Table 13.

Statistical results of 1000D unimodal functions

Function	GA	PSO	GSA	SCA
	Mean ± Std	Mean ± Std	Mean ± Std	Mean ± Std
F11	8.66E+15 ± 1.52E+06 $\ominus$	4.40E+02 ± 7.51E+00 $\ominus$	8.10E+05 ± 3.86E+00 $\ominus$	4.86E+03 ± 6.84E+02 $\ominus$
F12	2.53E+09 ± 8.96E+05 $\ominus$	2.06E+05 ± 2.75E+02 $\ominus$	1.07E+07 ± 5.54E+03 $\ominus$	4.28E+08 ± 6.55E+06 $\ominus$
F13	9.31E+05 ± 8.64E+02 $\ominus$	9.44E+03 ± 9.80E+01 $\ominus$	2.08E+04 ± 9.34E+02 $\ominus$	5.23E–02 ± 1.70E–03 $\ominus$
F14	2.97E–02 ± 6.00E–04 $\ominus$	2.92E+00 ± 5.00E–03 $\ominus$	1.45E–17 ± 6.35E–18 $\ominus$	3.19E+05 ± 3.25E+03 $\ominus$
F15	1.12E+10 ± 6.47E+02 $\ominus$	1.95E+04 ± 3.65E+02 $\ominus$	1.51E+07 ± 9.17E+05 $\ominus$	2.16E+09 ± 6.32E+07 $\ominus$
F16	4.28E+04 ± 1.28E+02 $\ominus$	4.76E+02 ± 8.47E+01 $\ominus$	5.71E+03 ± 6.02E+02 $\ominus$	1.06E+03 ± 3.27E+02 $\ominus$
F17	9.78E+01 ± 1.65E+00 $\ominus$	9.95E–01 ± 5.00E–03 $\ominus$	3.18E+01 ± 1.52E+01 $\ominus$	9.91E+01 ± 1.60E+01 $\ominus$
F18	inf $\ominus$	4.83E+02 ± 1.39E+01 $\ominus$	6.31E+01 ± 3.12E+00 $\ominus$	inf $\ominus$
F19	3.54E+03 ± 1.56E+01 $\ominus$	8.27E+01 ± 5.00E–02 $\ominus$	4.62E+06 ± 6.15E+03 $\ominus$	1.51E+11 ± 3.65E+06 $\ominus$
F20	2.64E+06 ± 5.61E+02 $\ominus$	3.11E+02 ± 3.50E+01 $\ominus$	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	3.08E+05 ± 2.49E+04 $\ominus$
F21	1.23E+07 ± 6.12E+03 $\ominus$	1.56E+05 ± 1.20E–02 $\ominus$	4.23E+05 ± 3.31E+02 $\ominus$	1.30E+06 ± 2.14E+04 $\ominus$
F22	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$
$\ominus$	11	11	10	11
$\oplus$	0	0	0	0
$\odot$	1	1	2	1
	SELO	HBO	LFD	SETO
	Mean ± Std	Mean ± Std	Mean ± Std	Mean ± Std
F11	5.12E–04 ± 9.45E–05 $\ominus$	1.45E+01 ± 5.02E+00 $\ominus$	1.66E–06 ± 8.55E–08 $\ominus$	0.00E+00 ± 0.00E+00
F12	1.00E+00 ± 6.00E–03 $\ominus$	1.56E+05 ± 1.26E+03 $\ominus$	1.00E+00 ± 4.15E–28 $\ominus$	6.67E–01 ± 0.00E+00
F13	2.58E–05 ± 7.00E–04 $\ominus$	8.61E+02 ± 7.64E+00 $\ominus$	2.53E–06 ± 1.19E–08 $\ominus$	0.00E+00 ± 0.00E+00
F14	5.66E–06 ± 6.48E–08 $\ominus$	7.19E–09 ± 1.75E–10 $\ominus$	1.77E–03 ± 2.56E–05 $\ominus$	0.00E+00 ± 0.00E+00
F15	9.97E+02 ± 6.03E+01 $\oplus$	1.76E+03 ± 1.42E+02 $\ominus$	9.89E+02 ± 3.26E–02 $\oplus$	9.99E+02 ± 0.00E+00
F16	2.47E–04 ± 3.60E–04 $\ominus$	2.05E+01 ± 6.56E+00 $\ominus$	1.98E–01 ± 3.90E–04 $\ominus$	0.00E+00 ± 0.00E+00
F17	7.97E+01 ± 7.55E–01 $\ominus$	9.87E+01 ± 8.05E+00 $\ominus$	6.94E–04 ± 6.31E–07 $\ominus$	0.00E+00 ± 0.00E+00
F18	1.30E+193 ± 6.64E+85 $\ominus$	inf $\ominus$	inf $\ominus$	0.00E+00 ± 0.00E+00
F19	1.15E–03 ± 4.70E–05 $\ominus$	6.64E+06 ± 5.64E+03 $\ominus$	7.01E–43 ± 3.95E–45 $\ominus$	0.00E+00 ± 0.00E+00
F20	2.60E–08 ± 6.00E–06 $\ominus$	6.27E–03 ± 3.40E–04 $\ominus$	6.32E–05 ± 8.32E–07 $\ominus$	0.00E+00 ± 0.00E+00
F21	1.03E–07 ± 5.60E–04 $\ominus$	1.39E+03 ± 9.66E+01 $\ominus$	3.01E-04 ± 1.70E–05 $\ominus$	0.00E+00 ± 0.00E+00
F22	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	$\mathbf{0.00}\mathbf{E}+\mathbf{00}\pm \mathbf{0.00}\mathbf{E}+\mathbf{00}\odot$	0.00E+00 ± 0.00E+00
$\ominus$	10	11	10	–
$\oplus$	1	1	1	–
$\odot$	1	1	1	–

Best results are illustrated in boldface