## 5 Results and Discussion
### The Performance of the SIDE Variant
#### 5.3.2 Comparative Results of SIDE with the State-Of-The-Art Algorithms
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable (\(\overline{p_{j}}\))** & SIDE & **QO Rao-1 [35]** & **ODSKA + CP** \\ \hline \(x_{a}\) (mm) & 20.1582 & 4.9497 & 11.5875 \\ \(y_{a}\) (mm) & 3.9543 & 16.4130 & 20.3173 \\ \(x_{d}\) (mm) & \(-\)80.0000 & 81.72747 & \(-\)63.4658 \\ \(y_{d}\) (mm) & 80.0000 & \(-\)6.0726 & 47.7211 \\ \(l_{2}\) (mm) & 9.5007 & 8.8223 & 8.0705 \\ \(l_{3}\) (mm) & 66.5475 & 44.9536 & 49.8586 \\ \(l_{4}\) (mm) & 78.5406 & 47.6238 & 42.9186 \\ \(l_{b}\) (mm) & 11.9414 & 8.3934 & 10.4609 \\ \(q_{b}\) (rad) & 5.8299 & \(-\)1.1323 & \(-\)4.0483 \\ \(q_{2,1}\) (rad) & 6.1716 & 6.1876 & 6.3003 \\ \(q_{2,2}\) (rad) & 0.591315 & 6.8961 & 6.9958 \\ \(q_{2,3}\) (rad) & 1.30173 & 7.5968 & 7.7068 \\ \(q_{2,4}\) (rad) & 2.01028 & 8.2880 & 8.4197 \\ \(q_{2,5}\) (rad) & 2.71449 & 8.9621 & 2.8449 \\ \(q_{2,6}\) (rad) & 3.41391 & 9.6439 & 3.5525 \\ \(q_{2,7}\) (rad) & 4.10476 & 10.3350 & 4.2469 \\ \(q_{2,8}\) (rad) & 4.79219 & 11.0451 & 4.9363 \\ \(q_{2,9}\) (rad) & 5.4767 & 11.7562 & 5.6147 \\ \(q_{2,10}\) (rad) & 6.1716 & 6.1876 & 6.3002 \\ \hline \(l(\overline{p})\) & \(1.4870\times 10^{-4}\) & \(9.5753\times 10^{-4}\) & \(5.8199\times 10^{-4}\) \\ \hline \hline \end{tabular} Note: the prescribed time in Table 28 was increased by \(q_{2,0}=6.2441\) for QO Rao-1.  
\end{table} 
Table 20: Best parameters obtained with SIDE in contrast to the best results in state-of-the-art algorithms for case study C1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable (\(\overline{p_{j}}\))** & SIDE & **QO Rao-1 [35]** \\ \hline \(x_{a}\) (mm) & 16.5532 & 10.2439 \\ \(y_{a}\) (mm) & \(-\)48.1475 & \(-\)3.8363 \\ \(x_{d}\) (mm) & 48.6904 & 60.2057 \\ \(y_{d}\) (mm) & \(-\)13.5287 & \(-\)5.7904 \\ \(l_{2}\) (mm) & 8.8474 & 1.4472 \\ \(l_{3}\) (mm) & 25.0467 & 1.4474 \\ \(l_{4}\) (mm) & 50.0000 & 50.0000 \\ \(l_{b}\) (mm) & 50.0000 & 12.3135 \\ \(q_{b}\) (rad) & 5.7108 & 0.3474 \\ \hline \hline \end{tabular} Note: the prescribed time in Table 28 was increased by \(q_{2,0}=6.2441\) for QO Rao-1.  
\end{table} 
Table 21: Best parameters obtained with SIDE in contrast to the best results in state-of-the-art algorithms for case study C2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable (\(\overline{p_{j}}\))** & SIDE & **QO Rao-1 [35]** \\ \hline \(x_{a}\) (mm) & 20.1582 & 4.9497 & 11.5875 \\ \(y_{a}\) (mm) & 3.9543 & 16.4130 & 20.3173 \\ \(x_{d}\) (mm) & \(-\)80.0000 & 81.72747 & \(-\)63.4658 \\ \(y_{d}\) (mm) & 80.0000 & \(-\)6.0726 & 47.7211 \\ \(l_{2}\) (mm) & 9.5007 & 8.8223 & 8.0705 \\ \(l_{3}\) (mm) & 66.5475 & 44.9536 & 49.8586 \\ \(l_{4}\) (mm) & 78.5406 & 47.6238 & 42.9186 \\ \(l_{b}\) (mm) & 11.9414 & 8.3934 & 10.4609 \\ \(q_{b}\) (rad) & 5.8299 & \(-\)1.1323 & \(-\)4.0483 \\ \(q_{2,1}\) (rad) & 6.1716 & 6.1876 & 6.3003 \\ \(q_{2,2}\) (rad) & 0.591315 & 6.8961 & 6.9958 \\ \(q_{2,3}\) (rad) & 1.30173 & 7.5968 & 7.7068 \\ \(q_{2,4}\) (rad) & 2.01028 & 8.2880 & 8.4197 \\ \(q_{2,5}\) (rad) & 2.71449 & 8.9621 & 2.8449 \\ \(q_{2,6}\) (rad) & 3.41391 & 9.6439 & 3.5525 \\ \(q_{2,7}\) (rad) & 4.10476 & 10.3350 & 4.2469 \\ \(q_{2,8}\) (rad) & 4.79219 & 11.0451 & 4.9363 \\ \(q_{2,9}\) (rad) & 5.4767 & 11.7562 & 5.6147 \\ \(q_{2,10}\) (rad) & 6.1716 & 6.1876 & 6.3002 \\ \hline \(l(\overline{p})\) & \(1.4870\times 10^{-4}\) & \(9.5753\times 10^{-4}\) & \(5.8199\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 22: Best parameters obtained with SIDE in contrast to the best results in state-of-the-art algorithms for case study C3.