## 4 Results
### Algorithm Performance Analysis
#### 4.2.1 Descriptive Statistics
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Algorithm-CHT** & **Mean** & **Std.** & **Median** & **Min** & **Max** & **NFS** \\ \hline R1B-FR & 0.02357 & 0.01494 & 0.03304 & 0.002539 & 0.04297 & 0 \\ GA-FR & 0.03521 & 0.01041 & 0.03816 & 0.01467 & 0.05109 & 0 \\ PSO-FR & 0.03724 & **0.00713** & 0.03643 & 0.02442 & 0.05452 & 0 \\ MUMSA-FR & 0.03205 & 0.009535 & 0.03412 & 0.01266 & 0.048 & 0 \\ R1B-SR & 0.02685 & 0.01408 & 0.03331 & 0.002685 & 0.04368 & 0 \\ GA-SR & 0.04522 & 0.01005 & 0.04495 & 0.02564 & 0.06512 & 0 \\ PSO-SR & 0.0353 & 0.01015 & 0.03663 & 0.003119 & 0.05145 & 0 \\ MUMSA-SR & 0.03064 & 0.01027 & 0.03104 & 0.01039 & 0.05104 & 0 \\ R1B-eC & 0.02956 & 0.009226 & 0.03264 & 0.01179 & 0.04592 & 0 \\ GA-eC & 0.03973 & 0.009862 & 0.03818 & 0.02489 & 0.05877 & 0 \\ PSO-eC & 0.03608 & 0.009744 & 0.03674 & 0.01091 & 0.05446 & 0 \\ MUMSA-eC & 0.02675 & 0.01264 & 0.03091 & **0.002507** & 0.05102 & 0 \\ R1B-PF & 0.02509 & 0.01224 & **0.02461** & 0.002746 & 0.04512 & 0 \\ GA-PF & 0.03458 & 0.01353 & 0.04058 & 0.005144 & 0.05076 & 0 \\ PSO-PF & 0.03452 & 0.01104 & 0.03651 & 0.01113 & 0.05355 & 0 \\ MUMSA-PF & 0.02689 & 0.007722 & 0.02891 & 0.00876 & **0.03767** & 0 \\ R1B-NCH & **0.02336** & 0.01577 & 0.03441 & 0.002572 & 0.04166 & 0 \\ \hline \end{tabular}
\end{table} 
Table 6: Descriptive statistics of the obtained results for each metaheuristic algorithm in study case 1 with trajectory 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Algorithm-CHT** & **Mean** & **Std.** & **Median** & **Min** & **Max** & **NFS** \\ \hline R1B-FR & 0.02619 & 0.01033 & 0.03075 & 0.003966 & 0.04198 & 0 \\ GA-FR & 0.03709 & 0.006465 & 0.03808 & 0.02067 & 0.05163 & 0 \\ PSO-FR & 0.03626 & 0.01057 & 0.03566 & 0.02025 & 0.05834 & 0 \\ MUMSA-FR & 0.03233 & 0.007363 & 0.03338 & 0.01265 & 0.0421 & 0 \\ R1B-SR & 0.03088 & 0.008759 & 0.03394 & 0.002988 & 0.04118 & 0 \\ GA-SR & 0.03578 & 0.01002 & 0.03773 & 0.01142 & 0.05438 & 0 \\ PSO-SR & 0.02846 & 0.007408 & **0.02765** & 0.004439 & 0.04094 & 0 \\ MUMSA-SR & 0.03104 & 0.00883 & 0.0341 & 0.01653 & 0.04237 & 0 \\ R1B-eC & 0.03395 & **0.004956** & 0.03378 & 0.02432 & 0.04756 & 0 \\ GA-eC & 0.04107 & 0.009803 & 0.04155 & 0.01859 & 0.0544 & 0 \\ PSO-eC & 0.03441 & 0.007179 & 0.03341 & 0.02315 & 0.0567 & 0 \\ MUMSA-eC & 0.02708 & 0.01299 & 0.0295 & 0.003726 & 0.04752 & 0 \\ R1B-PF & 0.02486 & 0.01167 & 0.03135 & 0.003076 & **0.03391** & 0 \\ GA-PF & 0.0397 & 0.008355 & 0.038 & 0.02922 & 0.05966 & 0 \\ PSO-PF & 0.03371 & 0.01283 & 0.03478 & 0.005304 & 0.06198 & 0 \\ MUMSA-PF & 0.02407 & 0.009266 & 0.02789 & 0.009579 & 0.03866 & 0 \\ R1B-NCH & **0.02255** & 0.01324 & 0.02978 & **0.002167** & 0.03585 & 0 \\ \hline \end{tabular}
\end{table} 
Table 5: Descriptive statistics of the obtained results for each metaheuristic algorithm in study case 1 with trajectory 1. Table 8 shows the descriptive statistics for study case 2 using trajectory 2 in the synthesis process. The columns of such tables contain the same terms explained above. In this analysis, the R1B-NCH algorithm reliability is studied under a trajectory change in the cam-linkage mechanism. According to the results in Table 8, all metaheuristic algorithms find feasible solutions except for PSO-FR, R1B-SR, and PSO-eC (see \"NFS\" column). MUMSA-FR, R1B-NCH, and MUMSA-SR obtain the three best solutions in that order. The R1B-NCH presents a very slight increment of around 0.68% with respect to the obtained result given in MUMSA-FR (see \"min\" column). The R1B-NCH also obtains the best values in the mean, the standard deviation, the median, and the maximum value of the objective function.