A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization
Table 3
Mean normalized optimization results in fourteen benchmark functions. The values shown are the minimum objective function values found by each algorithm, averaged over 100 Monte Carlo simulations.
ā
ACO
BA
BBO
DE
ES
GA
HS
HSBA
PSO
SGA
F01
2.31
3.33
1.15
2.02
3.38
2.72
3.47
1.09
2.66
1.00
F02
24.58
25.82
1.58
8.94
24.35
5.45
15.69
1.00
13.96
1.33
F03
3.16
60.72
1.93
5.44
23.85
3.22
77.22
1.00
25.77
1.42
F04
1.00
3.0E38
4.0E32
5.6E33
2.7E38
3.1E32
1.4E39
2.3E32
4.1E36
9.6E31
F05
1.00
1.1E8
299.42
1.5E6
4.6E8
5.4E3
4.1E8
215.51
5.5E7
111.10
F06
489.01
6.8E3
35.32
308.29
1.8E4
274.83
1.5E4
1.00
2.5E3
10.09
F07
8.09
11.55
1.28
6.56
11.87
6.17
10.22
1.00
8.44
1.80
F08
42.25
29.01
2.29
7.59
59.99
9.05
47.85
1.00
12.04
2.15
F09
3.17
20.26
1.99
13.58
13.33
1.81
19.92
1.00
17.61
1.15
F10
1.75
3.73
1.38
2.95
4.93
1.25
4.22
1.00
2.48
1.48
F11
1.05
19.70
1.83
7.14
23.12
11.13
19.45
1.00
13.22
2.46
F12
1.86
4.03
1.00
2.99
3.91
1.92
3.74
1.38
2.38
1.12
F13
98.30
150.84
3.80
19.03
226.52
47.74
182.32
1.00
72.91
4.02
F14
7.73
120.48
3.93
13.31
102.56
11.53
146.55
1.00
63.44
3.28
TimE
2.74
1.00
1.32
1.64
1.67
1.79
2.33
1.43
2.03
1.76
*The values are normalized so that the minimum in each row is 1.00. These are not the absolute minima found by each algorithm, but the average minima found by each algorithm.