Table 2.

Comparison with WOA Mirjalili and Lewis (2016)

Function	Proposed approach	WOA Mirjalili and Lewis (2016)	$f({\mathit{x}}_{\mathrm{opt}})$
$f_1$	0.775955 ± 0.222759	1.41E−30 ± 4.91E−30	0
$f_4$	5.154556 ± 2.273995	0.072581 ± 0.39747	0
$f_5$	0.759658 ± 0.251091	1.06E−21 ± 2.39E−21	0
$f_6$	26.778816 ± 3.804910	27.86558 ± 0.763626	0
$f_9$	0.809812 ± 0.088605	0.000289 ± 0.001586	0
$f_{10}$	2.230591 ± 0.810609	7.4043 ± 9.897572	0
$f_{11}^{†}$	− 12554.89 ± 33.2842	− 5080.76 ± 695.7968	− 12569.48
$f_{13}$	− 1.031611 ± 3.73E-05	− 1.03163 ± 4.2E−07	− 1.0316
$f_{15}$	0.998004 ± 5.98E-10	2.111973 ± 2.498594	0.998004 $\approx$ 1

${}^{†}$This version of Schwefel min $f({\mathit{x}}_{\mathrm{opt}})=$ − 418.9829$\times$30 (see Mirjalili and Lewis 2016)