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In this way, tournament selection based ABC algorithm has more adaptability for
various optimization problems and can be applied easily in both minimum and
maximum optimizations.
Table 4.
Optimizations of ABC algorithm and TSABC algorithm with ʻ = 0.05
Roulette wheel selection
Tournament selection (
ʻ
=0.05)
Function
avg
SD
avgFES
avg
SD
avgFES
f
1
3.91E-43
5.08E-43
52376
1.06E-43
1.14E-43
59140
f
2
1.05E-23
4.64E-24
102296
6.39E-23
2.51E-23
89383
f
3
3254.14
929.843
-
3614.27
634.464
-
f
4
0.583742
0.169694
-
0.340325
0.0652423
-
f
5
0.0242212
0.028179
217184
0.0796629
0.150301
208400
f
6
0
0
11230
0
0
28800
f
7
0.0312633
0.00682426
-
0.0281961
0.00804064
278200
f
8
-12569.5
2.03E-12
103856
-12569.5
2.11E-12
122890
f
9
0
0
84203
0
0
104443
f
10
7.67E-15
6.49E-16
108773
1.00E-14
2.49E-15
104423
f
11
0.000246535
0.00135033
82875
0
0
72593
f
12
1.57E-32
8.35E-48
43533
1.57E-32
8.35E-48
49766
f
13
1.35E-32
5.57E-48
56303
1.35E-32
5.57E-48
57413
5
Conclusions
In this paper, we proposed a tournament selection based ABC (TSABC) algorithm
and compared its performance with traditional ABC algorithm. Comparative
experiments have been conducted on 13 benchmark functions. In the experiment, we
applied elitist strategy to keep the historically optimal solution. This method can
prevent the abandon of the best solution that has been found so far. The experimental
results show that the TS strategy can be applied flexibly in both minimum and
maximum optimization, and can adjust selection pressure for different optimization
problems. Moreover, TSABC is easy for implementation for that TS strategy does not
need to calculate the select probability of each solution.
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