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To avoid interference from other influencing factors, all experiments were run for
300,000 function evaluations and each of them was repeated 30 times independently.
The population size
SN
is 50, and the parameter
limit
is set as 1000. In addition, elitist
strategy is applied in both ABC and TSABC algorithm. The experiments were divided
into two parts. The first part is optimizing the benchmark functions by TSABC
algorithm and comparing their optimal solutions under different values of parameter
ʻ
in the TS strategy. The other part is the optimizations of benchmark functions by
traditional ABC algorithm and comparing them with the experiment results of
TSABC algorithm.
In the experiment of TSABC algorithm, the proportion of solutions (
) is set as
0.02, 0.1, 0.2, 0.4, 0.6, 0.8, and 0.9, respectively. The experiments are proceeded
independently and the results are showed in Table 2 and Table 3, where the
bold
values is the minimum values in each function column,
avg
and
SD
present the
average of fitness values and the standard deviation in 30 times respectively. It can be
concluded from the experiment result that for different benchmark functions, the best
results are obtained by TSABCs that use different values of
ʻ
. That is to say, different
functions should be optimized with different selection pressure. In TSABC algorithm,
we can control the selection pressure through determining different proportions of
solutions (
ʻ
ʻ
) in the TS strategy.
Table 2.
Comparison among different value of parameter ʻ in tournament selection strategy
with benchmark functions (
f
1
(
x
) -
f
7
(
x
)
)
f
1
(
x
)
f
2
(
x
)
f
3
(
x
)
f
4
(
x
)
f
5
(
x
)
f
6
(
x
)
f
7
(
x
)
ʻ
avg
SD
9.70E-47
8.70E-47
2.15E-24
9.70E-25
4653.3
943.819
0.787244
0.118832
0.0780279
0.108088
0
0
0.0329599
0.00681458
0.02
avg
SD
1.79E-37
1.54E-37
9.57E-20
3.73E-20
2136.7
479.985
0.102241
0.023434
0.0484923
0.0703702
0
0
0.0172999
0.00451125
0.1
avg
SD
6.88E-34
7.01E-34
5.97E-18
3.83E-18
1302.43
412.324
0.0512829
0.00898793
0.0646095
0.142791
0
0
0.0135199
0.00400185
0.2
avg
SD
3.06E-31
4.92E-31
1.00E-16
5.05E-17
666.061
219.095
0.0292305
0.00804453
0.0899865
0.206365
0
0
0.00810017
0.0026816
0.4
avg
SD
3.32E-30
2.76E-30
4.93E-16
3.31E-16
452.737
194.462
0.0231311
0.00465257
0.0511788
0.0677494
0
0
0.00536595
0.00184911
0.6
avg
SD
2.07E-29
1.57E-29
1.30E-15
8.60E-16
411.615
172.012
0.0230305
0.00592132
0.105486
0.164903
0
0
0.0047305
0.00180727
0.8
avg
SD
9.71E-29
1.60E-28
1.62E-15
5.77E-16
315.263
143.722
0.0223896
0.005066
0.182286
0.243687
0
0
0.00455137
0.00150967
0.9
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