## 5 Comparative Experimental Study
### Statistical Analysis of the Overall Performance
The first step is to guarantee that at least one comparison of the constraint-handling technique in the metaheuristic algorithms is different. The 95%-confidence Friedman test is applied for that purpose, and the results are presented in Table A10 of Appendix D. The obtained \(p\)-value near to zero proves the existence of such differences with confidence close to 100%. Once the first step was done, the Friedman test for multiple comparisons with the Holm post-hoc error correction method was performed to make the general conclusions of comparisons and confirm the results' confidence. The forty samples (four CHTs included in ten algorithms), conformed to each one by the best thirty objective functions of the executions, can be compared if both CHTs are incorporated in the same metaheuristic algorithm. In Table A11 of Appendix D, the results obtained by the multi-comparative analysis are shown. The two-sided alternative hypothesis was selected, which means that, in the case that the \(p\)-value of the test is less than the 5% statistical significance, the comparison between the CHT \(A\) and the one in \(B\) for the same algorithm presents significant differences (the alternative hypothesis is accepted). On the contrary, if the results are not convincing, and significant differences are not observed in the comparative result then the null hypothesis is accepted. Once the alternative hypothesis is accepted, the Friedman \(z\)-value sign defines the winner between both CHTs in the algorithms. The negative sign of \(z\) indicates that the CHT in the algorithm \(A\) was better than the one in \(B\), and vice versa. Three comparisons related to the four CHTs are made per each metaheuristic algorithm. A total of thirty comparisons are carried out per each CHT at each study case (considering \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Study Case 1**} & \multicolumn{3}{c}{**Study Case 2**} & \multicolumn{3}{c}{**Study Case 3**} \\  & **FR** & **SR** & \(e\)**C** & **PF** & **FR** & **SR** & \(e\)**C** & **PF** & **FR** & **SR** & \(e\)**C** & **PF** \\ \hline DER1B & 14 & 1 & 7 & 8 & 11 & 2 & 3 & 14 & 12 & 0 & 7 & 11 \\ DER1E & 10 & 0 & 7 & 13 & 14 & 7 & 2 & 7 & 11 & 0 & 6 & 13 \\ DEB1B & 11 & 2 & 5 & 12 & 14 & 2 & 7 & 7 & 15 & 3 & 2 & 10 \\ DEB1E & 15 & 0 & 8 & 7 & 13 & 0 & 5 & 12 & 15 & 0 & 7 & 8 \\ CR & 10 & 0 & 8 & 12 & 10 & 15 & 1 & 4 & 11 & 13 & 6 & 0 \\ DECB & 11 & 0 & 5 & 14 & 13 & 8 & 1 & 8 & 8 & 5 & 15 & 2 \\ DECR1B & 14 & 0 & 8 & 8 & 8 & 14 & 0 & 8 & 13 & 5 & 10 & 2 \\ DECR1E & 11 & 5 & 2 & 12 & 13 & 5 & 0 & 12 & 8 & 1 & 15 & 6 \\ GA & 11 & 0 & 14 & 5 & 3 & 8 & 6 & 13 & 11 & 13 & 6 & 0 \\ PSO & 8 & 0 & 13 & 9 & 5 & 2 & 8 & 15 & 1 & 4 & 14 & 11 \\ \hline
**Total** & **115** & 8 & 77 & 100 & **104** & 63 & 33 & 100 & **105** & 44 & 88 & 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance analysis of the CHTs using descriptive statistics. the ten algorithms), and the highest number of wins defines the most suitable constraint-handling technique in the synthesis of lower limb rehabilitation mechanisms for each study case. A total of ninety comparisons was carried out, considering the three CHT comparisons with the ten metaheuristic algorithm for the three study cases. The number of wins per CHT in algorithms from the comparisons is presented in Table 8. The results indicate that the feasible rules improve the algorithm performance in the comparisons at 66.66% for study case 1, 40% for study case 2, and 53.33% for study case 3. The overall improvement for the ninety comparisons (in all study cases) with the FR is around 53.3%. It is also observed in Table A11 of Appendix D that only eight comparisons with other CHTs (DECB EC, DECR1B SR, DECR1E EC, GA SR, GA PF, PSO SR, PSO \(e\)C, and PSO PF) outperformed the values obtained in FR (around 8.8% of the total comparisons).