Self-Adaptive Inversion Mutation - Self-Adaptive Heuristics for Evolutionary Computation - page 87

8

SA-INV-c 5-1
SA-INV 5-1

7

6

5

4

3

2

1

0 10 20 30 40 50 60 70 80 90 100

generations

600000

SA-INV-c 5-1
SA-INV 5-1

550000

500000

450000

400000

350000

300000

250000

200000

0 10 20 30 40 50 60 70 80 90 100

generations

Fig. 5.6. Comparison of the mutation strength k (upper part) and the fitness (lower
part) of SA-INV-c 5 − 1 and SA-INV 5 − 1 on problem bier127 averaged over 25 runs. Once
k reaches the region around one it is constantly set to k = 1. The fitness development
shows the superiority of SA-INV-c in comparison to SA-INV, in particular at later
generations.

settings around b . But the bound itself may be an optimal setting. All other
settings produce potentially worse solutions. Consequently, the success proba-
bility is smaller than p s with the setting b . A bound of strategy variables is a
phenomenon that occurs almost naturally for discrete strategy variables.
In order to overcome this problem we propose the following modification SA-
INV-c, which is based on SA-INV. Let u be the number of individuals with k =1.
If u

λ

2 we set k = 1 constantly and cancel the self-adaptation of k during the
following generations. This modification makes sense under the assumption that
after κ generations the optimal strategy setting is k = 1 and for k> 1onlyworse
solutions are produced. We assume that g is reached if the condition u

≥

λ

2 is
fulfilled. This bound is reasonable: if at least 50% of the strategy parameters

≥