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Table 6 Results of testing benchmark functions

From: A new fruit fly optimization algorithm enhanced support vector machine for diagnosis of breast cancer based on high-level features

Function Metric LFOA FOA MFO BA DA FPA PSO SCA
f 1 mean 1.53E-09 9.27E-07 1.00E+ 03 1.53E+ 01 1.36E+ 03 1.71E+ 03 1.39E+ 02 7.65E+ 00
std 3.71E-09 7.92E-09 3.05E+ 03 2.32E+ 00 1.11E+ 03 4.11E+ 02 1.77E+ 01 1.07E+ 01
rank 1 2 6 4 7 8 5 3
f 2 mean 2.20E-04 5.26E-03 3.51E+ 01 1.84E+ 01 2.20E+ 01 4.90E+ 01 7.48E+ 01 1.33E-02
std 2.25E-04 3.13E-05 2.09E+ 01 1.99E+ 00 1.69E+ 01 1.20E+ 01 1.43E+ 01 1.47E-02
rank 1 2 6 4 5 7 8 3
f 3 mean 1.85E-07 2.91E-04 2.12E+ 04 9.62E+ 01 1.51E+ 04 2.59E+ 03 5.14E+ 02 7.18E+ 03
std 3.20E-07 2.66E-06 1.25E+ 04 2.99E+ 01 1.13E+ 04 8.39E+ 02 1.13E+ 02 4.60E+ 03
rank 1 2 8 3 7 5 4 6
f 4 mean 4.12E-06 1.76E-04 5.95E+ 01 2.25E+ 00 2.38E+ 01 2.91E+ 01 4.69E+ 00 3.36E+ 01
std 4.15E-06 7.28E-07 1.27E+ 01 4.90E-01 7.36E+ 00 3.35E+ 00 2.77E-01 1.05E+ 01
rank 1 2 8 3 5 6 4 7
f 5 mean 8.32E+ 00 2.87E+ 01 5.35E+ 06 4.07E+ 03 5.02E+ 05 2.44E+ 05 1.64E+ 05 1.84E+ 05
std 6.92E+ 00 1.10E-04 2.92E+ 07 1.10E+ 03 7.48E+ 05 9.91E+ 04 3.81E+ 04 8.00E+ 05
rank 1 2 8 3 7 6 4 5
f 6 mean 4.47E-03 7.51E+ 00 1.34E+ 03 1.57E+ 01 1.47E+ 03 1.64E+ 03 1.36E+ 02 2.00E+ 01
std 3.29E-03 2.67E-05 3.46E+ 03 1.99E+ 00 9.07E+ 02 4.54E+ 02 1.62E+ 01 3.46E+ 01
rank 1 2 6 3 7 8 5 4
f 7 mean 2.41E-04 2.16E-04 2.23E+ 00 1.01E+ 01 4.73E-01 4.75E-01 9.93E+ 01 6.57E-02
std 2.33E-04 1.16E-04 4.13E+ 00 6.23E+ 00 3.03E-01 1.58E-01 2.44E+ 01 4.57E-02
rank 2 1 6 7 4 5 8 3
f 8 mean −1.00E+ 03 −9.36E+ 01 −8.83E+ 03 −7.41E+ 03 − 5.19E+ 03 −7.63E+ 03 −6.89E+ 03 −3.78E+ 03
std 7.16E+ 02 4.62E+ 01 7.31E+ 02 8.71E+ 02 5.72E+ 02 1.67E+ 02 8.35E+ 02 2.90E+ 02
rank 7 8 1 3 5 2 4 6
f 9 mean 3.83E-07 1.84E-04 1.59E+ 02 2.65E+ 02 1.53E+ 02 1.39E+ 02 3.71E+ 02 3.65E+ 01
mean 7.64E-07 1.86E-06 4.23E+ 01 1.96E+ 01 6.13E+ 01 2.07E+ 01 2.43E+ 01 3.09E+ 01
rank 1 2 6 7 5 4 8 3
f 10 mean 1.65E-05 7.04E-04 1.48E+ 01 4.94E+ 00 9.29E+ 00 1.44E+ 01 8.52E+ 00 1.20E+ 01
std 2.21E-05 4.06E-06 7.11E+ 00 2.71E+ 00 1.86E+ 00 1.12E+ 00 4.74E-01 9.24E+ 00
rank 1 2 8 3 5 7 4 6
f 11 mean 1.99E-10 6.19E-08 6.89E+ 00 5.98E-01 1.71E+ 01 1.53E+ 01 1.03E+ 00 8.30E-01
std 5.63E-10 8.26E-10 2.28E+ 01 5.98E-02 1.46E+ 01 3.27E+ 00 5.56E-03 4.20E-01
rank 1 2 6 3 8 7 5 4
