## 4 Experimental Results
### Population Size Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Model** & \(\pi\) & **Min** & **Mean** & **Max** & **SD** & **CPU Time (s)** & \
\begin{tabular}{c} **Mean Rank in the** \\ **Freidman Test** \\ \end{tabular} &
\begin{tabular}{c} **Sum Rank in the** \\ **Freidman Test** \\ \end{tabular} \\ \hline \multirow{5}{*}{SD} & 10 & 9.860219 \(\times 10^{-4}\) & 1.006557 \(\times 10^{-3}\) & 1.268819 \(\times 10^{-3}\) & 5.47 \(\times 10^{-5}\) & 48.59 & 6.0 & 180 \\  & 20 & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 8.17 \(\times 10^{-7}\) & 48.02 & 3.6 & 106.5 \\  & 40 & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 6.30 \(\times 10^{-17}\) & 37.42 & 2.6 & 76.5 \\  & 50 & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 3.24 \(\times 10^{-17}\) & 40.23 & 2.5 & 74.5 \\  & 80 & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 8.960219 \(\times 10^{-4}\) & 4.85 \(\times 10^{-7}\) & 41.11 & 2.9 & 87 \\  & 100 & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 9.860219 \(\times 10^{-4}\) & 4.66 \(\times 10^{-17}\) & 50.89 & 3.5 & 105.5 \\ \hline \multirow{5}{*}{DD} & 10 & 9.849747 \(\times 10^{-4}\) & 1.046876 \(\times 10^{-3}\) & 1.199696 \(\times 10^{-3}\) & 5.90 \(\times 10^{-5}\) & 52.52 & 5.6 & 169 \\  & 20 & 9.832470 \(\times 10^{-4}\) & 9.909079 \(\times 10^{-4}\) & 1.016172 \(\times 10^{-3}\) & 8.43 \(\times 10^{-6}\) & 55.21 & 3.9 & 116 \\  & 40 & 9.928488 \(\times 10^{-4}\) & 9.869593 \(\times 10^{-4}\) & 1.0202805 \(\times 10^{-4}\) & 4.35 \(\times 10^{-6}\) & 53.12 & 2.9 & 87 \\  & 50 & 9.826501 \(\times 10^{-4}\) & 9.861925 \(\times 10^{-4}\) & 9.948859 \(\times 10^{-4}\) & 2.43 \(\times 10^{-6}\) & 50.93 & 3.0 & 90 \\  & 80 & 9.828489 \(\times 10^{-4}\) & 9.8606955 \(\times 10^{-4}\) & 9.890527 \(\times 10^{-4}\) & 1.43 \(\times 10^{-6}\) & 38.32 & 2.6 & 78 \\  & 100 & 9.836909 \(\times 10^{-4}\) & 9.878873 \(\times 10^{-4}\) & 1.014303 \(\times 10^{-3}\) & 6.14 \(\times 10^{-6}\) & 36.53 & 3.0 & 90 \\ \hline \multirow{5}{*}{PVM} & 10 & 2.425057 \(\times 10^{-3}\) & 2.435725 \(\times 10^{-3}\) & 2.4986906 \(\times 10^{-3}\) & 1.99 \(\times 10^{-5}\) & 48.36 & 6.0 & 180 \\  & 20 & 2.425057 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.14 \(\times 10^{-16}\) & 44.27 & 4.1 & 124 \\ \cline{1-1}  & 40 & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 1.24 \(\times 10^{-16}\) & 46.07 & 2.7 & 81 \\ \cline{1-1}  & 50 & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 3.65 \(\times 10^{-17}\) & 44.76 & 2.8 & 84.5 \\ \cline{1-1}  & 80 & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.65 \(\times 10^{-17}\) & 39.16 & 2.5 & 75 \\ \cline{1-1}  & 100 & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 2.425075 \(\times 10^{-3}\) & 3.17 \(\times 10^{-17}\) & 39.84 & 2.9 & 85.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: An analysis of the effect of population size on ICO performance for different PV models. Figure 5: Convergence curves of ICO with different population sizes in solving (**a**) SDM, (**b**) DDM, and (**c**) PVMM.