# Estimation of Distribution Algorithms with Fuzzy Sampling for Stochastic Programming Problems
## 4 Numerical Experiments
### Global Optimization Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **SS** & & **DSS** & & **DEDA** & \\ \hline \(f\) & **Av.** & **Std.** & **Suc.** & **Av.** & **Std.** & **Suc.** & **Av.** & **Std.** & **Suc.** \\ \hline \(RC\) & \(3.58\times 10^{-7}\) & \(8.48\times 10^{-10}\) & 100 & \(3.58\times 10^{-7}\) & \(5.83\times 10^{-10}\) & 100 & \(3.58\times 10^{-7}\) & 0.00 & 100 \\ \(GP\) & \(4.69\times 10^{-11}\) & \(1.85\times 10^{-6}\) & 100 & \(5.35\times 10^{-11}\) & \(7.65\times 10^{-9}\) & 100 & \(7.82\times 10^{-14}\) & 0.00 & 100 \\ \(R_{2}\) & \(1.10\times 10^{-11}\) & \(3.68\times 10^{-10}\) & 100 & \(2.56\times 10^{-11}\) & \(1.22\times 10^{-9}\) & 100 & \(7.69\times 10^{-5}\) & \(5.91\times 10^{-3}\) & 100 \\ \(H_{3,4}\) & \(2.11\times 10^{-6}\) & \(2.71\times 10^{-9}\) & 100 & \(2.15\times 10^{-6}\) & \(2.79\times 10^{-9}\) & 100 & \(2.15\times 10^{-6}\) & 0.00 & 100 \\ \(S_{4,7}\) & \(2.94\times 10^{-7}\) & \(9.16\times 10^{-8}\) & 100 & \(3.22\times 10^{-7}\) & \(2.65\times 10^{-7}\) & 100 & \(5.67\times 10^{-7}\) & \(7.49\times 10^{-16}\) & 100 \\ \(P_{4,0.5}\) & \(6.10\times 10^{-1}\) & \(4.80\times 10^{-2}\) & 13 & \(5.52\times 10^{-1}\) & \(5.90\times 10^{-3}\) & 27 & \(1.07\times 10^{-1}\) & \(2.19\times 10^{-2}\) & 0 \\ \(T_{6}\) & \(2.39\times 10^{-3}\) & \(8.87\times 10^{-4}\) & 80 & \(2.70\times 10^{-3}\) & \(3.01\times 10^{-3}\) & 77 & \(2.52\times 10^{-3}\) & \(9.44\times 10^{-1}\) & 0 \\ \(RT_{10}\) & \(4.66\times 10^{-6}\) & \(1.29\times 10^{-6}\) & 100 & \(1.92\times 10^{-6}\) & \(4.34\times 10^{-7}\) & 100 & \(3.27\times 10^{-13}\) & 8.18 & 100 \\ \(R_{10}\) & \(1.85\times 10\) & 3.59 & 0 & \(1.50\times 10\) & 1.69 & 0 & \(5.42\times 10^{-1}\) & \(9.97\times 10^{-1}\) & 0 \\ \(RT_{20}\) & \(3.56\) & 1.10 & 0 & \(5.01\) & \(7.88\times 10^{-1}\) & 0 & 8.43 & \(7.04\times 10^{-50}\) & 0 \\ \(R_{20}\) & \(4.58\times 10\) & \(2.79\times 10\) & 0 & \(2.98\times 10\) & 2.13\(\times 10\) & 0 & 7.55 & \(6.27\times 10^{-1}\) & 0 \\ \(PW_{24}\) & \(4.71\times 10\) & \(2.11\times 10\) & 0 & \(1.62\times 10\) & 7.67 & 0 & \(2.05\times 10^{-10}\) & \(1.27\times 10^{-7}\) & 100 \\ \(DP_{25}\) & \(3.51\) & 2.68 & 0 & \(1.43\) & \(2.31\times 10^{-1}\) & 0 & \(6.80\times 10^{-1}\) & \(5.01\times 10^{-2}\) & 0 \\ \(AK_{30}\) & \(1.04\times 10\) & 1.95 & 0 & \(8.28\) & 3.02 & 0 & \(4.44\times 10^{-15}\) & \(5.89\times 10^{-13}\) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Compared results of the DEDA, SS, and DSS methods using Test Set A. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No. ** & \(f\) & **Av. ** & **Std. ** & **No. ** & \(f\) & **Av. ** & **Std. ** \\ \hline \(1\) & \(RC\) & \(3.58\times 10^{-7}\) & 0.00 & 2 & \(B_{2}\) & 0.00 & 0.00 \\ \(3\) & \(ES\) & \(3.86\times 10^{-12}\) & 0.00 & 4 & \(GP\) & \(7.82\times 10^{-14}\) & 0.00 \\ \(5\) & \(SH\) & \(1.48\times 10^{-1}\) & 1.51 & 6 & \(BL\) & \(3.73\times 10^{-15}\) & \(7.30\times 10^{-15}\) \\ \(7\) & \(BO\) & 0.00 & 0.00 & 0.00 & 8 & \(MT\) & \(2.34\times 10^{-27}\) & \(5.21\times 10^{-25}\) \\ \(9\) & \(HM\) & \(8.65\times 10^{-8}\) & 0.00 & 10 & \(SC_{2}\) & \(2.16\times 10^{7}\) &