A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution

Table 1

Error values obtained  by  BSA and HBD for 30-dimensional CEC-2013 benchmark functions.

	BSA	HBD
	AVGEr  ± STDEr	AVGEr  ± STDEr		value
	4.17E − 30 ± 1.40E − 29	1.36E − 29 ± 4.17E − 29	=	0.359375
	1.22E + 06 ± 5.54E + 05	3.15E + 05 ± 1.52E + 05	+	0.000014
	7.52E + 06 ± 8.54E + 06	4.38E + 06 ± 8.11E + 06	+	0.045010
	1.25E + 04 ± 3.47E + 03	5.05E + 03 ± 2.23E + 03	+	0.000016
	0.00E + 00 ± 0.00E + 00	0.00E + 00 ± 0.00E + 00	=	1.000000
	3.04E + 01 ± 2.54E + 01	1.12E + 01 ± 1.47E + 01	+	0.001721
	7.39E + 01 ± 1.03E + 01	5.03E + 01 ± 1.61E + 01	+	0.000101
	2.09E + 01 ± 5.95E − 02	2.10E + 01 ± 3.17E − 02	=	0.142532
	2.70E + 01 ± 2.29E + 00	2.12E + 01 ± 4.26E + 00	+	0.000081
	1.78E − 01 ± 1.34E − 01	9.15E − 02 ± 5.25E − 02	+	0.009417
	7.96E − 02 ± 2.75E − 01	3.58E − 01 ± 6.34E − 01	=	0.062500
	8.41E + 01 ± 1.51E + 01	8.09E + 01 ± 1.53E + 01	=	0.396679
	1.44E + 02 ± 2.37E + 01	1.29E + 02 ± 2.90E + 01	=	0.061480
	3.70E + 00 ± 1.68E + 00	2.83E + 00 ± 1.82E + 00	+	0.034670
	3.73E + 03 ± 4.27E + 02	3.50E + 03 ± 4.82E + 02	=	0.097970
	1.31E + 00 ± 2.14E − 01	1.31E + 00 ± 2.38E − 01	=	0.903627
	3.09E + 01 ± 1.97E − 01	3.09E + 01 ± 1.79E − 01	=	0.840072
	1.20E + 02 ± 1.80E + 01	9.46E + 01 ± 2.11E + 01	+	0.000980
	1.16E + 00 ± 1.79E − 01	1.23E + 00 ± 2.28E − 01	=	0.312970
	1.15E + 01 ± 4.55E − 01	1.11E + 01 ± 5.89E − 01	=	0.057836
	2.78E + 02 ± 6.63E + 01	2.95E + 02 ± 7.95E + 01	=	0.431762
	4.45E + 01 ± 1.91E + 01	4.48E + 01 ± 1.35E + 01	=	0.443172
	4.46E + 03 ± 5.40E + 02	4.16E + 03 ± 5.07E + 02	=	0.103553
	2.32E + 02 ± 1.17E + 01	2.28E + 02 ± 8.92E + 00	=	0.157770
	2.87E + 02 ± 1.41E + 01	2.80E + 02 ± 8.80E + 00	=	0.087527
	2.00E + 02 ± 2.17E − 02	2.00E + 02 ± 6.81E − 03	+	0.000020
	8.80E + 02 ± 1.49E + 02	7.52E + 02 ± 1.33E + 02	+	0.003822
	3.00E + 02 ± 1.65E − 13	3.00E + 02 ± 1.32E − 13	+	0.016377
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