## 3 Results
### Performance Evaluation of Selected Solutions  
Figure 9 shows the response in the angle graph (left side) and power graph (right side), for one of the initial conditions (10 degrees of ankle dorsiflexion), of the solutions in Table 2 for SS-NSGA-II. Figure 10 shows the same information but for SS-RVEA. On the ankle angle response graph of both figures, the reference signal was added for clarity.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multicolumn{4}{c}{**Evaluations by Objective**} & \multicolumn{4}{c}{**Set of Parameters**} \\ \cline{2-10}  & \
\begin{tabular}{c} **MSE** \\ \(\times\)**10\({}^{-2}\)** \\ \end{tabular} & **Osc.** & **Energy** & \(Kp\) & \(Kd\) & \(Kp_{s}\) &
\begin{tabular}{c} \(Kd_{s}\) \\ \(\times\)**10\({}^{-4}\)** \\ \end{tabular} & **K1** & \(B1\) & **K2** \\ \hline \multicolumn{10}{c}{RVEA} \\ \hline Best MSE & 0.2422 & 0.1662 & 0.5241 & 1728.7 & 0.0315 & 0.0073 & 0.2027 & 30555.5 & 2.938 & 43.608 \\ Best osc. & 0.6021 & 0.1547 & 0.4294 & 1357.0 & 0.0336 & 0.0095 & 0.2069 & 30776.0 & 2.982 & 43.608 \\ Best energy & 0.8121 & 0.1713 & 0.2025 & 155.9 & 0.0065 & 0.1558 & 0.1771 & 30776.0 & 0.298 & 43.627 \\ Balanced & 0.4628 & 0.2060 & 0.3937 & 1360.9 & 0.0292 & 0.0100 & 0.1621 & 35658.5 & 2.320 & 44.263 \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
Figure 10: Solutions from SS-RVEA that resulted in the best score regarding every objective, compared to the most balanced solution with respect to their mean. All the evaluations were initialized with an ankle angle of 10 degrees. Ankle angle output (**a**) and power output (**b**).  
Figure 9: Solutions from SS-NSGA-II that resulted in the best score regarding every objective, compared to the most balanced solution with respect to their mean. All the evaluations were initialized with an ankle angle of 10 degrees. Ankle angle output (**a**) and power output (**b**).  
The mean \(\mu\) and standard deviation \(\sigma\) by objective, for every set of solutions, is shown in Table 3, and the mean and standard deviation of 5-RS were added (excluding RS-3, which exceeded the angle limit).  
In order to appreciate the robustness of the solutions to the initial ankle angle, Figure 11 shows the ankle angle signal and the power signal resulting from simulating the best individual, chosen by MSE objective from the SS-NSGA-II, at the different initial conditions (from 7 to 13 degrees). Figure 12 shows the same cases for SS-RVEA.  
Figure 11: NSGA-II. Robustness to different initial ankle angles during the gait cycle, for the best MSE solution. Plot (**a**) is the ankle angle output over time, and (**b**) is the power output over time, for each initial condition in ankle angle.  
Figure 12: RVEA. Robustness to different initial ankle angles during the gait cycle, for the best MSE solution. Plot (**a**) is the ankle angle output over time, and (**b**) is the power output over time, for each initial condition in ankle angle.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Objective** & \multicolumn{2}{c}{**Random**} & \multicolumn{2}{c}{**NSGA-II**} & \multicolumn{2}{c}{**RVEA**} \\ \hline  & \(\mu\) & \(\sigma\) & \(\mu\) & \(\sigma\) & \(\mu\) & \(\sigma\) \\ \hline MSE & 0.0072 & 0.0025 & 0.0031 & 0.0021 & 0.0047 & 0.0023 \\ Oscillations & 0.3104 & 0.058 & 0.2150 & 0.0490 & 0.1954 & 0.0307 \\ Energy & 0.6640 & 0.2531 & 0.4465 & 0.2244 & 0.3728 & 0.0918 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean and standard deviation of the the NSGA-II set of solutions, the RVEA set of solutions, and the random set of solutions (excluding RS-3).