A Particle Swarm Optimization Algorithm with Gradient Perturbation and Binary Tree Depth First Search Strategy

Table 4

Mean and standard deviations of the function values.

	Criteria	CMOPSO	SAPSO	H-PSO-SCAC	IGPSO	GB-PSO
	Mean	2.90E − 10	2.92E − 08	1.13E − 20	6.42E − 11	2.01E − 31
	S.D.	4.24E − 09	1.96E − 10	5.23E − 22	1.45E − 10	4.47E − 31
	Mean	4.68E − 11	2.21E − 10	1.29E − 09	2.23E − 19	4.20E − 33
	S.D.	2.09E − 11	4.37E − 10	5.34E − 08	4.34E − 19	5.31E − 33
	Mean	1.51E − 20	3.66E − 08	3.59E − 13	1.18E − 15	1.06E − 34
	S.D.	8.83E − 19	6.10E − 07	7.74E − 13	3.61E − 13	4.46E − 34
	Mean	3.65E − 07	6.96E − 08	6.08E − 09	1.08E − 06	1.21E − 21
	S.D.	7.28E − 07	8.72E − 08	4.31E − 08	1.16E − 06	4.44E − 20
	Mean	3.68E − 07	2.52E − 3	1.79E − 02	3.19E − 08	2.68E − 12
	S.D.	7.23E − 07	4.51E − 3	3.87E − 02	5.46E − 08	5.58E − 11
	Mean	2.13E − 13	1.22E − 09	2.19E − 06	3.16E − 13	4.34E − 26
	S.D.	4.66E − 13	2.28E − 08	4.68E − 06	7.08E − 13	9.21E − 26
	Mean	1.66E − 09	3.71E − 18	4.35E − 16	7.31E − 16	3.06E − 30
	S.D.	2.12E − 09	6.87E − 18	5.38E − 16	1.11E − 15	5.45E − 30
	Mean	1.38E − 19	5.46E − 14	3.23E − 13	7.49E − 10	2.19E − 17
	S.D.	2.27E − 19	1.13E − 13	8.08E − 12	5.82E − 10	4.91E − 17
	Mean	4.56E − 12	6.75E − 14	8.14E − 11	7.49E − 12	4.89E − 29
	S.D.	6.96E − 11	3.95E − 14	7.89E − 10	8.98E − 12	8.92E − 28
	Mean	2.95E − 10	5.13E − 04	3.59E − 06	3.34E − 09	7.72E − 10
	S.D.	7.92E − 10	7.96E − 04	6.69E − 05	7.48E − 09	8.18E − 09
	Mean	2.97E − 06	1.86E − 20	3.59E − 12	1.33E − 15	5.01E − 30
	S.D.	7.66E − 05	6.83E − 20	8.19E − 11	8.78E − 15	8.92E − 30
	Mean	0.1435	0.0273	0.0489	0.5570	0.0032
	S.D.	0.0718	0.0118	0.0023	0.7658	0.0013
	Mean	−426.9618	−436.7843	−416.1015	−377.6605	−427.0233
	S.D.	2.3443	7.8668	12.39	3.2649	18.7899
	Mean	−389.23	−401.67	−389.67	−421.89	−430.23
	S.D.	10.34	23.34	30.34	30.12	9.15
	Mean	407.6742	407.1695	406.4978	406.3855	396.4175
	S.D.	12.34	23.89	5.84	14.56	6.89
	Mean	−256.34	−306.45	−297.45	−245.49	−319.91
	S.D.	4.78	5.78	12.23	16.21	7.89
	Mean	−136.12	−136.89	−130.51	−129.45	−134.89
	S.D.	5.12	12.12	9.19	11.91	6.51
	Mean	−171.34	−169.77	−173.88	−174.12	−175.23
	S.D.	5.86	10.23	6.44	5.23	3.81
	Mean	−801.34	−821.22	−802.41	−825.21	−880.78
	S.D.	12.72	9.12	12.24	8.12	6.12
	Mean	−371.09	−367.91	−381.33	−389.11	−409.78
	S.D.	13.56	14.34	12.99	10.21	12.33
	Mean	2.91E − 02	6.15E − 03	1.23	5.48E − 04	3.31E − 07
	S.D.	0.45	5.15E − 02	3.11	5.98E − 03	7.32E − 06
	Mean	−125.78	−142.99	−126.44	−144.89	−165.98
	S.D.	12.77	8.33	12.36	12.63	5.99

Mean: mean of objective values; S.D: standard deviation.