IEEE Computational Intelligence Magazine - February 2023 - 99

3) DQ-HSES vs. the Baselines
Tables VII to X shows the results
obtained by cDE, CoBiDE, jSO, and
DQ-HSES on the CEC 2018 test functions
in 10D, 30D, 50D, and 100D.
cDE, CoBiDE, and jSO are implemented
51 times. The values ofBM and
the results of the hypothesis test on the
functions excluding the training functions
are presented in the parentheses in
the tables. They show the following:
❏ On 10D functions, DQ-HSES performs
better than cDE on 11 functions
and worse on 13 functions,
better than CoBiDE on five functions
and worse on 18, and better
than jSO on four functions and
worse on 16 functions.
❏ On 30D functions, DQ-HSES performs
better than cDE on 23 functions
and worse on two functions,
better than CoBiDE on 15 functions
and worse on seven functions, and
better than jSO on 10 functions and
worse on nine functions.
❏ On 50D functions, DQ-HSES performs
better than cDE on 26 functions
and worse on three functions,
better than CoBiDE on 26 functions
and worse on three functions, and
better than jSO on 16 functions and
worse on seven functions.
TABLE VIII Results on 30D 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
5.68e+01x
5.06e+01x
0.00e+00
9.20e+01x
5.81e+01x
7.53e-01x
2.32e+03x
2.02e+01x
2.02e+04x
5.27e+01x
3.41e+01x
1.86e+01x
4.87e+02x
9.68e+01x
3.16e+01x
1.53e+01x
1.00e+02y
2.57e+02x
2.07e+02x
3.98e+02x
4.80e+02x
3.86e+02
1.55e+03x
4.96e+02y
3.23e+02x
5.19e+02x
2.12e+03x
5(4)
2/4/23(2/3/19)
STD
0.00e+00
0.00e+00
1.08e+01
6.17e+00
0.00e+00
6.45e+00
9.17e+00
1.44e+00
2.87e+02
1.19e+01
1.44e+04
2.30e+01
9.23e+00
4.81e+00
1.36e+02
2.90e+01
5.46e+00
2.31e+00
5.48e+01
7.19e+00
5.37e+02
6.56e+00
8.44e+00
4.74e-01
2.03e+02
1.24e+01
4.63e+01
4.89e+01
1.45e+02
MEAN
0.00e+00
0.00e+00
4.20e+01x
3.99e+01x
3.91e-08x
7.11e+01x
3.91e+01x
0.00e+00y
1.82e+03x
1.62e+01x
2.83e+03x
2.50e+01
1.08e+01y
6.85e+00
3.78e+02x
4.38e+01y
1.85e+01y
4.77e+00x
4.31e+01y
2.42e+02x
1.00e+02
3.88e+02x
4.64e+02x
3.86e+02
1.36e+03x
4.96e+02y
3.27e+02x
4.29e+02y
2.05e+03
9(6)
7/7/15(5/5/14)
❏ On 100D functions, DQ-HSES performs
better than cDE on 28 functions
and is not worse than it on any
function, is better than CoBiDE on
29 functions and not worse than it
on any function, and is better than
jSO on 22 functions and worse on
two functions.
❏ DQ-HSES delivers the best performance
on all functions excluding
the training functions, on 30D,
50D, and 100D functions.
In general, except for the test functions
in 10D, DQ-HSES obtains the
largest BM values.
CoBiDE
jSO
STD
0.00e+00
0.00e+00
2.82e+01
9.75e+00
4.48e-08
1.01e+01
1.07e+01
0.00e+00
4.56e+02
9.81e+00
5.20e+03
8.67e+00
4.70e+00
2.79e+00
1.47e+02
3.29e+01
8.65e+00
1.44e+00
5.79e+01
9.26e+00
0.00e+00
8.96e+00
1.18e+01
4.72e-01
2.90e+02
1.04e+01
4.77e+01
4.68e+01
8.41e+01
MEAN
0.00e+00
0.00e+00
5.86e+01x
8.55e+00x
0.00e+00
3.89e+01x
9.09e+00x
0.00e+00
1.52e+03x
3.03e+00y
1.70e+02x
1.48e+01y
2.18e+01x
1.08e+00y
7.89e+01y
3.29e+01y
2.04e+01
4.50e+00x
2.93e+01y
2.09e+02x
1.00e+02
3.50e+02
4.26e+02x
3.86e+02
9.20e+02
4.97e+02y
3.08e+02y
4.33e+02
1.97e+03y
15(13)
9/10/10(8/7/9)
STD
0.00e+00
0.00e+00
7.77e-01
2.09e+00
2.71e-08
1.45e+00
1.83e+00
0.00e+00
2.77e+02
2.64e+00
1.01e+02
4.83e+00
1.24e+00
6.91e-01
8.47e+01
8.07e+00
2.87e+00
1.73e+00
5.85e+00
1.95e+00
0.00e+00
3.29e+00
2.46e+00
7.72e-03
4.29e+01
7.00e+00
3.02e+01
1.36e+01
1.89e+01
MEAN
0.00e+00
0.00e+00
4.11e+00
6.95e+00
0.00e+00
3.53e+01
6.48e+00
2.63e-02
8.43e+02
1.61e+01
2.38e+01
3.01e+01
1.55e+01
1.16e+01
2.93e+02
6.33e+01
1.89e+01
3.78e+00
1.58e+02
2.07e+02
1.00e+02
3.52e+02
4.19e+02
3.86e+02
9.03e+02
5.25e+02
3.15e+02
4.62e+02
2.06e+03
15(13)
DQ-HSES
STD
0.00e+00
0.00e+00
9.37e+00
2.11e+00
0.00e+00
1.31e+00
2.06e+00
2.22e-01
3.36e+02
2.29e+01
9.60e+01
1.53e+01
9.35e+00
1.17e+01
1.81e+02
9.21e+01
6.85e+00
2.04e+00
5.88e+01
3.05e+00
0.00e+00
8.79e+00
5.30e+00
2.25e-02
1.37e+02
9.05e+00
3.73e+01
7.25e+01
4.91e+01
FEBRUARY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 99
IEEE Computational Intelligence Magazine - February 2023

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