## 5 Optimization Model
Figure 14 shows Pareto front obtained by NSGAII, and the projection plane for criteria f2 and f6, obtained by method proposed herein (such projection plane is indicated in Figure 13). The NSGAII algorithm was run for the population size of 50 chromosomes and 100 iterations. (File containing data with Pareto \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **\# eval. f1** & **\# eval. f2** & **\# eval. f3** & **\# eval. f4** & **\# eval. f5** & **\# eval. f6** & **\# Total eval.** & **Front Size** \\ \hline Variant 1 & 8291 & 8242 & 8265 & 8266 & 8178 & 8322 & 49,564 & 2471 \\ \hline Variant 2 & 21,367 & 21,189 & 21,227 & 21,299 & 21,112 & 21,440 & 12,7634 & 3143 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of the objective function evaluations size of the Pareto optimal solutions for the multiobjective optimization tasks performed. Figure 13: Set of Pareto optimal solutions presented in the form of scatter matrix plot for the 2 nd variant of optimization task. optimal solutions in each generation are included in supplementary material). As can be seen, the location of the Pareto front found by both algorithms is comparable; however, IMGAMO found more a widespread one. This comparison also shows the high probability of the correct location of the Pareto front for this problem, found using the method proposed herein. Extreme solutions for each objective functional are collected in Table 2, whereas Figure 15 presents ghd optimal shape of the actuator for that extremes. Additionally, for comparison, actuators with straight arms (traditional geometry) for different widths of the beam equal to 2.5 \(\upmu\)m, 5.0 \(\upmu\)m and 10.0 \(\upmu\)m are included. For such geometry, the pre-bending angle was assumed to \(\varphi=1.3^{\circ}\) and a sharp connection between arm and the anchor was assumed. It is natural, that a significantly higher maximal value of the equivalent von Mises stress was observed. Table 3 contains the value of the design variables obtained for the extreme solutions. Representation of the set of Pareto optimal solutions by means of scatter plot matrix, provides good insight into the nature of the problem. Shapes of the consecutive tradeoffs show dependences between particular objectives. The rapid change at some region of the Pareto front can be very useful information for the designer (small changes in one criterion may cause great changes in the other). However, a higher number of criteria, analyzing too many charts simultaneously, can be a serious \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & f1 [\(\upmu\)m\({}^{3}\)] & f2 [MPa] & f3 [\(\upmu\)m] & f4 [\(\upmu\)W] & f5 [\(\,\)] & f6 [\(\upmu\)N] \\ \hline min f1 & **110,000.50** & 502.83 & \(-\)6.09 & 2.83 & \(-\)0.09 & \(-\)28.59 \\ min f2 & 112,632.01 & **61.86** & \(-\)2.37 & 3.51 & \(-\)0.72 & \(-\)483.25 \\ max f3 & 112,030.51 & 736.10 & \(\mathbf{-17.76}\) & 2.70 & \(-\)0.04 & \(-\)166.56 \\ min f4 & 111,819.23 & 436.27 & \(-\)3.68 & **2.47** & \(-\)0.12 & \(-\)9.20 \\ max f5 & 227,916.45 & 1216.51 & \(-\)2.03 & 32.90 & \(\mathbf{-563.10}\) & \(\mathbf{-353.35}\) \\ max f6 & 211,171.86 & 1285.59 & \(-\)3.39 & 18.79 & \(-\)165.30 & \(\mathbf{-7548.54}\) \\ \hline Straight b. 2.5 & 121,001.05 & 1737.54 & \(-\)9.05 & 5.45 & \(-\)0.69 & \(-\)571.85 \\ Straight b. 5.0 & 142,001.45 & 2279.89 & \(-\)3.80 & 10.48 & \(-\)8.49 & \(-\)706.27 \\ Straight b. 10.0 & 184,000.66 & 4199.03 & \(-\)1.34 & 20.78 & \(-\)178.30 & 0.00 \\ \hline compromise-solution & 146,834.58 & 1027.59 & \(-\)5.88 & 5.14 & \(-\)2.09 & \(-\)1678.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the optimization—values of the objective functions. Figure 14: Comparison between Pareto front obtained by NSGAII projection plane for criteria f2 and f6 obtained by means of IMGAMO algorithm. obstacle in the effective selection of the interesting solutions. As previously mentioned, utilizing the SOMs as a visualization tool may help to overcome that difficulty and could be very useful for the designer.