A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution

Table 2

Error values obtained by BSA and HBD for 10- and 50-dimensional CEC-2013 benchmark functions.

		BSA	HBD				BSA	HBD
		AVGEr  ± STDEr	AVGEr  ± STDEr		value		AVGEr  ± STDEr	AVGEr  ± STDEr		value
		0.00E + 00 ± 0.00E + 00	0.00E + 00 ± 0.00E + 00	=	1.000000		1.69E − 29 ± 3.04E − 29	1.48E − 29 ± 4.26E − 29	=	0.582031
		8.59E + 04 ± 2.30E + 05	4.75E + 03 ± 5.65E + 03	+	0.000065		2.77E + 06 ± 8.09E + 05	1.11E + 06 ± 4.38E + 05	+	0.000014
		5.46E + 04 ± 1.36E + 05	1.44E + 02 ± 6.95E + 02	+	0.000012		4.95E + 07 ± 4.00E + 07	1.25E + 07 ± 1.20E + 07	+	0.000140
		5.04E + 02 ± 3.66E + 02	5.67E + 01 ± 1.10E + 02	+	0.000014		3.22E + 04 ± 5.16E + 03	2.04E + 04 ± 4.88E + 03	+	0.000023
		0.00E + 00 ± 0.00E + 00	0.00E + 00 ± 0.00E + 00	=	1.000000		3.06E − 38 ± 1.53E − 37	0.00E + 00 ± 0.00E + 00	=	0.250000
		1.60E + 00 ± 3.25E + 00	2.75E + 00 ± 4.50E + 00	=	0.220852		5.42E + 01 ± 1.87E + 01	4.42E + 01 ± 7.78E − 01	+	0.000046
		6.96E + 00 ± 6.85E + 00	1.73E + 00 ± 2.49E + 00	+	0.045010		8.48E + 01 ± 1.02E + 01	8.38E + 01 ± 1.06E + 01	=	0.756995
		2.04E + 01 ± 7.79E − 02	2.04E + 01 ± 5.55E − 02	=	0.989266		2.11E + 01 ± 3.33E − 02	2.11E + 01 ± 2.32E − 02	=	0.562928
		3.54E + 00 ± 8.43E − 01	2.47E + 00 ± 1.29E + 00	+	0.006313		5.44E + 01 ± 3.73E + 00	5.50E + 01 ± 3.85E + 00	=	0.657069
		8.49E − 02 ± 3.51E − 02	7.75E − 02 ± 5.50E − 02	=	0.989266		3.99E − 01 ± 2.11E − 01	1.14E − 01 ± 6.51E − 02	+	0.000018
		0.00E + 00 ± 0.00E + 00	0.00E + 00 ± 0.00E + 00	=	1.000000		7.96E − 02 ± 2.75E − 01	0.00E + 00 ± 0.00E + 00	=	0.062500
		1.10E + 01 ± 3.31E + 00	1.09E + 01 ± 3.48E + 00	=	0.599802		1.92E + 02 ± 2.87E + 01	1.68E + 02 ± 2.65E + 01	+	0.007423
		1.68E + 01 ± 7.18E + 00	1.60E + 01 ± 7.27E + 00	=	0.736617		3.25E + 02 ± 3.81E + 01	2.88E + 02 ± 4.17E + 01	+	0.001569
		1.31E − 01 ± 5.44E − 02	1.28E − 01 ± 8.94E − 02	+	0.000296		2.17E + 01 ± 5.08E + 00	2.12E + 01 ± 4.56E + 00	=	0.287862
		6.10E + 02 ± 1.78E + 02	4.67E + 02 ± 1.74E + 02	+	0.022988		8.25E + 03 ± 4.91E + 02	8.13E + 03 ± 4.40E + 02	=	0.142532
		6.54E − 01 ± 1.92E − 01	6.23E − 01 ± 2.50E − 01	=	0.989266		1.88E + 00 ± 2.67E − 01	1.82E + 00 ± 2.86E − 01	=	0.427339
		7.77E + 00 ± 2.88E + 00	8.37E + 00 ± 2.87E + 00	=	0.427339		5.44E + 01 ± 6.11E − 01	5.45E + 01 ± 6.85E − 01	=	0.924971
		2.67E + 01 ± 4.85E + 00	2.05E + 01 ± 4.06E + 00	+	0.000665		2.65E + 02 ± 2.44E + 01	2.45E + 02 ± 3.23E + 01	+	0.039554
		2.45E − 01 ± 9.51E − 02	2.15E − 01 ± 1.19E − 01	=	0.657069		2.67E + 00 ± 3.30E − 01	2.80E + 00 ± 2.59E − 01	=	0.312970
		2.92E + 00 ± 3.60E − 01	2.57E + 00 ± 4.67E − 01	+	0.019941		2.09E + 01 ± 7.34E − 01	2.08E + 01 ± 4.44E − 01	=	0.819095
		3.16E + 02 ± 1.32E + 02	3.04E + 02 ± 1.21E + 02	=	0.444824		6.94E + 02 ± 4.53E + 02	8.72E + 02 ± 3.27E + 02	=	0.675764
		1.49E + 01 ± 4.29E + 00	1.42E + 01 ± 4.11E + 00	=	0.544910		5.96E + 01 ± 1.39E + 01	6.10E + 01 ± 9.87E + 00	=	0.544910
		8.60E + 02 ± 1.53E + 02	8.06E + 02 ± 2.04E + 02	=	0.818641		9.53E + 03 ± 6.62E + 02	9.41E + 03 ± 7.87E + 02	=	0.599802
		1.50E + 02 ± 3.69E + 01	1.56E + 02 ± 4.44E + 01	=	0.716423		2.70E + 02 ± 1.04E + 01	2.58E + 02 ± 1.09E + 01	+	0.001569
		1.93E + 02 ± 2.44E + 01	1.84E + 02 ± 3.39E + 01	=	0.241820		3.79E + 02 ± 1.40E + 01	3.65E + 02 ± 2.10E + 01	+	0.013817
		1.13E + 02 ± 5.23E + 00	1.11E + 02 ± 1.87E + 01	=	0.109386		2.00E + 02 ± 7.33E − 02	2.00E + 02 ± 4.44E − 02	+	0.000012
		3.13E + 02 ± 2.39E + 01	3.32E + 02 ± 4.73E + 01	=	0.676637		1.53E + 03 ± 1.89E + 02	1.39E + 03 ± 2.01E + 02	+	0.028314
		2.20E + 02 ± 1.00E + 02	2.04E + 02 ± 1.02E + 02	=	0.802856		4.00E + 02 ± 1.33E − 13	4.00E + 02 ± 1.43E − 13	+	0.000001
				9/19/0					13/15/0