f 12 mean 4.13E-04 1.67E+ 00 4.65E+ 00 1.36E+ 01 2.00E+ 03 1.71E+ 02 5.22E+ 00 3.14E+ 02
std 2.30E-04 5.08E-06 3.79E+ 00 6.00E+ 00 8.44E+ 03 5.53E+ 02 8.48E-01 1.06E+ 03
rank 1 2 3 5 8 6 4 7
f 13 mean 6.07E-03 6.18E-01 1.37E+ 07 2.47E+ 00 1.04E+ 05 9.76E+ 04 2.61E+ 01 4.49E+ 04
std 3.92E-03 9.19E-02 7.49E+ 07 3.21E-01 2.72E+ 05 1.03E+ 05 4.32E+ 00 1.55E+ 05
rank 1 2 8 3 7 6 4 5
f 14 mean 1.25E+ 01 1.27E+ 01 1.53E+ 00 4.84E+ 00 1.69E+ 00 9.98E-01 2.71E+ 00 1.53E+ 00
std 9.16E-01 3.27E-15 1.31E+ 00 4.74E+ 00 1.01E+ 00 2.63E-04 2.02E+ 00 8.92E-01
rank 6 7 2 5 3 1 4 2
f 15 mean 4.82E-04 8.04E-04 9.76E-04 5.15E-03 9.75E-03 7.60E-04 1.37E-03 1.01E-03
std 1.81E-04 2.93E-04 3.11E-04 7.79E-03 1.34E-02 1.05E-04 3.33E-04 3.58E-04
rank 1 3 4 7 8 2 6 5
f 16 mean −5.77E-01 −1.68E-01 −1.03E+ 00 −1.03E+ 00 −1.03E+ 00 −1.03E+ 00 −1.03E+ 00 −1.03E+ 00
std 2.82E-01 1.32E-01 6.78E-16 5.25E-04 2.03E-09 1.69E-08 1.82E-03 3.43E-05
rank 2 3 1 1 1 1 1 1
f 17 mean 5.33E-01 1.98E+ 00 3.98E-01 3.98E-01 3.98E-01 3.98E-01 3.99E-01 3.99E-01
std 2.75E-01 1.01E+ 00 0.00E+ 00 5.57E-04 1.00E-13 6.22E-09 1.13E-03 1.15E-03
rank 3 4 1 1 1 1 2 2
f 18 mean 3.04E+ 01 6.00E+ 02 3.00E+ 00 3.06E+ 00 3.00E+ 00 3.00E+ 00 3.10E+ 00 3.00E+ 00
std 3.42E+ 00 1.73E-03 1.70E-15 5.86E-02 1.89E-14 7.88E-07 1.29E-01 5.38E-05
rank 4 5 1 2 1 1 3 1
f 19 mean −3.71E+ 00 −3.63E+ 00 −3.86E+ 00 −3.84E+ 00 −3.85E+ 00 −3.86E+ 00 −3.85E+ 00 −3.85E+ 00
std 1.20E-01 2.23E-01 2.71E-15 1.50E-02 6.36E-02 1.09E-06 1.37E-02 1.96E-03
rank 4 5 1 3 2 1 2 2
f 20 mean −2.15E+ 00 −1.81E+ 00 −3.23E+ 00 −2.84E+ 00 − 3.23E+ 00 − 3.32E+ 00 −2.86E+ 00 −2.95E+ 00
std 5.03E-01 4.24E-01 5.40E-02 1.29E-01 1.22E-01 4.20E-03 1.74E-01 3.53E-01
rank 6 7 2 5 2 1 4 3
f 21 mean −5.54E+ 00 −3.47E+ 00 −6.55E+ 00 −4.60E+ 00 −9.31E+ 00 −1.01E+ 01 −3.88E+ 00 − 3.29E+ 00
std 9.25E-01 7.98E-01 3.33E+ 00 2.32E+ 00 1.92E+ 00 4.78E-02 1.14E+ 00 1.82E+ 00
rank 4 7 3 5 2 1 6 8
f 22 mean −6.16E+ 00 −3.42E+ 00 −7.45E+ 00 −5.51E+ 00 −9.52E+ 00 −1.03E+ 01 −4.25E+ 00 −4.00E+ 00
std 1.39E+ 00 8.57E-01 3.49E+ 00 2.86E+ 00 2.00E+ 00 1.06E-01 1.26E+ 00 1.68E+ 00
rank 4 8 3 5 2 1 6 7
f 23 mean −5.55E+ 00 −3.51E+ 00 −8.54E+ 00 −6.10E+ 00 −9.64E+ 00 −1.04E+ 01 −4.02E+ 00 − 4.20E+ 00
std 8.64E-01 7.50E-01 3.41E+ 00 3.15E+ 00 2.04E+ 00 1.28E-01 1.27E+ 00 1.24E+ 00
rank 5 8 3 4 2 1 7 6
Sum of rank 59 88 101 89 104 88 108 99
Average rank 2.5652 3.8261 4.3913 3.8696 4.5217 3.8261 4.6957 4.3043
Overall rank 1 2 5 3 6 2 7 4