Table 12 The IEEE CEC2005 test functions’ P values at the 5% significant level using the Wilcoxon rank- sum test.

From: An enhanced opposition-based African vulture optimizer for solving engineering design problems and global optimization

Func	SCA vs EOBAVO		PSO vs EOBAVO		WOA vs EOBAVO		SSA vs EOBAVO		AVO vs EOBAVO		OBAVO vs EOBAVO		ROBAVO vs EOBAVO
Func	P values	H	P values	H	P values	H	P values	H	P values	H	P values	H	P values	H
F1	1.40E−08	+	1.13E−08	+	5.79E−06	+	1.02E−06	+	6.32E−06	+	1.01E−05	+	9.33E−06	+
F2	7.85E−09	+	8.72E−09	+	1.50E−05	+	4.64E−06	+	3.36E−01	−	3.97E−06	+	9.58E−06	+
F3	6.95E−09	+	1.29E−08	+	7.94E−06	+	1.35E−05	+	5.40E−06	+	1.71E−06	+	4.69E−01	−
F4	4.58E−09	+	8.71E−09	+	1.12E−05	+	1.25E−05	+	3.54E−06	+	2.56E−01	−	1.29E−01	−
F5	9.45E−10	+	1.43E−08	+	2.89E−06	+	3.0915E 00	−	5.49E−06	+	4.12E−01	−	3.13E−01	−
F6	1.45E−08	+	9.25E−09	+	3.22E−06	+	3.51E−06	+	2.01E−06	+	2.69E−01	+	5.42E−06	+
F7	1.36E−08	+	9.40E−09	+	6.85E−07	+	6.21E−06	+	1.49E−05	+	3.13E−06	+	7.13E−06	+
F8	1.67E−08	+	1.47E−08	+	2.83E−06	+	8.12E−06	+	9.95E−06	+	4.78E−06	+	8.50E−06	+
F9	1.67E−08	+	6.76E−09	+	4.67E−06	+	1.04E−05	+	1.14E−05	+	2.90E−06	+	4.06E−01	−
10	9.31E−09	+	2.25E−09	+	2.97E−06	+	6.18E−06	+	1.32E−05	+	1.50E−05	+	1.92E−01	−
F11	1.29E−08	+	4.82E−10	+	1.49E−06	+	7.75E−06	+	8.35E−06	+	1.34E−06	+	1.02E−05	+
F12	1.58E−08	+	1.27E−08	+	2.02E−06	+	1.25E−05	+	1.46E−06	+	8.79E−06	+	4.84E−06	+
F13	1.42E−08	+	1.04E−08	+	NA	−	6.15E−07	+	NA	−	6.88E−06	+	9.74E−06	+
F14	4.14E−01	−	1.18E−08	+	3.46E−06	+	4.23E−06	+	9.83E−01	−	1.65E−05	+	2.59E−06	+
F15	7.55E−09	+	3.57E−09	+	6.10E−06	+	1.20E−05	+	1.25E−05	+	1.88E−06	+	8.06E−06	+
F16	2.16E−09	+	2.28E−09	+	8.43E−06	+	1.50E−05	+	7.23E−06	+	6.67E−06	+	8.92E−06	+
F17	1.60E−08	+	2.44E−10	+	1.16E−01	+	8.57E−06	+	2.14E−06	+	1.62E−05	+	8.68E−07	+
F18	1.02E−08	+	5.87E−09	+	6.59E−07	+	8.92E−01	−	4.75E−06	+	1.45E−05	+	NA	−
F19	3.83E−09	+	9.88E−09	+	1.34E−05	+	1.80E−01	−	6.08E−06	+	1.37E−01	−	NA	−
F20	1.13E−08	+	6.57E−09	+	1.05E−05	+	7.50E−06	+	1.08E−05	+	4.32E−06	+	1.06E−06	+
F21	NA	−	7.33E−09	+	1.37E−06	+	8.92E−06	+	9.56E−06	+	2.86E−06	+	1.66E−05	+
F22	1.00E−01	−	1.51E−08	+	1.46E−05	+	4.06E−01	−	5.97E−06	+	1.12E−05	+	NA	−
F23	1.90E−09	+	5.83E−09	+	1.54E−05	+	4.51E−01	−	1.65E−05	+	1.56E−05	+	1.36E−05	+

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Table 12 The IEEE CEC2005 test functions’ P values at the 5% significant level using the Wilcoxon rank- sum test.

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