Modified Biogeography-Based Optimization with Local Search Mechanism

Table 3

Comparisons with improved BBO algorithms.

	OBBO	PBBO	MOBBO	RCBBO	MLBBO
	Mean (std)	Mean (Std)	Mean (std)	Mean (std)	Mean (std)
f1	6.88𝐸−05(2.58𝐸−05)^+	2.23𝐸−11(2.77𝐸−12)^+	1.70𝐸−09(9.30𝐸−09)^∼	2.26𝐸−03(1.06𝐸−03)^+	2.11𝐸−31(1.25𝐸−31)
f2	2.76𝐸−02(4.80𝐸−03)^+	3.47𝐸−06(2.67𝐸−07)^+	2.74𝐸−05(1.48𝐸−04)^∼	8.96𝐸−02(1.58𝐸−02)^+	1.58𝐸−21(7.25𝐸−22)
f3	6.29𝐸−01(4.23𝐸−01)^+	2.06𝐸−02(1.70𝐸−02)^+	3.25𝐸−02(4.50𝐸−02)^+	2.19𝐸+01(9.34𝐸+00)^+	1.42𝐸−20(1.70𝐸−20)
f4	1.47𝐸−02(3.18𝐸−03)^+	1.20𝐸−02(3.30𝐸−03)^+	2.43𝐸−02(6.74𝐸−03)^+	1.20𝐸+00(1.25𝐸+00)^+	5.28𝐸−08(1.02𝐸−07)
f5	3.65𝐸+01(2.20𝐸+01)^+	3.60𝐸+01(3.40𝐸+01)^+	6.32𝐸+01(8.33𝐸+01)^+	4.25𝐸+01(3.74𝐸+01)^+	5.34𝐸−21(1.10𝐸−20)
f6	0.00𝐸+00(0.00𝐸+00)^∼	0.00𝐸+00(0.00𝐸+00)^∼	0.00𝐸+00(0.00𝐸+00)^∼	0.00𝐸+00(0.00𝐸+00)^∼	0.00𝐸+00(0.00𝐸+00)
f7	4.02𝐸−04(3.48𝐸−04)^−	2.86𝐸−04(2.68𝐸−04)^−	9.79𝐸−04(8.00𝐸−04)^−	4.21𝐸−04(3.81𝐸−04)^−	2.33𝐸−03(1.04𝐸−03)
f8	2.40𝐸+02(1.82𝐸+02)^+	1.70𝐸−11(2.26𝐸−12)^+	1.55𝐸−11(8.50𝐸−11)^∼	8.17𝐸−05(3.15𝐸−05)^+	0.00𝐸+00(0.00𝐸+00)
f9	5.59𝐸−03(2.07𝐸−03)^+	2.80𝐸−07(1.37𝐸−06)^∼	5.45𝐸−05(2.99𝐸−04)^∼	1.38𝐸−02(5.11𝐸−03)^+	0.00𝐸+00(0.00𝐸+00)
f10	7.38𝐸−03(1.88𝐸−03)^+	2.08𝐸−06(5.39𝐸−06)^+	9.74𝐸−08(5.97𝐸−09)^+	2.94𝐸−02(6.63𝐸−03)^+	6.10𝐸−15(6.49𝐸−16)
f11	2.68𝐸−02(2.49𝐸−02)^+	4.98𝐸−03(1.29𝐸−02)^∼	5.08𝐸−03(1.05𝐸−02)^∼	7.92𝐸−02(4.36𝐸−02)^+	1.73𝐸−03(4.00𝐸−03)
f12	1.82𝐸−06(2.26𝐸−06)^+	6.71𝐸−11(3.18𝐸−10)^∼	3.46𝐸−03(1.89𝐸−02)^∼	3.39𝐸−05(3.47𝐸−05)^+	2.35𝐸−32(3.98𝐸−32)
f13	2.04𝐸−05(1.99𝐸−05)^+	1.65𝐸−09(7.99𝐸−09)^∼	6.33𝐸−13(3.44𝐸−12)^∼	6.43𝐸−04(9.66𝐸−04)^+	5.64𝐸−32(3.38𝐸−32)
