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Table 7.2.
Above: Experimental analysis of a (15/2, 100)-DSES with intermediary
recombination and an initial step size of
σ
i
=0
.
1 on problem g01. The DSES is able
to approximate the optimum with arbitrary accuracy while DP fails on g01. Below: A
(15/2, 100)-DSES with intermediary recombination on problem g07. We observe signif-
icant better results in comparison to DP and achieve the best results with the slowest
-reduction. On the other hand the slow reduction causes an explosion of constraint
function calls. The constraint violation of each best solution is 0.
DSES
best
avg
worst dev
σ
ffc
cfc
g01
[400; 0
.
5]
−
15
.
0
−
14
.
9999999991
−
14
.
99999999 1.7E-9 2.0E-10
93 224 3 174 166
[400; 0
.
3]
−
15
.
0
−
14
.
9999999988
−
14
.
99999998 2.3E-9 2.1E-10
75 484 2 035 043
[400; 0
.
1]
−
15
.
0
−
14
.
9999999976
−
14
.
99999995 8.9E-9 3.7E-10
55 992 1 136 101
[100; 0
.
5]
−
15
.
0
−
14
.
9199999995
−
12
.
99999999 0.399
6.8E-11
51 764
548 682
[100; 0
.
3]
−
15
.
0
−
14
.
8181247506
−
12
.
45311878 0
.
634
1.3E-10
40 372
312 837
[100; 0
.
1]
−
15
.
0
−
14
.
7537488912
−
12
.
84372234 0
.
681
2.6E-10
37 716
260 461
DP
−
15
.
0
−
14
.
1734734986
−
11
.
58255662 1
.
106
5.1E-11
33 067
110 120
g07
[70; 0.7] 24.306237739205
24.3067230937
24.30819910 4.5E-4 3.8E-9
1655956 11159837
[70; 0.5] 24.306330953891
24.3074746341
24.31034458 9.5E-4 9.1E-10
936436
6287404
[70; 0.3] 24.306433546473
24.3095029336
24.32761195 0.004
1.7E-9
577736
3850091
[40; 0.7] 24.308209926624
24.3350151850
24.37713109 0.019
6.3E-11
68436
401509
[40; 0.5] 24.315814462518
24.3570108927
24.47858422 0.039
8.3E-11
47996
263890
[40; 0.3] 24.337966344507
24.4005297646
24.57785438 0.055
2.1E-10
37084
189393
DP
24.449127539670
26.3375776765
30.93483255 1.472
1.2E-11
30835
87884
100 times higher. The behavior of various [
;
ϑ
]-settings on problem g01 have
already been described in section 7.4.2. On g02 the experiments show that also a
slow reduction of
can only improve the quality of the results slightly. It has to
be paid with a high number of fitness and constraint function calls. No significant
improvement can be achieved on problem g02, although we pay with ineciency.
For the DSES it is not dicult to obtain arbitrary convergence to the optimum
of problem g04. On problem g06 all tested DSES variants achieved promising
results. But the standard DP has to be recommended as the
cfc
values are lower
in comparison. The behavior of the DSES on g07 has already been described.
Like on g06 the DSES and DP are able to approximate the optimum of g08 very
well. But here, the method DP exhibits no significant performance advantages.
Only the slowest decrease of
on problem g09 enables the DSES to approximate
the optimum better than DP and better than
faster
DSES variants. Again, this
improvement has to be paid with higher
ffc
and
cfc
. While problem g11 can be
approximated suciently, the results of the DSES on problems g12 and g16 are
exceeding good. As already stated, the method DP performs well on problem
g24 while the DSES performs similarly on this problem.
We summarize: the DSES is based on the reduction of a minimum step size
which prevents premature step size reduction. It is able to approximate most
constrained problems of the
g-test suite
. The DSES is ecient concerning fitness
function calls, but inecient concerning constraint function calls.
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