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. 2022 Apr 15;12:6302. doi: 10.1038/s41598-022-09744-2

Table 2.

Result comparison of different well-known metaheuristics on CEC2019 benchmark functions.

Function Stats EHOI EHO SCA SSA GOA WOA BBO MFO PSO FA OBSCA-FS
CEC01 Mean 4.76E+04 1.35E+07 9.83E+09 3.21E+09 1.61E+10 1.03E+10 3.52E+10 7.17E+09 6.75E+11 7.43E+04 4.83E+03
Std 2.14E+03 7.91E+06 6.95E+09 1.42E+09 8.99E+9 9.14E+09 2.32E+10 8.69E+09 2.34E+11 4.49E+03 4.21E+03
CEC02 Mean 1.70E+01 1.72E+01 1.75E+01 1.73E+01 1.74E+01 1.73E+01 8.87E+01 1.74E+01 8.56E+02 2.85E+01 2.41E+00
Std 3.66E−16 7.29E−15 5.19E−03 6.55E−05 3.23E−02 1.95E−03 2.45E+01 4.17E−15 3.87E+02 3.21E+02 5.32E+01
CEC03 Mean 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01 1.27E+01
Std 3.95E−16 7.44E−16 3.25E−04 3.11E−15 6.47E−04 7.94E−06 5.25E−07 4.38E−05 4.12E−04 5.22E−01 4.03E−01
CEC04 Mean 1.28E+01 1.55E+01 8.32E+02 3.25E+01 1.51E+02 2.65E+02 6.95E+01 1.38E+02 6.92E+01 3.89E+01 1.00E+01
Std 4.26E+00 8.52E+00 3.85E+02 1.09E+01 1.13E+02 1.39E+02 2.99E+01 1.15E+02 5.43E+01 2.32E−01 1.19E+00
CEC05 Mean 1.05E+00 1.07E+00 2.23E+00 1.35E+00 1.33E+00 1.67E+00 1.31E+00 1.13E+00 1.55E+00 1.13E+00 1.01E+00
Std 3.25E−03 2.41E−02 7.81E−02 2.33E−01 1.21E−01 3.86E−02 9.63E−02 6.56E−02 1.18E−01 4.26E−02 2.17E−02
CEC06 Mean 8.33E+00 9.45E+00 1.04E+01 3.79E+00 6.19E+00 9.14E+00 5.78E+00 4.92E+00 1.03E+01 1.05E+01 1.86E+00
Std 6.23E−01 1.31E+00 8.15E+00 1.23E+00 1.33E+00 1.05E+00 2.99E−01 2.13E+00 3.35E+00 6.20E−01 4.46E−02
CEC07 Mean 1.42E+02 1.81E+02 6.38E+02 2.89E+02 2.87E+02 4.53E+02 4.92E+00 3.19E+02 5.97E+02 4.91E+02 3.85E+00
Std 1.13E+02 1.51E+02 2.78E+02 2.25E+02 1.75E+02 2.25E+02 1.21E+00 2.15E+02 1.89E+02 1.23E+02 8.36E+01
CEC08 Mean 2.69E+00 3.15E+00 5.77E+00 5.08E+00 5.49E+00 5.75E+00 4.81E+00 5.45E+00 5.10E+00 2.78E+00 2.83E+00
Std 9.15E−02 1.44E+00 7.29E−01 7.83E−01 5.14E−01 7.29E−01 1.03E+00 5.62E−01 7.33E−01 8.99E−01 9.13E−01
CEC09 Mean 2.29E+00 2.41E+00 8.75E+01 2.38E+00 2.45E+00 5.16E+00 3.75E+00 2.46E+00 2.65E+00 4.95E+00 1.73E+00
Std 5.55E−03 2.18E−02 5.63E+01 5.33E−02 6.41E−02 5.29E−01 3.14E−01 6.76E−02 8.45E−02 2.83E−01 1.54E−02
CEC10 Mean 1.92E+01 2.11E+01 2.08E+01 2.03E+01 2.00E+01 2.05E+01 2.07E+01 2.02E+01 2.06E+01 2.02E+01 1.32E+01
Std 3.49E+00 7.29E+00 6.45E+00 8.19E+00 6.67E+00 3.52E−01 7.13E−00 6.66E−01 9.81E+02 9.13E−02 1.56E−02