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The TSES on All Functions
Table 7.5 shows the experimental results of the TSES on all considered prob-
lems. While DP completely fails on Schwefel's constrained problem 2.40 the
(8+8,13+87)-TSES reaches the optimum in every run. The same behavior can
be observed on Schwefel's problem 2.41. In contrast to these problems the TSES
is not able to approximate the optimum of problem TR2 arbitrarily. But at least
a significant improvement in comparison to the results with DP can be observed.
The behavior of the TSES on g01 has already been described. Despite an increase
of the population sizes, the TSES could not achieve sucient results on problem
g02. On problem g04 a (8+8,15-85)-TSES failed, but the TSES with an offspring
sex ratio of 13+87 and 10+90 found the optimum in every run. Again, the im-
provement in comparison to death penalty is significant. On problem g06, a
highly constrained problem with a ratio of only 0
.
0066% of feasible search space,
all algorithms, including death penalty were successful. Similar to problem g02
an increase of population sizes could not obtain promising approximation of the
optimum of problem g07. The TSES could improve the results on problem g08
in comparison to death penalty, but demands a higher number of
ffc
and
cfc
.
The results of the TSES on g09 were not satisfying, but slightly better than DP.
Again, this improvement has to be paid with approximately 5 to 10 times higher
number of
ffc
and
cfc
. On problem g11 various experiments around the sex ratio
(8+8,13+87) like recommended by Kramer and Schwefel [75] could not achieve
promising results. Tests around the ratio (8+8,10+200) were more successful.
All experiments with the (8+8,10+200)-TSES and
κ
= 200 or
κ
= 300 showed
sucient results. A higher
κ
causes a loss of eciency. We have to emphasize
that DP shows comparable results. But the number of constraint function calls
cfc
is about ten times higher than the
cfc
of the TSES. So, we can observe an
Table 7.5.
Comparison of experimental results of the TSES on our constrained test
problems. In most cases the TSES shows satisfying approximation results.
TSES
κ
best
avg
worst
dev
2.40 (8+8,13+87)
50
−
5000
.
0000000000
−
4999
.
9999999999
−
4999
.
9999999997
3.3E-7
2.41 (8+8,13+87)
50
−
17857
.
1428571482
−
17857
.
1428571426
−
17857
.
1428571374 8.5E-10
TR2 (8+8,13+87)
300
2
.
0000000000
2
.
0000000095
2
.
0000000633
1.1E-8
−
14
.
9999999999
−
14
.
9999999999
−
14
.
9999999999 5.3E-15
g01 (40+40,50+400)
50
g02 (40+40,50+400)
50
−
0
.
7926079090
−
0
.
6583469345
−
0
.
4352731883
9.7E-3
g04 (8+8,13+87)
50
−
30665
.
5386717833
−
30665
.
5386717833
−
30665
.
5386717832 1.7E-11
g06 (8+8,10+90)
50
−
6961
.
8138755801
−
6961
.
8138755801
−
6961
.
8138755801 8.6E-13
g07 (40+40,50+400)
50
24.3171014481
24.4613633236
24.8935876076
1.0E-2
g08 (8+8,15+85)
50
−
0
.
0958250414
−
0
.
0958250414
−
0
.
0958250414 5.6E-18
g09 (8+8,13+87)
50
680
.
6303038768
680
.
6345393750
680
.
6530448662
4.6E-4
g11 (8+8,10+200)
300
0
.
7499900000
0
.
7499900169
0
.
7499903953
4.4E-9
g12 (8+8,10+90)
50
−
1
.
0000000000
−
0
.
9999999999
−
0
.
9999999999 7.4E-16
g16 (40+40,50+400)
50
−
1
.
9051552585
−
1
.
9051552585
−
1
.
9051552585 1.6E-15
g24 (8+8,10+90)
50
−
5
.
5080132715
−
5
.
5080132715
−
5
.
5080132715 4.3E-13
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