Biased Mutation for Evolution Strategies - Self-Adaptive Heuristics for Evolutionary Computation - page 66

• sharp ridge, α =1,

• parabolic ridge, α =2.

The following experimental settings have been used.

Experimental settings
Population model

(15,100)

1
√

1
√ 2 √ N

Mutation types ES, BMO, cBMO, DMO, γ =0 . 1, τ 0 = ,τ 1 =

N

Crossover type intermediate, ρ =2

Selection type comma

Initialization [-100,100]

Termination 1000 generations

Runs 25

Earlier experiments showed [17] that self-adaptive step size control on ridge
functions may result in premature step size reduction. These results could not
be observed in our experiments.

Comparison of Variants

The outcome of the BMO variants on the two ridge functions can be found in
table 4.9. The experimental results confirm the above mentioned assumption:
the bias increases the speed along the ridge. This holds for the parabolic ridge
as well as for the sharp ridge. Furthermore, the experiments show that the BMO
and cBMO are slightly faster than the DMO. Figure 4.7 shows the fitness devel-
opment of typical runs of the variants on the parabolic ridge. The approximation
speed of the biased variants BMO, cBMO and DMO is higher than the speed of
the unbiased ES. The comparison does not reveal significant differences among
the behavior of the successful biased variants.

Table 4.9. Experimental results of the BMO variants on the functions parabolic ridge
(upper part) and sharp ridge (lower part). The BMO variants are significantly faster
than standard Gaussian mutation.

ES BMO cBMO DMO

parabol ic
best -3.34E+190 -5.69E+240 -8.02E+239 -2.13E+228

median -2.30E+187 -4.16E+236 -1.32E+236 -7.98E+224

worst -7.54E+181 -8.26E+231 -8.90E+229 -6.22E+219

mean -2.81E+189 -2.32E+239 -5.37E+238 -1.89E+227

sharp
best -3.52E+188 -1.93E+234 -5.46E+235 -3.06E+226

median -2.40E+181 -8.49E+229 -2.79E+230 -7.34E+221

worst -9.49E+174 -6.22E+206 -9.08E+210 -6.24E+215

mean -2.52E+187 -1.09E+233 -2.22E+234 -1.44E+225