## 3 Results
### Solution Sets from the MOO Algorithms  
Figure 6 shows the set of solutions obtained by the NSGA-II algorithm (SS-NSGA-II) (Figure 5(a)) and the set of solutions obtained by the RVEA algorithm (SS-RVEA) (Figure 5(b)). It is possible to appreciate that NSGA-II preserves the initial population size, and all the elements in the set are non-dominated. Meanwhile, RVEA reduced the population from 65 (initial population for 10 reference vectors) to 44, and only 19 elements are non-dominated (red solutions in Figure 5(b)). Figures 7 and 8 show the different views of the SS-NSGA-II and SS-RVEA, respectively, in order to see with more detail the compromise between each pair of objectives.  
Table 2 presents a list of the best solutions of SS-NSGA-II and SS-RVEA, from the perspective of every objective. The list contains the evaluation of the rest of the objectives and the set of parameters (solution selected). This table also shows the solution of every set that resulted in the best balance with regard to their respective means.  
Figure 5: Performance of some random sets of parameters, named RS-0 through RS-4, compared to a reference ankle angle signal. The (**a**) plot shows ankle angle output and the (**b**) plot power output, both with an initial condition of 10 degrees of ankle rotation. The plots for RS-3 end prematurely because that set of parameters causes the system to diverge.  
Figure 8: Planar views of the RVEA set of solutions, projecting them onto different combinations of two cost components. From left to right: MSE vs. Oscillations, MSE vs. Energy, and Oscillations vs. Energy.  
Figure 6: Set of solutions from the optimization algorithms. The solutions from NSGA-II shown in (**a**) are all non-dominated. RVEA produced both dominated and non-dominated solutions, shown in (**b**) as red points and blue points, respectively.  
\begin{table}
\begin{tabular}{c 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}  & \multicolumn{2}{c}{**MSE**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**\(Kp\)**} & \multicolumn{1}{c}{**\(Kd\)**} & \multicolumn{1}{c}{\(Kp_{s}\)**} & \multicolumn{1}{c}{\(Kd_{s}\)**} & \multicolumn{1}{c}{\(K1\)**} & \multicolumn{1}{c}{\(B1\)**} & \multicolumn{1}{c}{\(K2\)**} \\  & \multicolumn{2}{c}{\(\times\)\(10^{-2}\)**} & \multicolumn{1}{c}{**Osc.**} & \multicolumn{1}{c}{**Energy**} & \multicolumn{1}{c}{**\(Kp\)**} & \multicolumn{1}{c}{**\(Kd\)**} & \multicolumn{1}{c}{\(Kp_{s}\)**} & \multicolumn{1}{c}{\(\times\)\(10^{-4}\)**} & \multicolumn{1}{c}{**\(K1\)**} & \multicolumn{1}{c}{\(B1\)**} & \multicolumn{1}{c}{\(K2\)**} \\ \hline \multicolumn{10}{c}{NSGA-II} \\ \hline Best MSE & 0.1307 & 0.3173 & 1.0838 & 9479.7 & 0.0413 & 0.0222 & 0.2210 & 37121.0 & 6.350 & 47.864 \\ Best osc. & 0.7220 & 0.1494 & 0.2499 & 282.4 & 0.0273 & 0.0485 & 0.2006 & 25592.0 & 6.764 & 42.050 \\ Best energy & 0.8022 & 0.1658 & 0.2117 & 150.2 & 0.0438 & 0.1531 & 0.2436 & 23288.0 & 4.954 & 58.551 \\ Balanced & 0.2708 & 0.1877 & 0.4432 & 1943.7 & 0.0454 & 0.0097 & 0.0354 & 5099.0 & 15.454 & 12.201 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Best solutions by objective, for each optimization algorithm. The last row for each algorithm shows a balanced solution from its set, without emphasizing a single objective.  
Figure 7: Planar views of the NSGA-II set of solutions, projecting them onto different combinations of two cost components. From left to right: MSE vs. Oscillations, MSE vs. Energy, and Oscillations vs. Energy.