## 6 Evaluated Algorithms
### Results over 2017 IEEE Congress on Evolutionary Computation (CEC2017)
Furthermore, in F20, FVIMDE once again ranks first with a mean of 2.00E+03, outperforming sophisticated algorithms like MTDE (2.45E+03) and DOA (2.37E+03). This  
\begin{table}
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trend continues in F21, where FVIMDE performs commendably with a mean of 2.31E+03, demonstrating superior results compared to other algorithms such as CPO (2.35E+03) and ROA (2.35E+03). The Wilcoxon rank-sum test results for the CEC2017 benchmark functions (F1-F30) provide an in-depth analysis of how FVIMDE compares with various other optimization algorithms, as seen in Tables 10 and 11. These results are presented in terms of significance (S), non-significance (N), or equality (E), indicating whether FVIMDE's performance is significantly different, not significantly different, or statistically equal to that of the competing algorithms. \begin{table}
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**Function** & **WOA** & **PSO** & **MFO** & **SHIO** & **ZOA** & **MTDE** & **SCA** & **DOA** & **SCSO** & **GA** & **SA** \\ \hline F16 & Mean & 1.98E+03 & 1.84E+03 & 1.79E+03 & 1.91E+03 & 1.8  
Across the majority of the benchmark functions, FVIDDE shows a statistically significant performance advantage over other algorithms, with almost all comparisons marked as S. Specifically, in functions like F2, F4, F6, F9, and F12, FVIDDE consistently outperforms the other algorithms, achieving significant results with extremely low p-values, such as 3.02E-11. This consistency across multiple functions highlights FVIDDE's robustness and efficacy as an optimization algorithm. There are a few cases where the comparisons yield equal (E) results, indicating that FVIDDE's performance is statistically on par with other algorithms. For example, in F1, FVIDDE shows a non-significant result (N) when compared to CPO and an equal result (E) when compared to the MFO and GA algorithms. These results suggest that while FVIDDE generally excels, it performs similarly to these specific algorithms for certain functions. The boxplot results for the FVIDDE algorithm in comparison with other optimizers across the CEC2017 benchmarks (F1-F12) (see Figures A3 and A4) reveal a consistent trend of superior performance. FVIDDE exhibits minimal error measures and significantly lower variance in comparison to other algorithms. For example, in functions like F1, F2, and F7, FVIDDE's error measures are close to zero, indicating its effectiveness in optimization. Other algorithms, such as MTDE and SPBO, show much higher error measures with substantial variability, particularly evident in F7 and F9, where the error measures reach extreme values. Moreover, in functions like F10 and F12, FVIDDE outperforms by maintaining a lower error distribution compared to the others, which display higher medians and larger interquartile ranges. This highlights FVIDDE's robustness and stability across a diverse set of optimization problems, positioning it as a highly reliable choice for optimization tasks, particularly when precision and consistency are paramount. The boxplot results for FVIDDE across the CEC2017 benchmarks (F13-F24), as shown in Figures A5 and A6, further reinforce its consistent and superior performance. In all functions, FVIDDE demonstrates minimal error measures, often near zero, and exhibits low variance. This stability and precision are contrasted with other algorithms such as MTDE, which frequently show larger error measures and greater variability. For instance, in functions like F13, F15, F19, and F22, MTDE presents significantly higher errors and broader interquartile ranges, indicating less reliable performance. In functions like F14 and F16, FVIDDE maintains its robustness, with other algorithms like SPBO and AO showing comparatively higher error measures. Additionally, the presence of outliers in many other algorithms highlights the inconsistency of their performance across these benchmark functions.