## 4 Simulation Results
### Results on Fuel Cell Stack Design Optimization
Furthermore, on the mean FirstHitEvals metric, [PERSON] outperforms [PERSON] 10 out of the 13 times. Again, [PERSON] beats [PERSON] 9-3-1 on the success count metric. Results of Smith-Satterthwaite tests (Table 10) show that for the best-of-run cost metric, the \(t\)-statistic is positive in all cases but one, but the one-tailed \(p\)-values are not less than 0.05. Thus we do not have a strong reason at the 5% significance level to reject the null hypothesis that the two means of the best-of-run costs are equal. For the best-of-run metric, the single negative \(t\)-score in Table 10 corresponds to a \(p\)-value that is close to 0.5, indicating no reason to consider [PERSON] to be significantly better than [PERSON] on that case. The FirstHitEvals metric shows [PERSON] to be significantly better (at the 5% level) in two of the 12 cases, the other cases being ties at that level of significance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**PopSize**} & \multirow{2}{*}{**Gens**} & \multicolumn{4}{c}{**Best-of-Run Fitness**} & \multicolumn{4}{c}{**FirstHitEvals**} \\ \cline{3-10}  & & **Best** & **Mean** & **Std Dev** & **Success** & **Best** & **Mean** & **Std Dev** \\ \hline
20 & 10 & 13.6162 & 13.6885 & 0.0759 & 3 & 127 & 172.0 & 31.9479 \\
15 & 20 & 13.6161 & 13.6255 & 0.0190 & 21 & 128 & 254.8095 & 47.8187 \\
20 & 20 & 13.6159 & 13.6376 & 0.0523 & 21 & 127 & 310.0 & 71.8338 \\
20 & 25 & 13.6159 & 13.6302 & 0.0484 & 25 & 127 & 335.8 & 89.0222 \\
25 & 40 & 13.6157 & 13.6164 & 0.0023 & 29 & 89 & 510.6897 & 166.4118 \\
40 & 25 & 13.6158 & 13.6184 & 0.0044 & 25 & 291 & 654.24 & 213.3435 \\
20 & 100 & 13.6157 & 13.6158 & \(8.7813\times 10^{-5}\) & 30 & 127 & 436.1333 & 304.5035 \\
100 & 20 & 13.6159 & 13.6195 & 0.0029 & 20 & 463 & 1491.5 & 437.1448 \\
30 & 100 & 13.6157 & 13.6158 & 0.0002 & 30 & 370 & 585.4667 & 230.4605 \\
100 & 30 & 13.6158 & 13.6179 & 0.0022 & 25 & 463 & 1675.08 & 550.3110 \\
40 & 100 & 13.6157 & 13.6160 & 0.0006 & 30 & 291 & 778.9333 & 385.4906 \\
100 & 40 & 13.6157 & 13.6174 & 0.0022 & 26 & 463 & 1737.1154 & 622.4179 \\
100 & 100 & 13.6157 & 13.6162 & 0.0010 & 29 & 463 & 2155.3103 & 1395.2800 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of Slyaya on the fuel cell problem (each row corresponds to 30 independent runs). Most numbers are shown with rounding at the fourth place after the decimal. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**PopSize**} & \multirow{2}{*}{**Gens**} & \multicolumn{4}{c}{**Best-of-Run Fitness**} & \multicolumn{4}{c}{**FirstHitEvals**} \\ \cline{3-10}  & & **Best** & **Mean** & **Std Dev** & **Success** & **Best** & **Mean** & **Std Dev** \\ \hline
20 & 10 & 13.6213 & 13.7026 & 0.0713 & 0 & — & — & \\
15 & 20 & 13.6160 & 13.6374 & 0.0342 & 13 & 124 & 241.8462 & 45.9378 \\
20 & 20 & 13.6163 & 13.6367 & 0.0483 & 20 & 298 & 363.65 & 31.7636 \\
20 & 25 & 13.6160 & 13.6312 & 0.0463 & 25 & 298 & 382.36 & 48.3867 \\
25 & 40 & 13.6158 & 13.6298 & 0.0520 & 28 & 144 & 540.6071 & 144.4191 \\
40 & 25 & 13.6158 & 13.6229 & 0.0236 & 26 & 250 & 739.5 & 170.0993 \\
20 & 100 & 13.6157 & 13.6182 & 0.0126 & 29 & 298 & 454.6897 & 236.2226 \\
100 & 20 & 13.6160 & 13.7947 & 0.9338 & 14 & 907 & 1595.2857 & 360.2738 \\
30 & 100 & 13.6157 & 15.1444 & 8.2308 & 29 & 368 & 740.6207 & 546.2285 \\
100 & 30 & 13.6159 & 13.7910 & 0.9344 & 25 & 907 & 1922.44 & 492.2595 \\
40 & 100 & 13.6157 & 13.6202 & 0.0237 & 29 & 250 & 787.5517 & 222.2544 \\
100 & 40 & 13.6157 & 13.7907 & 0.9345 & 26 & 907 & 1972.7308 & 544.2687 \\
100 & 100 & 13.6157 & 13.7900 & 0.9346 & 27 & 907 & 2118.4074 & 914.8884 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of Jaya on the fuel cell problem (each row corresponds to 30 independent runs). Most numbers are shown with rounding at the fourth place after the decimal. Table 11 shows results of Wilcoxon signed-rank tests for the PEMFC problem. For each of the two metrics, the \(W\)-statistic is less than the critical \(W\).