Biased Mutation for Evolution Strategies - Self-Adaptive Heuristics for Evolutionary Computation - page 70

10000

BMO on 2.40
DMO on 2.40
ES on 2.40

100

1

0.01

0.0001

1e-006

1e-008

1e-010

1e-012

1e-014

0 50 100 150 200 250 300 350

generations

Fig. 4.8. Comparison between BMO, DMO and ES on problem 2.40. Typical runs
are shown on a logarithmic scale. While the standard ES early suffers from premature
steps size reduction, BMO and DMO show logarithmically linear approximation of the
optimum.

Table 4.13. Experimental results of the BMO variants on the constrained function
g04. BMO and DMO achieve a satisfying approximation while the ES is outperformed.

ES BMO cBMO DMO

best -30665.53867 -30665.53867 -30665.53867 -30665.53867

median -30665.53227 -30665.53867 -30665.53867 -30665.53867

worst -30644.23102 -30665.53867 -30662.83143 -30665.53867

mean -30664.23109 -30665.53867 -30665.41105 -30665.53867

dev 4.3651 0.0005 0.5403 0.0003

bias does not offer the necessary degree of freedom to shift the mutation ellipsoid
appropriately.
A comparison of the BMO variants and ES with DP shows figure 4.9, where
typical runs on problem g04 are drawn. BMO and DMO are able to approximate
the optimum, while BMO is faster. This run of the ES fails. The results are
similar to the behavior on problem 2.40. The results of 25 runs of all algorithms
on problem g04 are shown in table 4.13. Again, the ES does not show satisfying
results, the cBMO is slightly better. But BMO and DMO reach the optimum
in every run with a small standard deviation. Similar results were obtained on
other constrained functions.