A Modified Social Spider Optimization for Economic Dispatch with Valve-Point Effects

Table 3

Comparisons of the results among the algorithms with D = 50.

Function		SSO [29]	NISSO [37]	MSSO [38]	OBSSO [39]	CLPSO [40]	JADE [41]	ISSO
Sphere	Min	2.39E − 06	5.70E − 20	7.44E − 35	4.57E − 28	1.38E − 53	8.22E − 45	2.84E − 63
	Mean	6.88E − 06	1.63E − 19	1.40E − 34	5.09E − 26	1.70E − 52	5.60E − 44	7.05E − 62
	Std	7.06E − 07	9.44E − 20	8.21E − 35	7.49E − 28	4.41E − 53	3.15E − 45	1.11E − 62
	At (s)	7.47	5.86	7.05	5.34	4.14	4.94	3.68
SumSquare	Min	1.88E − 16	4.66E − 32	5.49E − 43	8.73E − 35	1.79E − 59	5.14E − 52	4.61E − 59
	Mean	4.30E − 14	7.68E − 30	4.87E − 42	8.44E − 34	8.60E − 57	1.80E − 51	3.87E − 58
	Std	5.79E − 15	3.13E − 30	9.40E − 43	4.97E − 34	9.63E − 58	3.19E − 52	7.53E − 59
	At (s)	7.41	5.79	7.14	5.61	4.05	5.01	3.74
Schwefel 2.21	Min	9.29E − 01	5.11E − 01	8.44E − 02	5.94E − 01	8.63E − 03	2.05E − 02	4.72E − 03
	Mean	3.52E + 01	2.20E + 00	2.01E − 01	1.33E + 00	2.24E − 02	3.81E − 02	7.38E − 03
	Std	3.03E + 00	4.93E − 01	4.62E − 02	5.33E − 01	9.82E − 03	4.57E − 03	9.46E − 04
	At (s)	7.69	5.83.	6.93	5.44	4.10	4.86	3.79
Schwefel 2.22	Min	7.27E − 06	5.60E − 09	4.33E − 15	2.61E − 12	3.04E − 29	7.83E − 24	1.58E − 31
	Mean	5.69E − 04	8.05E − 07	4.20E − 14	7.44E − 12	3.47E − 27	9.53E − 23	4.84E − 31
	Std	2.56E − 04	8.77E − 08	6.73E − 15	9.25E − 13	6.89E − 28	6.80E − 23	9.15E − 32
	At (s)	7.51	5.90	7.02	5.29	4.22	4.57	3.70
Rosenbrock	Min	7.29E + 01	3.60E + 01	4.34E − 01	2.05E + 00	1.05E − 01	5.60E − 01	1.17E − 01
	Mean	1.14E + 02	6.51E + 01	1.39E + 00	2.48E + 01	1.88E − 01	6.47E − 01	1.20E − 01
	Std	1.58E + 01	7.20E + 01	1.11E + 01	8.95E + 00	1.03E + 00	6.97E − 01	2.93E − 01
	At (s)	7.60	5.94	7.15	5.48	4.27	4.95	3.91
Rastrigin	Min	7.23E − 02	4.80E − 05	3.09E − 09	3.25E − 08	6.64E − 14	5.57E − 11	2.31E − 14
	Mean	4.36E − 01	6.49E − 04	3.22E − 08	8.20E − 08	1.08E − 13	4.51E − 10	3.16E − 14
	Std	7.66E − 02	9.17E − 05	1.37E − 08	9.79 E − 09	5.43E − 14	9.03E − 11	1.27E − 14
	At (s)	7.55	5.98	7.17	5.69	4.59	5.20	3.84
Ackley	Min	4.26E − 09	7.15E − 10	2.09E − 14	8.32E − 10	2.53E − 14	3.28E − 14	2.86E − 14
	Mean	2.30E − 06	3.29E − 08	7.83E − 14	1.55E − 09	6.14E − 14	4.70E − 14	3.30E − 14
	Std	4.61E − 07	2.40E − 08	9.76E − 15	8.40E − 10	1.25E − 13	8.34E − 15	6.87E − 15
	At (s)	7.63	6.03	7.09	5.58	4.19	4.97	3.77
Levy	Min	8.85E − 10	3.19E − 16	8.74E − 23	4.89E − 23	1.25E − 31	7.82E − 27	3.58E − 31
	Mean	3.41E − 08	6.84E − 14	1.48E − 22	8.47E − 21	5.63E − 31	3.61E − 26	4.25E − 31
	Std	1.37E − 08	9.07E − 15	4.61E − 23	8.99E − 22	3.01E − 31	8.64E − 27	2.53E − 31
	At (s)	7.56	6.15	7.01	5.45	4.16	5.03	3.62