Biased Mutation for Evolution Strategies - Self-Adaptive Heuristics for Evolutionary Computation - page 71

10000

BMO on g04
DMO on g04
ES on g04

100

1

0.01

0.0001

1e-006

1e-008

1e-010

1e-012

0 100 200 300 400 500

generations

Fig. 4.9. Fitness development on function g04. Again, we compare typical runs of
BMO, DMO and ES on a logarithmic scale. The approximation speed of DMO is
better than the speed of BMO. ES does not approximate the optimum.

Parameter Study of γ

We conduct an experimental study of the strategy variable mutation parameter γ
on problem g04, see table 4.14. A similar result like in the other γ studies can be ob-
served: parameter settings around γ =0 . 1 like γ =0 . 05 or γ =0 . 15 show the best
approximation behavior. Although many entries of the table are similar to each
other, the standard deviation reveals the stability of the convergence properties.

Table 4.14. Parameter study of γ for the BMO on the constrained function g04.
Settings around γ =0 . 1 maintain the fastest approximation capabilities.

0.0001 0.01 0.05 0.1 0.15 0.5 1.0
best -30665.538 -30665.538 -30665.538 -30665.538 -30665.538 -30665.538 -30665.538
mean -30658.772 -30663.003 -30665.538 -30665.538 -30665.538 -30665.538 -30661.160
dev 14.22802 6.72839 0.00056 0.00056 0.00039 0.00079 21.72168

Selection Pressure and Population Ratios

We examine the behavior of various population sizes and ratios on the constrained
function g04 and show the results in table 4.15. All results were satisfying with ex-
ception of the (50,100)-BMO. The ratio (50,100) is a very weak selection
pressure. But a weak selection pressure slows down the approximation, so that