Skip to main content
. 2025 Aug 22;15:30874. doi: 10.1038/s41598-025-16513-4

Table 8.

Wilcoxon rank sum test results (CEC2017 test set).

Function vs. HGS vs. CDO vs. SCSO vs. AOA vs. AGWO vs. WOA vs. GWO vs. PSO
CEC01 2.39E-08 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11
CEC03 2.52E-01 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11
CEC04 1.11E-04 3.02E-11 4.50E-11 3.02E-11 3.02E-11 2.78E-07 7.09E-08 1.58E-04
CEC05 5.07E-08 3.00E-11 2.03E-09 3.00E-11 3.00E-11 3.00E-11 4.08E-05 3.00E-11
CEC06 1.78E-10 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11
CEC07 5.09E-08 3.02E-11 2.37E-10 3.02E-11 3.69E-11 3.02E-11 2.81E-02 1.78E-10
CEC08 1.13E-05 3.01E-11 6.51E-09 9.90E-11 2.37E-10 6.05E-11 1.05E-01 2.83E-08
CEC09 1.01E-08 3.01E-11 3.01E-11 3.01E-11 3.01E-11 3.01E-11 4.96E-11 3.01E-11
CEC10 3.81E-07 3.02E-11 1.31E-08 1.78E-10 1.70E-08 1.09E-10 5.32E-03 6.12E-10
CEC11 8.29E-06 3.02E-11 3.34E-11 3.02E-11 3.34E-11 3.69E-11 2.87E-10 2.61E-10
CEC12 4.03E-03 3.02E-11 8.10E-10 4.98E-11 3.02E-11 4.08E-11 3.35E-08 3.02E-11
CEC13 6.73E-01 3.02E-11 1.09E-01 2.50E-03 1.73E-07 1.75E-05 1.03E-02 7.66E-05
CEC14 7.38E-10 3.47E-10 6.52E-09 4.98E-11 2.87E-10 2.61E-10 6.12E-10 1.56E-08
CEC15 6.70E-11 3.02E-11 4.62E-10 3.02E-11 1.17E-09 8.15E-11 6.07E-11 1.21E-10
CEC16 4.69E-08 3.02E-11 3.20E-09 3.02E-11 3.16E-05 1.46E-10 3.52E-07 1.21E-10
CEC17 1.49E-06 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.02E-11 3.69E-11 3.02E-11
CEC18 5.57E-10 3.02E-11 9.26E-09 4.18E-09 3.02E-11 1.29E-09 1.09E-10 5.46E-09
CEC19 8.84E-07 3.02E-11 2.84E-04 8.99E-11 2.78E-07 5.07E-10 4.08E-05 1.68E-04
CEC20 9.79E-05 3.01E-11 3.33E-11 3.01E-11 3.01E-11 3.01E-11 4.50E-11 4.07E-11
CEC21 1.85E-08 3.02E-11 7.04E-07 6.52E-09 8.99E-11 3.01E-07 1.49E-06 2.67E-09
CEC22 2.38E-03 3.02E-11 7.22E-06 3.02E-11 5.07E-10 3.02E-11 3.81E-07 7.12E-09
CEC23 1.87E-07 3.02E-11 8.99E-11 3.02E-11 3.02E-11 5.49E-11 2.01E-04 5.57E-10
CEC24 3.02E-11 3.02E-11 3.16E-10 1.31E-08 3.02E-11 1.09E-10 4.31E-08 2.68E-06
CEC25 3.59E-05 3.02E-11 3.25E-07 3.69E-11 7.66E-05 2.49E-06 1.78E-04 1.37E-03
CEC26 3.16E-10 3.02E-11 2.39E-08 3.02E-11 5.07E-10 3.16E-10 2.57E-07 2.92E-09
CEC27 9.23E-01 3.02E-11 2.50E-03 3.02E-11 4.64E-03 4.69E-08 1.91E-01 4.62E-10
CEC28 6.38E-08 3.02E-11 3.82E-09 3.02E-11 1.69E-09 6.09E-10 1.55E-09 1.01E-08
CEC29 7.62E-03 3.02E-11 4.74E-06 1.21E-10 3.03E-03 7.38E-10 5.57E-03 1.07E-09
CEC30 5.26E-04 3.02E-11 1.49E-06 3.02E-11 1.87E-07 9.26E-09 3.99E-04 5.97E-09
Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic