Table 4.

Optimization results of TOA and compared algorithms on high-dimensional test function.

		MPA	TSA	WOA	GWO	TLBO	GSA	PSO	GA	TOA
$F_8$	Ave	−3594.16321	−5740.3388	−1663.9782	−5885.1172	−7408.6107	−2849.0724	−6908.6558	−8184.4142	−9631.41
	std	811.32651	41.5	716.3492	467.5138	513.5784	264.3516	625.6248	833.2165	3.86 × 10−12
$F_9$	Ave	140.1238	5.70 × 10−3	4.2011	8.5265 × 10−15	10.2485	16.2675	57.0613	62.4114	0
	std	26.3124	1.46 × 10−3	4.3692 × 10−15	5.6446 × 10−30	5.5608 × 10−15	3.1776 × 10−15	6.3552 × 10−15	2.5421 × 10−14	0
$F_{10}$	Ave	9.6987 × 10−12	9.80 × 10−14	0.3293	1.7053 × 10−14	0.2757	3.5673 × 10−9	2.1546	3.2218	8.88 × 10−16
	std	6.1325 × 10−12	4.51 × 10−12	1.9860 × 10−16	2.7517 × 10−29	2.5641 × 10−15	3.6992 × 10−25	7.9441 × 10−16	5.1636 × 10−15	0
$F_{11}$	Ave	0	1.00 × 10−7	0.1189	0.0037	0.6082	3.7375	0.0462	1.2302	0
	std	0	7.46 × 10−7	8.9991 × 10−17	1.2606 × 10−18	1.9860 × 10−16	2.7804 × 10−15	3.1031 × 10−18	8.4406 × 10−16	0
$F_{12}$	Ave	0.0851	0.0368	1.7414	0.0372	0.0203	0.0362	0.4806	0.047	0.2463
	std	0.0052	1.5461 × 10−2	8.1347 × 10−12	4.3444 × 10−17	7.7579 × 10−19	6.2063 × 10−18	1.8619 × 10−16	4.6547 × 10−18	7.45 × 10−17
$F_{13}$	Ave	0.4901	2.9575	0.3456	0.5763	0.3293	0.002	0.5084	1.2085	1.25
	std	0.1932	1.5682 × 10−12	3.2539 × 10−12	2.4825 × 10−16	2.1101 × 10−16	4.2617 × 10−14	4.9650 × 10−17	3.2272 × 10−16	4.47 × 10−16