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. 2024 Mar 18;14:6432. doi: 10.1038/s41598-024-56919-0

Table 6.

Comparison between different swarm intelligence algorithms on 10-D problems.

BFs SSA MSWOA MSCA COGBSO
F1 Mean 5.94E−10 2.39E−67 1.85E−51 1.57E−67
Std 1.81E−10 1.44E−67 5.14E−51 2.37E−67
Min 3.76E−10 1.18E−67 2.67E−70 3.34E−69
Max 9.73E−10 4.54E−67 1.81E−50 8.80E−67
F2 Mean 9.59E+02 1.07E−54 1.81E−50 3.86E−55
Std 6.80E+02 2.00E−54 6.94E−50 1.18E−54
Min 1.44E+02 1.21E−55 7.93E−67 6.71E−58
Max 2.37E+03 3.87E−54 2.69E−49 4.64E−54
F3 Mean 4.03E+00 6.59E−39 1.59E−40 2.30E−42
Std 4.87E+00 1.02E−39 6.17E−40 8.70E−42
Min 3.45E−02 9.88E−48 2.56E−47 3.16E−47
Max 1.80E+01 3.48E−37 2.39E−39 3.38E−41
F4 Mean 1.89E+02 2.77E−62 1.04E−53 3.37E−66
Std 2.30E+02 5.48E−62 2.43E−53 6.91E−66
Min 9.14E+00 5.12E−68 9.56E−73 9.80E−69
Max 6.87E+02 3.78E−61 9.12E−53 2.69E−65
F5 Mean 1.41E−04 0.00E+00 1.76E−28 4.99E−38
Std 4.33E−05 0.00E+00 4.65E−28 7.29E−38
Min 7.53E−05 0.00E+00 2.92E−30 9.06E−40
Max 2.55E−04 0.00E+00 1.53E−27 2.22E−37
F6 Mean 4.58E−08 1.20E+00 6.47E+00 6.17E−10
Std 1.04E−08 2.10E+00 3.89E−01 4.60E−10
Min 4.20E−08 1.70E−07 6.15E+00 1.50E−10
Max 4.60E−08 5.96E+00 7.22E+00 1.08E−09
F7 Mean 2.38E−01 − 4.44E−16 − 4.44E−16 1.87E−15
Std 2.38E−01 − 4.44E−16 − 4.44E−16 1.38E−15
Min 5.12E−06 − 4.44E−16 − 4.44E−16 4.44E−16
Max 3.57E+00 − 4.44E−16 − 4.44E−16 3.11E−15
F8 Mean 2.20E−05 3.87E−05 1.86E−28 6.05E−18
Std 6.21E−06 1.50E−04 7.20E−28 1.61E−17
Min 1.55E−05 1.52E−17 2.91E−40 1.25E−33
Max 4.22E−05 5.80E−04 2.79E−27 5.15E−17
F9 Mean 1.62E−02 0.00E+00 0.00E+00 5.64E−02
Std 3.87E−02 0.00E+00 0.00E+00 3.48E−02
Min 1.16E−09 0.00E+00 0.00E+00 9.86E−03
Max 1.35E−01 0.00E+00 0.00E+00 1.21E−01
F10 Mean 9.95E+00 5.62E+00 9.95E+00 4.31E+00
Std 8.50E−11 3.33E+00 9.95E+00 2.15E+00
Min 9.95E+00 9.95E−01 9.95E+00 9.95E−01
Max 9.95E+00 6.96E+00 9.95E+00 6.96E+00
F11 Mean 6.19E−05 6.41E−17 3.02E−11 3.37E−23
Std 8.24E−06 8.85E−17 1.10E−10 7.75E−23
Min 4.33E−05 6.86E−18 1.39E−19 1.33E−33
Max 7.46E−05 9.02E−17 4.27E−10 2.97E−22
F12 Mean 1.31E−05 7.20E−19 4.55E−18 3.76E−23
Std 1.67E−06 6.51E−19 1.76E−17 3.76E−23
Min 9.40E−06 6.26E−20 5.56E−28 4.06E−24
Max 1.48E−05 2.10E−13 6.83E−17 1.46E−22
F13 Mean 1.40E−58 0.00E+00 3.25E−229 1.48E−267
Std 2.25E−58 0.00E+00 0.00E+00 0.00E+00
Min 8.32E−61 0.00E+00 1.36E−317 2.43E−283
Max 7.85E−58 0.00E+00 4.76E−228 1.11E−266
F14 Mean 5.94E−05 2.94E−179 9.70E−28 3.71E−25
Std 1.13E−05 0.00E+00 3.73E−27 4.45E−25
Min 3.89E−05 3.59E−182 7.51E−41 1.89E−26
Max 7.54E−05 2.50E−178 1.45E−26 1.67E−24
F15 Mean 9.12E−13 1.10E−01 4.38E+00 0.00E+00
Std 6.16E−19 4.20E−01 1.67E+00 0.00E+00
Min 9.12E−13 5.27E−04 4.72E−01 0.00E+00
Max 9.12E−13 1.63E+00 6.16E+00 0.00E+00

Optimal mean values are in bold.