Modified Biogeography-Based Optimization with Local Search Mechanism

Table 2

Comparisons with BBO and DE.

	DE			BBO			MLBBO
	Mean (std)	MeanFEs	SR	Mean (Std)	MeanFEs	SR	Mean (std)	MeanFEs	SR
f1	2.72𝐸−20(2.09𝐸−20)^+	4.47𝐸+04	30	3.23𝐸−01(1.18𝐸−01)^+	NaN	0	2.78𝐸−31(3.25𝐸−31)	2.83𝐸+04	30
f2	2.56𝐸−12(3.09𝐸−12)^+	1.06𝐸+05	30	4.84𝐸−01(9.06𝐸−02)^+	NaN	0	1.43𝐸−21(7.11𝐸−22)	5.74𝐸+04	30
f3	2.31𝐸−19(2.37𝐸−19)^+	1.51𝐸+05	30	1.26𝐸+02(5.19𝐸+01)^+	NaN	0	1.90𝐸−20(3.03𝐸−20)	1.40𝐸+05	30
f4	1.92𝐸−10(3.44𝐸−10)^∼	2.61𝐸+05	30	1.62𝐸+00(4.71𝐸−01)^+	NaN	0	4.49𝐸−08(1.25𝐸−07)	3.49𝐸+05	30
f5	1.05𝐸−28(8.92𝐸−29)^−	1.62𝐸+05	30	7.85𝐸+01(3.51𝐸+01)^+	NaN	0	3.34𝐸−21(9.08𝐸−21)	2.25𝐸+05	30
f6	8.67𝐸−01(1.20𝐸+00)^+	2.51𝐸+04	14	1.77𝐸+00(1.17𝐸+00)^+	1.19𝐸+05	3	0.00𝐸+00(0.00𝐸+00)	1.14𝐸+04	30
f7	5.65𝐸−03(2.10𝐸−03)^+	1.44𝐸+05	29	3.64𝐸−04(2.77𝐸−04)^−	2.21𝐸+04	30	2.23𝐸−03(9.91𝐸−04)	6.61𝐸+04	30
f8	7.29𝐸+03(2.32𝐸+02)^+	NaN	0	2.53𝐸−01(8.82𝐸−02)^+	NaN	0	0.00𝐸+00(0.00𝐸+00)	5.53𝐸+04	30
f9	1.76𝐸+02(1.01𝐸+01)^+	NaN	0	3.56𝐸−02(1.52𝐸−02)^+	NaN	0	0.00𝐸+00(0.00𝐸+00)	9.16𝐸+04	30
f10	5.77𝐸−07(3.16𝐸−06)^∼	7.87𝐸+04	29	2.06𝐸−01(4.94𝐸−02)^+	NaN	0	6.10𝐸−15(1.14𝐸−15)	5.05𝐸+04	30
f11	6.57𝐸−03(6.25𝐸−03)^+	4.54𝐸+04	12	2.81𝐸−01(9.76𝐸−02)^+	NaN	0	2.87𝐸−03(5.02𝐸−03)	3.33𝐸+04	22
f12	1.38𝐸−02(4.50𝐸−02)^∼	5.37𝐸+04	26	1.98𝐸−03(2.04𝐸−03)^+	NaN	0	5.88𝐸−28(3.22𝐸−27)	2.57𝐸+04	30
f13	1.90𝐸−20(5.93𝐸−20)^∼	4.65𝐸+04	30	2.09𝐸−02(9.94𝐸−03)^+	NaN	0	5.09𝐸−32(3.13𝐸−32)	2.71𝐸+04	30
F1	5.59𝐸−28(2.06𝐸−28)^+	4.58𝐸+04	30	7.23𝐸−02(3.27𝐸−02)^+	NaN	0	3.03𝐸−29(6.97𝐸−29)	2.90𝐸+04	30
F2	7.59𝐸−12(8.42𝐸−12)^+	1.72𝐸+05	30	3.55𝐸+03(1.35𝐸+03)^+	NaN	0	1.97𝐸−12(2.55𝐸−12)	1.58𝐸+05	30
F3	1.39𝐸+05(1.06𝐸+05)^+	NaN	0	1.14𝐸+07(4.90𝐸+06)^+	NaN	0	9.26𝐸+04(4.90𝐸+04)	NaN	0
F4	7.10𝐸−05(1.61𝐸−04)^∼	2.85𝐸+05	1	1.39𝐸+04(4.56𝐸+03)^+	NaN	0	7.00𝐸−05(1.87𝐸−04)	2.90𝐸+05	5
F5	5.31𝐸+01(1.37𝐸+02)^−	NaN	0	5.81𝐸+03(9.97𝐸+02)^+	NaN	0	8.34𝐸+02(3.81𝐸+02)	NaN	0
F6	1.58𝐸−13(7.82𝐸−13)^∼	1.46𝐸+05	30	2.23𝐸+02(8.03𝐸+01)^+	NaN	0	2.11𝐸−09(6.68𝐸−09)	1.85𝐸+05	30
F7	1.26𝐸−02(1.26𝐸−02)^∼	4.93𝐸+04	15	1.13𝐸+00(7.73𝐸−02)^+	NaN	0	1.59𝐸−02(1.16𝐸−02)	4.80𝐸+04	12
F8	2.09𝐸+01(5.20𝐸−02)^∼	NaN	0	2.08𝐸+01(1.06𝐸−01)^−	NaN	0	2.09𝐸+01(7.07𝐸−02)	NaN	0
F9	1.85𝐸+02(1.75𝐸+01)^+	NaN	0	3.97𝐸−02(2.04𝐸−02)^+	NaN	0	5.92𝐸−17(3.24𝐸−16)	7.71𝐸+04	30
F10	2.05𝐸+02(1.96𝐸+01)^+	NaN	0	5.26𝐸+01(1.19𝐸+01)^+	NaN	0	3.47𝐸+01(1.24𝐸+01)	NaN	0
F11	3.95𝐸+01(1.03𝐸+00)^+	NaN	0	3.09𝐸+01(3.05𝐸+00)^+	NaN	0	1.72𝐸+01(6.58𝐸+00)	NaN	0
F12	1.19𝐸+03(2.32𝐸+03)^∼	2.31𝐸+05	3	1.41𝐸+04(9.84𝐸+03)^+	NaN	0	2.07𝐸+03(2.92𝐸+03)	NaN	0
F13	1.59𝐸+01(1.12𝐸+00)^+	NaN	0	1.09𝐸+00(2.34𝐸−01)^−	NaN	0	3.03𝐸+00(1.44𝐸−01)	NaN	0
F14	1.34𝐸+01(1.51𝐸−01)^+	NaN	0	1.31𝐸+01(3.83𝐸−01)^+	NaN	0	1.27𝐸+01(2.40𝐸−01)	NaN	0
Better	16			24
Similar	9			0
Worse	2			3

Note: “+”, “−”, and “~” indicate that MLBBO is significantly better, worse, and indifferent, respectively, compared with other algorithms.