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initial step sizes
σ
i
=
|x
(0)
x
∗
|
−
N
,startingpoint
x
(0)
and optimum
x
∗
according to the recommendation of Schwefel [135]. As termination condition
we chose premature mutation strength reduction, i.e. the ES is terminated if the
difference between the best individuals of two successive generations is smaller
than
θ
=10
−
12
. All DP and DSES tests are based on a (15/2,100)-ES with
intermediary recombination.
with 1
≤
i
≤
N
Experimental settings
Population model (15,100)
Mutation type standard,
n
σ
=
N
,
τ
0
=(
√
2
n
)
−
1
and
τ
1
=(
2
√
n
)
−
1
Crossover type intermediate,
ρ
=2
Selection type comma
Initialization
σ
i
=
|x
(
0)
−x
∗
|
N
Termination fitness stagnation,
θ
=10
−
12
Runs
25
The measured parameters are the usual ones concerning the fitness of the best
individual in the last generation of the various runs (
best
,
avg
,
worst
and
dev
).
Parameter
σ
is the mean of the mutation strength in the last generation and
therefore an indicator for premature stagnation.
Ffc
counts the number of fitness
function calls,
cfc
the number of constraint function calls.
Parameter Analysis of the DSES
Table 7.2 shows the analysis of the DSES parameter settings. Above, the analysis
of the DSES on problem g01 reveals a significant improvement in comparison to
DP. The [400;0.5]-, the [400;0.3]- and the [400;0.1]-DSES were able to approxi-
mate the optimum with arbitrary accuracy. The
-reduction was performed too
fast for the [100,
ϑ
]-DSES with
ϑ
=0
.
1
,
0
.
3
,
0
.
5 in every run.
We analyze the behavior of the DSES on problem g07. In comparison to the
method death penalty a significant improvement of accuracy can be observed.
The slower
is decreased the more the quality of the results can be improved.
Butwehavetoadmitthat
ffc
and in particular
cfc
explode. Hence, we can only
recommend the DSES when
ffc
and
cfc
are not too expensive. The experiments
show that death penalty completely fails concerning the quality of the results.
The DSES on All Functions
The experimental results of the DSES on all considered problems are summa-
rized in table 7.3. On Schwefel's problems 2.40 and 2.41 the DSES is able to
approximate the optimum with most of the tested settings. DP fails on these
problems and suffers from premature mutation strength reduction. Problem TR2
is hard to tackle. But the results of a [15; 0.5]-DSES on TR2 are better than
the results of DP. As expected the number of
ffc
and
cfc
explode, i.e. they are
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