can also think of de-
coupling strategy from objective variables and use different kinds of selection
operators.

Experimental Example

To give an example for the benefits of self-adaptation we compare a (15,100)-
ES with a fixed mutation strength to a (15,100)-ES with self-adaptive mutation
strength control, see equations 3.4 to 3.6, on a 2- and on a 30-dimensional sphere
function. For the variants with a fixed mutation strength we set σ =0 . 001 and