Modified Atom Search Optimization Based on Immunologic Mechanism and Reinforcement Learning

Table 6

Test statistical results with different strategies.

Functions	Algorithms	Min	Mean	Max	STD
f1(x)	ASO	7.33E − 27	2.64E − 26	1.05E − 25	3.08E − 26
	ASO_chaos	2.69E − 27	38220.86	134747.6	49900.47
	ASO_vaccine	9.34E − 27	3.35E − 26	6.9E − 26	2.51E − 26
	ASO_rl	5.59E − 27	4.05E − 26	9.19E − 26	3.97E − 26
f2(x)	ASO	2.16E − 13	5.32E − 13	9.67E − 13	2.51E − 13
	ASO_chaos	2.99E − 13	1.58E + 18	2.84E + 19	6.35E + 18
	ASO_vaccine	5.68E − 13	7.88E − 13	1.01E − 12	1.6E − 13
	ASO_rl	3.18E − 13	1.25E − 12	2.35E − 12	7.73E − 13
f3(x)	ASO	5.73E − 26	1.73E − 25	3.92E − 25	1.03E − 25
	ASO_chaos	3.79E − 26	5651.508	17487.91	7310.399
	ASO_vaccine	8.75E − 26	2.01E − 25	5.32E − 25	1.86E − 25
	ASO_rl	1.23E − 25	3.62E − 25	5.3E − 25	1.63E − 25
f4(x)	ASO	0	0	0	0
	ASO_chaos	0	42588.7	116706	53955.46
	ASO_vaccine	0	0	0	0
	ASO_rl	0	0	0	0
f5(x)	ASO	0.003764	0.00772	0.011135	0.002189
	ASO_chaos	0.003324	72.91083	301.5848	100.3357
	ASO_vaccine	0.003663	0.005553	0.008711	0.00202
	ASO_rl	0.024793	0.032927	0.046203	0.010069
f6(x)	ASO	2.19E − 52	1.46E − 51	5.24E − 51	1.51E − 51
	ASO_chaos	2.34E − 53	94.61799	345.6983	134.9649
	ASO_vaccine	1.02E − 51	3.62E − 51	8.42E − 51	3.45E − 51
	ASO_rl	5.22E − 52	9.87E − 51	3.93E − 50	1.67E − 50
f7(x)	ASO	4.35E − 14	7.41E − 14	1.47E − 13	2.97E − 14
	ASO_chaos	5.42E − 14	8.462759	21.3434	10.63432
	ASO_vaccine	6.84E − 14	9.25E − 14	1.29E − 13	2.22E − 14
	ASO_rl	7.55E − 14	1.02E − 13	1.82E − 13	4.54E − 14
f8(x)	ASO	0	0	0	0
	ASO_chaos	0	344.9339	956.8887	437.1594
	ASO_vaccine	0	0	0	0
	ASO_rl	0	0	0	0
f9(x)	ASO	9.949591	14.5264	20.89413	3.356089
	ASO_chaos	7.959672	230.112	648.2703	274.7404
	ASO_vaccine	11.93951	16.11833	20.89413	4.065958
	ASO_rl	7.959672	12.33749	14.92438	2.68823
f10(x)	ASO	4106.132	4650.915	5626.077	521.8557
	ASO_chaos	4312.996	5089.873	5718.976	566.3842
	ASO_vaccine	4500.827	5160.146	5625.985	471.8367
	ASO_rl	3928.42	4852.266	5823.46	748.2354
f11(x)	ASO	4.23E − 14	8.76E − 14	1.97E − 13	4.72E − 14
	ASO_chaos	2.55E − 14	37.10606	116.9176	47.21336
	ASO_vaccine	7.52E − 14	1.12E − 13	1.6E − 13	3.61E − 14
	ASO_rl	7.19E − 14	1.3E − 13	2.7E − 13	8.45E − 14
f12(x)	ASO	2.78E − 27	6.39E − 27	2.1E − 26	5.59E − 27
	ASO_chaos	2.46E − 27	172.4654	562.9697	222.5449
	ASO_vaccine	2.06E − 27	1.86E − 26	6.71E − 26	2.73E − 26
	ASO_rl	3.9E − 27	1.11E − 26	1.95E − 26	7.21E − 27
f13(x)	ASO	0.111929	0.171566	0.247934	0.04255
	ASO_chaos	0.006224	0.221173	0.5	0.239022
	ASO_vaccine	0.18622	0.268834	0.353136	0.072799
	ASO_rl	0.094156	0.109595	0.122451	0.010779
f14(x)	ASO	12	18.70114	35.0005	6.254622
	ASO_chaos	9	226.4739	622.2764	263.4471
	ASO_vaccine	16.08234	23.04624	27.001	4.654738
	ASO_rl	13	23	30	6.892024
f15(x)	ASO	13.22012	14.72793	15.51416	0.63515
	ASO_chaos	14.05125	1691798	5141408	2180894
	ASO_vaccine	15.5044	15.89732	16.17919	0.26884
	ASO_rl	15.80763	16.45844	17.09231	0.562882
f16(x)	ASO	3.53E − 29	8.02E − 29	1.31E − 28	3.4E − 29
	ASO_chaos	2.17E − 29	2.2E + 09	8.17E + 09	2.87E + 09
	ASO_vaccine	3.97E − 29	1.23E − 28	1.94E − 28	6.21E − 29
	ASO_rl	3.35E − 29	1.49E − 28	4.22E − 28	1.59E − 28
	MASO	3.53E − 29	8.02E − 29	1.31E − 28	3.4E − 29
f17(x)	ASO	6.55E − 28	2.14E − 27	5.54E − 27	1.53E − 27
	ASO_chaos	6.04E − 28	1.47E + 09	5.17E + 09	1.96E + 09
	ASO_vaccine	7.69E − 28	2.92E − 27	7.94E − 27	2.89E − 27
	ASO_rl	7.23E − 28	2.19E − 27	5.26E − 27	1.84E − 27
f18(x)	ASO	4.71E − 14	9.18E − 14	1.75E − 13	3.96E − 14
	ASO_chaos	5.06E − 14	8.510808	21.42481	10.69466
	ASO_vaccine	6.13E − 14	1.59E − 13	4.34E − 13	1.55E − 13
	ASO_rl	1.04E − 13	1.34E − 13	1.82E − 13	2.95E − 14
f19(x)	ASO	8.954632	16.01884	19.89918	3.492605
	ASO_chaos	9.949591	226.8982	594.1118	268.2596
	ASO_vaccine	11.9395	22.28707	31.83867	7.629455
	ASO_rl	9.949591	14.5264	19.89917	4.750859
f20(x)	ASO	0	0	0	0
	ASO_chaos	0	375.431	1145.34	482.6689
	ASO_vaccine	0	0	0	0
	ASO_rl	0	0	0	0
f21(x)	ASO	4046.881	4920.749	5321.667	391.9594
	ASO_chaos	4561.110	5235.886	3421.026	339.6557
	ASO_vaccine	4817.261	5210.066	5626.202	326.6599
	ASO_rl	4540.61	5634.291	6731.833	945.2253