Biogeography-Based Optimization with Orthogonal Crossover

Table 6

Comparison of OX algorithms.

	OXDE		OLPSO		OXBBO
	Mean  (Std)	SR	Mean  (Std)	SR	Mean  (Std)	SR
𝑓1	1.58𝐸−16(1.41𝐸−16)^+	100%	1.55𝐸−41(3.32𝐸−41)^+	100%	8.84𝐸−64(8.92𝐸−64)	100%
𝑓2	4.38𝐸−12(1.93𝐸−12)^+	100%	5.76𝐸−31(5.46𝐸−31)^+	100%	5.25𝐸−46(3.50𝐸−46)	100%
𝑓3	6.41𝐸−07(4.98𝐸−07)^+	0%	2.17𝐸−04(2.72𝐸−04)^+	0%	1.81𝐸−11(1.77𝐸−11)	100%
𝑓4	1.49𝐸+00(9.62𝐸−01)^+	0%	2.81𝐸+00(1.47𝐸+00)^+	0%	2.39𝐸−01(2.58𝐸−01)	0%
𝑓5	1.59𝐸−01(7.97𝐸−01)^−	96%	4.78𝐸−01(1.32𝐸+00)^−	88%	2.61𝐸+01(9.85𝐸−01)	0%
𝑓6	0.00𝐸+00(0.00𝐸+00)	100%	0.00𝐸+00(0.00𝐸+00)	100%	0.00𝐸+00(0.00𝐸+00)	100%
𝑓7	2.95𝐸−03(1.32𝐸−03)^+	100%	1.35𝐸−03(1.40𝐸−03)	100%	9.41𝐸−04(3.76𝐸−04)	100%
𝑓8	0.00𝐸+00(0.00𝐸+00)	100%	2.84𝐸+01(6.19𝐸+01)^+	80%	0.00𝐸+00(0.00𝐸+00)	100%
𝑓9	4.06𝐸+00(1.95𝐸+00)^+	0%	1.99𝐸−01(4.06𝐸−01)	80%	1.23𝐸−01(4.05𝐸−01)	84%
𝑓10	2.99𝐸−09(1.54𝐸−09)^+	100%	3.52𝐸−15(1.55𝐸−15)^+	100%	2.66𝐸−15(0.00𝐸+00)	100%
𝑓11	1.48𝐸−03(3.02𝐸−03)^+	80%	0.00𝐸+00(0.00𝐸+00)	100%	0.00𝐸+00(0.00𝐸+00)	100%
𝑓12	6.94𝐸−18(7.55𝐸−18)^+	100%	1.57𝐸−32(5.59𝐸−48)	100%	1.57𝐸−32(5.59𝐸−48)	100%
𝑓13	4.07𝐸−17(2.68𝐸−17)^+	100%	1.35𝐸−32(5.59𝐸−48)	100%	1.35𝐸−32(5.59𝐸−48)	100%
𝑓14	1.24𝐸−16(1.12𝐸−16)^+	100%	3.64𝐸−16(3.95𝐸−16)^+	100%	8.88𝐸−18(4.44𝐸−17)	100%
𝑓15	5.12𝐸−19(1.49𝐸−19)^−	100%	1.56𝐸−04(1.29𝐸−04)^−	0%	3.35𝐸−04(6.74𝐸−05)	0%
𝑓16	1.81𝐸−15(6.04𝐸−15)	100%	4.44𝐸−16(0.00𝐸+00)^+	100%	3.46𝐸−16(1.12𝐸−16)	100%
𝑓17	1.62𝐸−11(7.29𝐸−11)	100%	1.67𝐸−16(0.00𝐸+00)	100%	1.67𝐸−16(0.00𝐸+00)	100%
𝑓18	4.97𝐸−15(1.65𝐸−15)^+	100%	9.02𝐸−15(4.37𝐸−15)^+	100%	2.91𝐸−15(1.35𝐸−15)	100%
𝑓19	4.44𝐸−16(0.00𝐸+00)	100%	3.59𝐸−14(5.28𝐸−14)^+	100%	0.00𝐸+00(0.00𝐸+00)	100%
𝑓20	9.51𝐸−03(3.29𝐸−02)	92%	6.47𝐸−08(3.23𝐸−07)	96%	9.51𝐸−03(3.29𝐸−02)	92%
𝑓21	2.03𝐸−01(2.77𝐸−01)^−	0%	7.79𝐸−02(2.25𝐸−01)^−	0%	2.34𝐸+00(3.07𝐸+00)	24%
𝑓22	1.68𝐸−07(2.20𝐸−07)	12%	2.71𝐸−01(1.33𝐸+00)	0%	2.67𝐸−01(1.34𝐸+00)	92%
𝑓23	2.78𝐸−07(4.58𝐸−07)	16%	3.67𝐸−03(1.43𝐸−02)	0%	2.94𝐸−01(1.14𝐸+00)	92%

+,−The value of 𝑡 with 48 degrees of freedom is significant at 0.05 confidence level by two-tailed test.
⁻The corresponding algorithm is better than our proposed OXBBO method.