## 5 Results and Discussion
### The Performance of the SIDE Variant
#### 5.3.1 Comparative Results of SIDE with the Most Promising DE Variants
\begin{table}
\begin{tabular}{l l l l l} \hline
**Test** & **Case C1** & **Case C2** & **Case C3** & **Case C4** \\ \hline best/1/exp vs. rand/1/exp & \((-)\) 1.5287 \(\times\) 10\({}^{-4}\) & \((\approx)\) 6.8747 \(\times\) 10\({}^{-1}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 5.4823 \(\times\) 10\({}^{-3}\) \\ best/1/exp vs. rand/2/dir & \((+)\) 4.6566 \(\times\) 10\({}^{-6}\) & \((\approx)\) 6.2806 \(\times\) 10\({}^{-1}\) & \((\approx)\) 7.9216 \(\times\) 10\({}^{-1}\) & \((\approx)\) 3.5988 \(\times\) 10\({}^{-1}\) \\ current-to-best/1 vs. current-to-rand/1 & \((-)\) 2.4786 \(\times\) 10\({}^{-2}\) & \((\approx)\) 1.0943 \(\times\) 10\({}^{-1}\) & \((-)\) 9.9026 \(\times\) 10\({}^{-5}\) & \((-)\) 2.0798 \(\times\) 10\({}^{-5}\) \\ current-to-best/1 vs. & \((-)\) 1.2048 \(\times\) 10\({}^{-2}\) & \((-)\) 8.8565 \(\times\) 10\({}^{-5}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((\approx)\) 3.9305 \(\times\) 10\({}^{-1}\) \\ current-to-rand/1/bin & \((-)\) 3.9041 \(\times\) 10\({}^{-5}\) & \((-)\) 5.7183 \(\times\) 10\({}^{-6}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((\approx)\) 7.3244 \(\times\) 10\({}^{-2}\) \\ current-to-best/1 vs. rand/1/exp & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 1.0598 \(\times\) 10\({}^{-2}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 1.8242 \(\times\) 10\({}^{-6}\) \\ current-to-best/1 vs. rand/2/dir & \((\approx)\) 5.1585 \(\times\) 10\({}^{-1}\) & \((-)\) 1.0598 \(\times\) 10\({}^{-2}\) & \((\approx)\) 5.4253 \(\times\) 10\({}^{-1}\) & \((-)\) 8.3260 \(\times\) 10\({}^{-6}\) \\ current-to-rand/1 vs. & \((\approx)\) 8.2358 \(\times\) 10\({}^{-1}\) & \((-)\) 3.6435 \(\times\) 10\({}^{-2}\) & \((-)\) 2.6077 \(\times\) 10\({}^{-6}\) & \((+)\) 1.8626 \(\times\) 10\({}^{-6}\) \\ current-to-rand/1/bin & \((-)\) 7.9107 \(\times\) 10\({}^{-5}\) & \((-)\) 1.3663 \(\times\) 10\({}^{-2}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((+)\) 1.5978 \(\times\) 10\({}^{-5}\) \\ current-to-rand/1 vs. rand/1/exp & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((\approx)\) 9.8359 \(\times\) 10\({}^{-1}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) \\ current-to-rand/1 vs. rand/2/dir & \((+)\) 2.3164 \(\times\) 10\({}^{-4}\) & \((\approx)\) 5.1041 \(\times\) 10\({}^{-1}\) & \((+)\) 3.2391 \(\times\) 10\({}^{-6}\) & \((-)\) 4.0318 \(\times\) 10\({}^{-3}\) \\ current-to-rand/1/bin vs. rand/1/bin & \((-)\) 1.0610 \(\times\) 10\({}^{-5}\) & \((\approx)\) 3.2847 \(\times\) 10\({}^{-1}\) & \((-)\) 4.4076 \(\times\) 10\({}^{-5}\) & \((-)\) 1.8529 \(\times\) 10\({}^{-2}\) \\ current-to-rand/1/bin vs. rand/1/exp & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((+)\) 1.9661 \(\times\) 10\({}^{-2}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) \\ current-to-rand/1/bin vs. rand/2/dir & \((+)\) 2.0913 \(\times\) 10\({}^{-4}\) & \((\approx)\) 1.4028 \(\times\) 10\({}^{-1}\) & \((+)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) \\ rand/1/bin vs. rand/1/exp & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((\approx)\) 4.3485 \(\times\) 10\({}^{-1}\) & \((-)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 3.7253 \(\times\) 10\({}^{-6}\) \\ rand/1/bin vs. rand/2/dir & \((+)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((\approx)\) 3.8180 \(\times\) 10\({}^{-1}\) & \((+)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((-)\) 1.0245 \(\times\) 10\({}^{-6}\) \\ rand/1/exp vs. rand/2/dir & \((+)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((\approx)\) 5.9191 \(\times\) 10\({}^{-1}\) & \((+)\) 1.8626 \(\times\) 10\({}^{-6}\) & \((+)\) 3.2391 \(\times\) 10\({}^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 14: Summary of Wilcoxon test wins by DE variant for all case studies. The Wilcoxon test was also applied to the DE variants rand\(/1/\exp\), best\(/1/\)bin, and SIDE with statistical significance \(\alpha=5\%\) to provide enough information about the algorithm performance.