IEEE Computational Intelligence Magazine - February 2023 - 98

are presented to show the process ofoptimization
of DQ-HSES in comparison
with that ofHSES in Figure 4.
For each function, HSES and DQFIGURE
4 The curves of optimization of six functions on the CEC 2014
test suite. (a) F16 in 10D, (b) F24 in 10D, (c) F11 in 30D, (d) F16 in 30D,
(e) F17 in 50D, and (f) F21 in 50D.
TABLE VII Results on 10D test functions of CEC 2018.
cDE
MEAN
F1
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
F13
F14
F15
F16
F17
F18
F19
F20
F21
F22
F23
F24
F25
F26
F27
F28
F29
F30
BM
y=
=x
0.00e+00
0.00e+00
0.00e+00
4.62e+00x
0.00e+00
1.55e+01x
5.73e+00x
0.00e+00
1.87e+02x
5.54e-01y
1.39e+02x
5.05e+00x
6.48e-01y
3.09e-01y
2.96e+00y
1.32e+00y
1.13e+00x
4.19e-03y
9.90e-02y
1.79e+02y
9.28e+01y
3.07e+02x
3.26e+02x
4.17e+02y
3.19e+02x
3.89e+02y
4.04e+02y
2.36e+02y
8.06e+04x
6(5)
13/5/11(11/1/9)
STD
0.00e+00
0.00e+00
0.00e+00
1.84e+00
0.00e+00
2.74e+00
2.11e+00
0.00e+00
1.10e+02
9.14e-01
1.60e+02
2.97e+00
9.73e-01
4.85e-01
1.68e+01
8.12e+00
3.92e+00
8.08e-03
1.97e-01
4.90e+01
2.65e+01
2.56e+00
4.62e+01
2.34e+01
1.30e+02
2.01e+00
1.39e+02
6.43e+00
2.45e+05
MEAN
0.00e+00
0.00e+00
0.00e+00
3.57e+00x
0.00e+00
1.34e+01x
3.76e+00x
0.00e+00
9.17e+01x
9.75e-02y
1.67e-01y
1.07e+00y
0.00e+00y
9.31e-03y
2.24e-01y
1.57e+00y
6.37e-03y
8.99e-03y
0.00e+00y
1.37e+02y
7.86e+01y
3.04e+02x
2.74e+02y
3.99e+02y
3.00e+02
3.88e+02y
3.05e+02y
2.29e+02y
3.95e+02y
18(14)
18/6/5(15/5/4)
HSES are run 11 times and the logarithm
ofthe mean ofthe function values
obtained during the search process are
plotted. The figures show that DQHSES
performs significantly better than
HSES, and usually requires fewer fitness
evaluations (nfes) to reach a better
solution than it.
CoBiDE
jSO
STD
0.00e+00
0.00e+00
0.00e+00
1.53e+00
0.00e+00
2.00e+00
1.71e+00
0.00e+00
9.56e+01
2.98e-01
1.31e-01
1.83e+00
0.00e+00
3.52e-02
1.52e-01
6.18e-01
2.77e-02
1.33e-02
0.00e+00
5.15e+01
4.16e+01
1.58e+00
1.02e+02
9.14e+00
0.00e+00
9.02e-01
3.97e+01
2.77e+00
3.50e+00
MEAN
0.00e+00
0.00e+00
0.00e+00
1.75e+00x
0.00e+00
1.17e+01x
1.95e+00x
0.00e+00
3.58e+01
0.00e+00y
2.66e+00y
2.96e+00y
5.85e-02y
2.20e-01y
5.68e-01y
5.02e-01y
3.08e-01y
1.07e-02y
3.42e-01y
1.32e+02y
1.00e+02
3.01e+02x
2.96e+02
4.05e+02y
3.00e+02
3.89e+02y
3.39e+02y
2.34e+02y
3.94e+02y
12(10)
16/9/4(13/7/4)
STD
0.00e+00
0.00e+00
0.00e+00
7.60e-01
0.00e+00
6.06e-01
7.43e-01
0.00e+00
5.54e+01
0.00e+00
1.67e+01
2.35e+00
2.36e-01
2.00e-01
2.64e-01
3.48e-01
1.95e-01
1.25e-02
1.28e-01
4.83e+01
0.00e+00
1.58e+00
7.93e+01
1.74e+01
0.00e+00
2.25e-01
9.65e+01
2.95e+00
4.49e-02
MEAN
0.00e+00
0.00e+00
0.00e+00
8.15e-01
0.00e+00
1.10e+01
7.01e-01
0.00e+00
8.88e+01
7.61e-01
2.26e+01
3.17e+00
6.00e+00
8.17e-01
4.41e+00
1.18e+01
7.02e-01
4.31e-01
6.98e+00
1.98e+02
1.00e+02
2.99e+02
3.21e+02
4.46e+02
3.00e+02
3.97e+02
5.92e+02
2.64e+02
4.13e+02
10(9)
DQ-HSES
STD
0.00e+00
0.00e+00
0.00e+00
8.79e-01
0.00e+00
5.61e-01
7.96e-01
0.00e+00
1.30e+02
3.50e+00
5.52e+01
2.58e+00
1.20e+01
1.73e+00
2.03e+01
9.95e+00
1.61e+00
8.89e-01
9.06e+00
1.76e+01
0.00e+00
2.13e+01
3.90e+01
1.18e+00
8.82e+00
1.93e+00
3.80e+01
1.10e+01
2.34e+01
98 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2023
IEEE Computational Intelligence Magazine - February 2023

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