Table 12.

The optimal result of various algorithms for Himmelblau problem, the bold numbers means the best performance among whole competitors.

	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$	${\mathit{g}}_1$	${\mathit{g}}_2$	${\mathit{g}}_3$	${\mathit{g}}_4$	${\mathit{g}}_5$	${\mathit{g}}_6$	Value	Constraints
ESOA	78	33	29.9984	45	36.77	−0.00018	−91.9998	−11.16	−8.841	−4.9988	−0.00120342	−30,664.5	Yes
PSO [16]	78	33	29.9953	45	36.77	0	−92	−11.15	−8.84	−5	0	−30,665.5	Yes
GA [5]	78.047	35.02	31.81	44.81	32.57	−0.27373	−91.7263	−10.95	−9.04	−4.98832	−0.0116773	−30,333.1	Yes
DE [6]	78	33.00	30.002	44.97	36.77	−0.00107	−91.9989	−11.15	−8.84	−4.99875	−0.00124893	−30,663.2	Yes
GWO [18]	78.0031	33.00	30.0069	45	36.75	−0.00201	−91.998	−11.15	−8.84	−4.99815	−0.0018509	−30,662.7	Yes
HHO [83]	78	33	32.4546	43.68	31.56	−0.86883	−91.1312	−12.05	−7.94	−5	9.56 × 10−7	−30,182.6	Yes
L-Shade [59]	78	33	27	27	27	−1.88843	−90.11157	−13.83258	−6.16742	−8.23715	3.23715	−32,217.4	No
iL-Shade [60]	78	33	27	27	27	−1.88843	−90.11157	−13.83258	−6.16742	−8.23715	3.23715	−32,217.4	No
MPEDE [90]	78	33	27	27	27	−1.88843	−90.11157	−13.83258	−6.16742	−8.23715	3.23715	−32,217.4	No