Biogeography-Based Optimization with Orthogonal Crossover

Table 3

Comparison of hybrid BBO algorithms and OXBBO for high-dimension of functions.

	BBO-EP [11]	DBBO [13]	eBBO [14]	DE/BBO [15]	OXBBO
	Mean (Std)	Mean (Std)	Mean (std)	Mean (std)	Mean (Std)
𝑓1	2.35𝐸−06(3.17𝐸−06)	7.76𝐸−36(3.80𝐸−35)	6.22𝐸−27(2.17𝐸−26)	8.66𝐸−28(5.21𝐸−28)	3.96𝐸−28(2.47𝐸−28)
𝑓2	5.03𝐸−07(3.17𝐸−08)	6.14𝐸−04(2.64𝐸−03)	4.46𝐸−23(1.28𝐸−22)	0.00𝐸+00(0.00𝐸+00)	1.12𝐸−19(4.01𝐸−20)
𝑓3	1.59𝐸−03(2.90𝐸−03)	1.52𝐸−11(1.86𝐸−11)	4.98𝐸+01(8.04𝐸+01)	2.26𝐸−03(1.58𝐸−03)	3.21𝐸−03(1.96𝐸−03)
𝑓4	6.66𝐸−04(4.62𝐸−05)	9.02𝐸−02(6.10𝐸−02)	7.68𝐸−08(1.37𝐸−07)	1.89𝐸−15(8.85𝐸−16)	2.61𝐸−15(8.83𝐸−15)
𝑓5	2.42𝐸+00(2.60𝐸+00)	6.71𝐸+01(2.61𝐸+01)	5.16𝐸+01(4.37𝐸+01)	1.90𝐸+01(7.52𝐸+00)	1.89𝐸+01(1.84𝐸−01)
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	1.70𝐸−03(5.90𝐸−04)	1.54𝐸−03(3.41𝐸−04)	1.88𝐸−03(3.60𝐸−03)	3.44𝐸−03(8.27𝐸−04)	2.01𝐸−03(6.45𝐸−04)
𝑓8	−12569.5(2.65𝐸−06)	2.10𝐸−01(2.91𝐸−01)	8.13𝐸−09(2.21𝐸−14)	0.00𝐸+00(0.00𝐸+00)	0.00𝐸+00(0.00𝐸+00)
𝑓9	3.97𝐸−04(5.32𝐸−04)	2.24𝐸−03(3.25𝐸−03)	0.00𝐸+00(0.00𝐸+00)	0.00𝐸+00(0.00𝐸+00)	0.00𝐸+00(0.00𝐸+00)
𝑓10	9.40𝐸−04(5.84𝐸−05)	4.63𝐸−03(1.47𝐸−02)	1.45𝐸−14(9.93𝐸−15)	1.07𝐸−14(1.90𝐸−15)	6.79𝐸−15(1.50𝐸−15)
𝑓11	6.70𝐸−08(9.55𝐸−09)	1.33𝐸−17(6.53𝐸−17)	6.57𝐸−03(9.00𝐸−03)	0.00𝐸+00(0.00𝐸+00)	0.00𝐸+00(0.00𝐸+00)
𝑓12	1.57𝐸−08(2.40𝐸−09)	9.64𝐸−06(3.68𝐸−05)	3.75𝐸−32(6.58𝐸−32)	7.16𝐸−29(6.30𝐸−29)	7.06𝐸−30(3.95𝐸−30)
𝑓13	2.52𝐸−07(1.10𝐸−07)	4.51𝐸−04(2.15𝐸−03)	1.08𝐸−26(2.76𝐸−26)	9.81𝐸−27(7.10𝐸−27)	7.45𝐸−29(3.00𝐸−29)

Note: the result of 𝑓₈ obtained by BBO-EP is fitness value but is fitness value error by the others.