Table 3.

Optimization results of TOA and compared algorithms on unimodal test function.

		MPA	TSA	WOA	GWO	TLBO	GSA	PSO	GA	TOA
$F_1$	Ave	3.2715 × 10−21	7.71 × 10−38	2.1741 × 10−9	1.09 × 10−58	8.3373 × 10−60	2.0255 × 10−17	1.7740 × 10−5	13.2405	0
	std	4.6153 × 10−21	7.00 × 10−21	7.3985 × 10−25	5.1413 × 10−74	4.9436 × 10−76	1.1369 × 10−32	6.4396 × 10−21	4.7664 × 10−15	0
$F_2$	Ave	1.57 × 10−12	8.48 × 10−39	0.5462	1.2952 × 10−34	7.1704 × 10−35	2.3702 × 10−8	0.3411	2.4794	0
	std	1.42 × 10−12	5.92 × 10−41	1.7377 × 10−16	1.9127 × 10−50	6.6936 × 10−50	5.1789 × 10−24	7.4476 × 10−17	2.2342 × 10−15	0
$F_3$	Ave	0.0864	1.15 × 10−21	1.7634 × 10−8	7.4091 × 10−15	2.7531 × 10−15	279.3439	589.492	1536.8963	0
	std	0.1444	6.70 × 10−21	1.0357 × 10−23	5.6446 × 10−30	2.6459 × 10−31	1.2075 × 10−13	7.1179 × 10−13	6.6095 × 10−13	0
$F_4$	Ave	2.6 × 10−8	1.33 × 10−23	2.9009 × 10−5	1.2599 × 10−14	9.4199 × 10−15	3.2547 × 10−9	3.9634	2.0942	0
	std	9.25 × 10−9	1.15 × 10−22	1.2121 × 10−20	1.0583 × 10−29	2.1167 × 10−30	2.0346 × 10−24	1.9860 × 10−16	2.2342 × 10−15	0
$F_5$	Ave	46.049	28.8615	41.7767	26.8607	146.4564	36.10695	50.26245	310.4273	26.2476
	std	0.4219	4.76 × 10−3	2.5421 × 10−14	0	1.9065 × 10−14	3.0982 × 10−14	1.5888 × 10−14	2.0972 × 10−13	3.26× 10−14
$F_6$	Ave	0.398	7.10 × 10−21	1.6085 × 10−9	0.6423	0.4435	0	20.25	14.55	0
	std	0.1914	1.12 × 10−25	4.6240 × 10−25	6.2063 × 10−17	4.2203 × 10−16	0	1.2564	3.1776 × 10−15	0
$F_7$	Ave	0.0018	3.72 × 10−4	0.0205	0.0008	0.0017	0.0206	0.1134	5.6799 × 10−3	9.92× 10−6
	std	0.001	5.09 × 10−5	1.5515 × 10−18	7.2730 × 10−20	3.8789 × 10−19	2.7152 × 10−18	4.3444 × 10−17	7.7579 × 10−19	1.74 × 10−20