F1	1.40𝐸−05(8.26𝐸−06)^+	2.67𝐸−11(9.69𝐸−11)^∼	1.16𝐸−07(6.34𝐸−07)^∼	3.50𝐸−04(9.25𝐸−05)^+	2.02𝐸−29(6.16𝐸−29)
F2	4.70𝐸+01(8.64𝐸+00)^+	2.92𝐸+00(2.02𝐸+00)^+	2.66𝐸+00(2.16𝐸+00)^+	8.72𝐸+02(4.43𝐸+02)^+	1.37𝐸−12(1.53𝐸−12)
F3	1.56𝐸+06(3.45𝐸+05)^+	2.10𝐸+06(6.86𝐸+05)^+	2.37𝐸+06(9.89𝐸+05)^+	4.46𝐸+06(1.58𝐸+06)^+	9.02𝐸+04(5.54𝐸+04)
F4	3.18𝐸+03(9.94𝐸+02)^+	7.74𝐸+02(3.86𝐸+02)^+	1.46𝐸+01(1.83𝐸+01)^+	2.17𝐸+04(8.50𝐸+03)^+	1.75𝐸−05(2.92𝐸−05)
F5	1.03𝐸+04(1.63𝐸+03)^+	3.68𝐸+03(6.27𝐸+02)^+	5.04𝐸+03(1.24𝐸+03)^+	6.31𝐸+03(1.18𝐸+03)^+	8.00𝐸+02(3.79𝐸+02)
F6	3.20𝐸+02(9.64𝐸+02)^∼	8.71𝐸+02(2.12𝐸+03)^+	2.76𝐸+02(8.46𝐸+02)^∼	8.45𝐸+02(2.69𝐸+03)^∼	3.55𝐸−09(1.40𝐸−08)
F7	2.46𝐸−02(1.52𝐸−02)^+	1.62𝐸−02(1.45𝐸−02)^∼	2.26𝐸−02(1.99𝐸−02)^+	7.64𝐸−01(1.39𝐸+00)^+	1.38𝐸−02(1.21𝐸−02)
F8	2.08𝐸+01(8.04𝐸−02)^−	2.09𝐸+01(1.69𝐸−01)^−	2.07𝐸+01(1.71𝐸−01)^−	2.07𝐸+01(8.51𝐸−02)^−	2.09𝐸+01(5.48𝐸−02)
F9	5.80𝐸−03(2.39𝐸−03)^+	9.69𝐸−07(3.88𝐸−06)^∼	1.22𝐸−07(6.61𝐸−07)^∼	1.32𝐸−02(5.53𝐸−03)^+	5.92𝐸−17(3.24𝐸−16)
F10	6.43𝐸+01(2.81𝐸+01)^+	3.29𝐸+01(8.80𝐸+00)^∼	7.14𝐸+01(2.06𝐸+01)^+	4.80𝐸+01(1.62𝐸+01)^+	3.69𝐸+01(1.45𝐸+01)
F11	2.36𝐸+01(3.19𝐸+00)^+	2.09𝐸+01(4.48𝐸+00)^∼	2.70𝐸+01(4.11𝐸+00)^+	3.19𝐸+01(3.90𝐸+00)^+	1.95𝐸+01(7.87𝐸+00)
F12	1.18𝐸+04(8.66𝐸+03)^+	4.68𝐸+03(4.44𝐸+03)^+	5.04𝐸+03(4.10𝐸+03)^+	1.29𝐸+04(8.94𝐸+03)^+	2.43𝐸+03(2.97𝐸+03)
F13	1.08𝐸+00(1.96𝐸−01)^−	1.14𝐸+00(2.07𝐸−01)^−	1.09𝐸+00(2.29𝐸−01)^−	9.61𝐸−01(1.57𝐸−01)^−	2.98𝐸+00(1.62𝐸−01)
F14	1.25𝐸+01(3.61𝐸−01)^∼	1.19𝐸+01(6.17𝐸−01)^−	1.33𝐸+01(3.44𝐸−01)^+	1.31𝐸+01(3.39𝐸−01)^+	1.27𝐸+01(2.39𝐸−01)
Better	21	13	13	22
Similar	3	10	11	2
Worse	3	4	3	3

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