## 6 Evaluated Algorithms
### Results over 2017 IEEE Congress on Evolutionary Computation (CEC2017)  
The FVIMDE algorithm continues to demonstrate its robustness and efficiency across the CEC2017 benchmark functions, as shown in Tables 6 and 7, outperforming many other algorithms in various instances. For example, in F1, FVIMDE achieves a mean value of 3.21E+03, which is significantly better than those obtained by algorithms like FLO (1.14E+10) and ROA (4.06E+09). This highlights FVIMDE's ability to find more optimal solutions where other optimizers struggle. Similarly, in F2, FVIMDE's mean of 1.51E+03 outperforms FVIM (3.00E+07) and STOA (1.98E+07), showcasing its efficiency in dealing with complex optimization landscapes. In addition to these successes, FVIMDE outperforms several modern metaheuristic optimizers. For instance, in F3, FVIMDE achieves a mean value of 3.01E+02, outclassing MFO (1.60E+04) and SHIO (7.13E+03). Moreover, in F5, FVIMDE leads with a mean value of 5.17E+02, demonstrating its superiority over FVIM (5.25E+02) and STOA (5.24E+02). This trend of outperformance continues in F6, where FVIMDE ranks first with a mean value of 6.00E+02, outperforming even well-regarded algorithms like PSO (6.15E+02) and SA (6.12E+02). \begin{table}
\begin{tabular}{l l l l l l l l l l l l l} \hline \hline
**Function** & **WOA** & **PSO** & **MFO** & **SHIO** & **ZOA** & **MTDE** & **SCA** & **DOA** & **SCSO** & **GA** & **SA** \\ \hline F1 & Mean & 1.39E+04 & 7.13E+02 & 1.79E+03 & 1.20E+03 & 4.84E+02 & 1.38E+04 & 1.72E+03 & 1.54E+03 & 5.11E+02 & 5.16E+04 & 1.07E+04 \\  & Std & 7.02E+03  
\begin{table}
\begin{tabular}{l l l l l l l l l l l l l} \hline \hline
**Function** & \multicolumn{2}{c}{**PVIMDE**} & \multicolumn{2}{c}{**FVIMDE**} & \multicolumn{2}{c}{**FIVIM**} & \multicolumn{2}{c}{**FLO**} & \multicolumn{2}{c}{**STOA**} & \multicolumn{2}{c}{**SOA**} & \multicolumn{2}{c}{**SPBO**} & \multicolumn{2}{c}{**AO**} & \multicolumn{2}{c}{**SSOA**} & \multicolumn{2}{c}{**Chimp**} & \multicolumn{2}{c}{**CPO**} & \multicolumn{2}{c}{**ROA**} \\ \hline F1 & Mean & 3.21E+03 & 5.68E+06 & 1.14E+10 & 1.99E+08 & 3.47E+08 & 8.71E+09 & 8.43E+05 & 1.17E+10 & 1.52E+09 & 2.21E+03 & 4.06E+09 \\  & Std & 1.66E+03 & 1.03E+07 & 3.75E+09 & 2.05E+08 & 1.81E+08 & 3.09E+09 & 4.58E+05 & 2.56E+09 & 1.50E+09 & 2.21E+03 & 1.97E+09 \\  & SEM & 6.78E+02 & 4.19  
The consistent performance of FVIMDE across these benchmarks, including more challenging ones like F10 and F11, further cements its position as a top contender in the field of optimization. In F10, FVIMDE achieves the best mean value of 1.45E+03, surpassing FVIM (1.65E+03) and even sophisticated algorithms like MTDE (1.01E+04). Similarly, in F11, FVIMDE records a mean value of 1.11E+03, significantly outperforming GA (6.05E+03) and other algorithms like DOA (1.61E+03). The performance of FVIMDE in comparison to optimization algorithms on the CEC2017 benchmark functions, as detailed in Tables 8 and 9, shows its significant capability to outperform many of its peers across various functions. For instance, in F16, FVIMDE  
\begin{table}
\begin{tabular}{l l l l l l l l l l l l} \hline \hline
**Function** & **WOA** & **PSO** & **MFO** & **SHIO** & **ZOA** & **MTDE** & **SCA** & **DOA** & **SCSO** & **GA** & **SA** \\ \hline F1 & Mean & 3.74E+06 & 2.54E+03 & 2.34E+07 & 7.84E+07 & 5.27E+08 & 1.80E+11 & 7.23E+08 & 2.31E+09 & 1.52E+07 & 4.94E+09 & 4.9  
achieves the lowest mean value of 1.61E+03, outperforming well-established algorithms like PSO (1.84E+03) and SHIO (1.91E+03). Similarly, in F17, FVIMDE ranks first with a mean of 1.73E+03, surpassing STOA (1.76E+03) and SOA (1.85E+03). Moreover, in more complex functions like F18 and F19, FVIMDE maintains its competitive edge. For F18, FVIMDE records the best performance with a mean of 1.81E+03, significantly outperforming FLO (1.10E+08) and ROA (7.97E+04). Similarly, in F19, FVIMDE outperforms several algorithms, including FVIM (8.26E+03) and SPBO (1.32E+07), with a mean value of 1.90E+03.