## 6 Evaluated Algorithms
### FVIDDE Results on 50 Benchmark Functions
** & **FVMDDE** & **FVIM** & **FLO** & **STOA** & **SOA** & **MYO** & **AO** & **SSOA** & **Chimp** & **CFO** & **ROA** \\ \hline F19 & Mean & 3.98E-01 & 3.98E-01 & 4.22E-01 & 3.98E-01 & 3.98E-01 & 3.98E-01 & 3.98E-01 & 8.11E-01 & 3.98E-01 & 3.98E-01 & 3.98E-01 \\  & Std & 0.00E+00 & 1.51E-06 & 5.24E-02 & 3.79E-05 & 1.05E-04 & 1.72E-07 & 1.52E-04 & 5.04E-01 & 6.40E-04 & 4.52E-08 & 3.27E-05 \\  & Rank & 1 & 13 & 20 & 15 & 16 & 10 & 17 & 21 & 18 & 7 & 14 \\ \hline F20 & Mean & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 1.37E-04 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 1.33E-16 \\  & Std & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 1.92E-04 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 2.98E-16 \\  & Rank & 1 & 1 & 1 & 1 & 1 & 21 & 1 & 1 & 1 & 1 & 19 \\ \hline F21 & Mean & 0.00E+00 & 9.11E+08 & 1.40E-01 & 9.70E-06 & 1.52E-05 & 2.22E-07 & 1.53E-04 & 1.16E-01 & 1.63E-04 & 4.76E-08 & 2.70E-04 \\  & Std & 0.00E+00 & 8.77E-08 & 1.93E-01 & 6.93E-06 & 6.80E-06 & 7.65E-08 & 1.87E-04 & 1.05E-01 & 1.59E-04 & 4.98E-08 & 4.24E-04 \\  & Rank & 1 & 10 & 21 & 12 & 13 & 11 & 15 & 20 & 16 & 7 & 18 \\ \hline F22 & Mean & 1.40E+01 & 1.02E+01 & 0.00E+00 & 4.50E+00 & 1.14E-14 & 9.79E+01 & 0.00E+00 & 0.00E+00 & 1.10E+00 & 0.00E+00 & 0.00E+00 \\  & Std & 6.21E+00 & 8.64E+00 & 0.00E+00 & 2.63E+00 & 2.54E-14 & 1.40E+01 & 0.00E+00 & 0.00E+00 & 1.75E+00 & 0.00E+00 & 0.00E+00 \\  & Rank & 16 & 15 & 1 & 14 & 11 & 19 & 1 & 1 & 12 & 1 & 1 \\ \hline F23 & Mean & -7.58E+03 & -5.35E+03 & -9.02E+03 & -5.41E+03 & -5.32E+03 & -8.31E+03 & -8.17E+03 & -2.46E+03 & -5.76E+03 & -4.80E+03 & -1.26E+04 \\  & Std & 1.09E+03 & 6.61E+02 & 8.01E-04 & 1.95E+02 & 6.45E+02 & 9.73E+02 & 4.06E+03 & 6.51E+02 & 6.41E+01 & 2.37E+03 & 9.22E-04 \\  & Rank & 8 & 16 & 2 & 15 & 17 & 7 & 6 & 7 & 21 & 13 & 18 & 1 \\ \hline F24 & Mean & -1.80E+00 & -1.80E+00 & -1.66E+00 & -1.64E+00 & -1.80E+00 & -1.80E+00 & -1.80E+00 & -1.14E+00 & -1.48E+00 & -1.80E+00 & -1.80E+00 \\  & Std & 0.00E+00 & 6.89E-07 & 1.93E-01 & 3.58E-01 & 3.22E-05 & 1.41E-07 & 4.15E-04 & 2.47E-01 & 4.38E-01 & 8.15E-08 & 4.28E-04 \\  & Rank & 1 & 12 & 17 & 19 & 13 & 10 & 15 & 21 & 20 & 8 & 14 \\ \hline F25 & Mean & -4.67E+00 & -4.50E+00 & -4.50E+00 & -3.07E+00 & -3.96E+00 & -4.32E+00 & -3.99E+00 & -2.12E+00 & -2.78E+00 & -3.88E+00 & -3.29E+00 \\  & Std & 2.29E-02 & 2.41E-02 & 3.39E-01 & 9.48E-01 & 5.60E-01 & 3.93E-01 & 3.66E-01 & 4.84E-01 & 6.79E-01 & 4.91E-01 & 6.74E-01 \\  & Rank & 2 & 5 & 18 & 17 & 13 & 8 & 12 & 21 & 20 & 14 & 16 \\ \hline F26 & Mean & -8.10E+00 & -8.10E+00 & -5.72E+00 & -5.20E+00 & -5.33E+00 & -6.64E+00 & -0.66E+00 & -2.87E+00 & -4.06E+00 & -7.75E+00 & -5.81E+00 \\  & Std & 1.47E+00 & 6.98E-01 & 5.38E-01 & 7.17E-01 & 1.11E+00 & 7.80E-01 & 1.25E+00 & 3.90E-01 & 5.45E-01 & 1.73E-00 & 6.61E-01 \\  & Rank & 2 & 3 & 16 & 18 & 17 & 10 & 12 & 21 & 20 & 20 & 5 & 14 \\ \hline F27 & Mean & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 3.46E-09 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 \\  & Std & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 3.26E-09 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 \\  & Rank & 1 & 1 & 1 & 1 & 1 & 19 & 1 & 1 & 1 & 1 & 1 \\ \hline F28 & Mean & -1.02E+00 & -1.03E+00 & -1.03E+00 & -1.03E+00 & -1.03E+00 & -1.03E+00 & -1.03E+00 & -1.01E+00 & -1.03E+00 & -1.03E+00 \\  & Std & 0.00E+00 & 3.88E-09 & 2.66E-03 & 4.14E-07 & 2.72E-07 & 5.25E-08 & 2.84E-04 & 1.26E-02 & 6.31E-06 & 1.34E-03 & 1.03E-05 \\  & Rank & 1 & 10 & 20 & 14 & 13 & 12 & 18 & 21 & 15 & 19 & 17 \\ \hline F29 & Mean & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 1.63E-04 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.00E+00 & 0.  
higher variability in their results, suggesting that they might be more sensitive to initial conditions or specific problem landscapes. As we can see in Tables 14 and 15, the results over the 50 benchmark functions (F37-F50) highlight the strengths and occasional weaknesses of FVIMDE relative to these other approaches, showcasing where it excels and where it may need further refinement.