## 5 Results and Discussion
### The Performance of the SIDE Variant
#### 5.3.1 Comparative Results of SIDE with the Most Promising DE Variants
The test results are shown in Table 16, and the summary of wins can be found in Table 17. The formats of these two tables coincided with those of Tables 13 and 14, respectively. Based on the information in Table 16, it is possible to determine that the SIDE had a performance that was comparable to that of best\(/1/\)bin for case C2 and that was better in the rest of the case studies. Concerning rand\(/1/\exp\), the performance of the SIDE is better in case C3, while there were no significant differences in the performance of these two variants for the other cases. The overall finding in the comparison results of the SIDE with respect to the two most outstanding DE variants based on Table 14 is that the SIDE tended to improve the search for solutions among the studied cases in comparison with the most outstanding DE variant, thereby increasing the likelihood that the problem would be solved successfully. Concerning time, Table 18 shows the minimum, maximum, mean, and standard deviation of the execution time \(t\) for the 30 independent runs of the SIDE for each case study. The values in gray indicate the cases where the SIDE outperformed the best results in Tables 8-11. The statistical information on the execution times in this table did not present important differences with respect to what was reported in Tables 8-11; thus, the SIDE was as efficient as the rest of the alternatives. Finally, Table 19 shows the minimum and maximum error \(e\) values achieved with the best mechanisms synthesized by the SIDE for all case studies. The values in gray indicate that the error \(e\) obtained with the SIDE was better or at least equal to the best results in Table 12. Thus, this table indicates that the accuracy of the mechanisms obtained with the SIDE was competitive with respect to the best error values obtained with the rest of the variants of DE. \begin{table}
\begin{tabular}{l c c c c} \hline
**Test** & **Case C1** & **Case C2** & **Case C3** & **Case C4** \\ \hline best\(/1/\)bin vs. SIDE & \((-)\) 1.8626 \(\times\)\(10^{-6}\) & \((=)\) 6.5517 \(\times\)\(10^{-1}\) & \((-)\) 2.5518 \(\times\)\(10^{-6}\) & \((-)\) 1.8242 \(\times\)\(10^{-6}\) \\ best\(/1/\)bin vs. rand\(/1/\)exp & \((-)\) 1.8626 \(\times\)\(10^{-6}\) & \((=)\) 5.9408 \(\times\)\(10^{-1}\) & \((-)\) 5.7183 \(\times\)\(10^{-6}\) & \((-)\) 1.8626 \(\times\)\(10^{-6}\) \\ SIDE vs. rand\(/1/\)exp & \((=)\) 3.0852 \(\times\)\(10^{-1}\) & \((=)\) 1.0000 & \((+)\) 8.3389 \(\times\)\(10^{-3}\) & \((=)\) 5.0840 \(\times\)\(10^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 16: Wilcoxon test results for the DE variants rand\(/1/\exp\), best\(/1/\)bin, and SIDE considering all case studies. \begin{table}
\begin{tabular}{c c c c c} \hline
**Case Study** & **Min \(J(\vec{p})\)** & **Max \(J(\vec{p})\)** & **Mean \(J(\vec{p})\)** & **Std \(J(\vec{p})\)** \\ \hline C1 & 3.3069 \(\times\)\(10^{-27}\) & 4.7144 \(\times\)\(10^{-2}\) & 4.2525 \(\times\)\(10^{-3}\) & 1.0397 \(\times\)\(10^{-2}\) \\ C2 & 7.8637 \(\times\)\(10^{-1}\) & 1.5482 \(\times\)\(10^{1}\) & 8.1343 & 7.4736 \\ C3 & 1.4870 \(\times\)\(10^{-4}\) & 8.3759 \(\times\)\(10^{-4}\) & 2.6975 \(\times\)\(10^{-4}\) & 1.9250 \(\times\)\(10^{-4}\) \\ C4 & 1.0585 \(\times\)\(10^{-2}\) & 2.5307 \(\times\)\(10^{-2}\) & 1.5362 \(\times\)\(10^{-2}\) & 4.8990 \(\times\)\(10^{-3}\) \\ \hline \end{tabular}
\end{table} 
Table 15: Results obtained with SIDE concerning the value of the objective function \(J(\vec{p})\) for each case study. Figure 6: Best mechanisms synthesized by SIDE for all case studies. The corresponding mechanism parameters can be consulted in the next Section 5.3.2.