# Use RBF as a Sampling Method in Multistart Global Optimization Method
## 3 Experiments
### Experimental Results
\begin{table}
\begin{tabular}{c c c} \hline \hline HARTMAN6 & 3014 & 6037 \\ \hline HIGHELLIPTIC & 4398 & 7306 \\ \hline RASTRIGIN & 3850 (0.83) & 6401 (0.77) \\ \hline ROSENBROCK4 & 6456 & 8584 \\ \hline ROSENBROCK8 & 7646 & 10095 \\ \hline SHEKEL5 & 3144 & 6215 \\ \hline SHEKEL7 & 3354 & 6508 \\ \hline SHEKEL10 & 3388 & 6860 \\ \hline SINU4 & 3935 & 6670 (0.97) \\ \hline SINU8 & 5547 & 8056 \\ \hline SINU16 & 19,313 & 35,751 (0.97) \\ \hline TEST2N4 & 3035 (0.87) & 6002 (0.97) \\ \hline TEST2N5 & 3127 (0.73) & 6042 (0.67) \\ \hline TEST2N6 & 3393 (0.40) & 6169 (0.47) \\ \hline TEST2N7 & 4075 (0.37) & 6443 (0.33) \\ \hline TEST30N3 & 3723 & 6322 \\ \hline TEST30N4 & 3736 & 6465 \\ \hline
**TOTAL** & **142,632 (0.923)** & **254,988 (0.916)** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c} \hline \hline
**FUNCTION** & **ISAMPLES = 100** & **ISAMPLES = 200** & **ISAMPLES = 500** \\ \hline BF1 & 1086 & 1159 & 1500 \\ \hline BF2 & 922 & 1026 & 1304 \\ \hline BRANIN & 503 & 590 & 899 \\ \hline CAMEL & 670 & 756 & 1060 \\ \hline CIGAR & 3482 & 3236 & 2849 \\ \hline CM4 & 1583 (0.83) & 1716 (0.83) & 1861 (0.90) \\ \hline DISCUS & 931 & 1206 & 1525 \\ \hline EASOM & 1063 & 401 & 704 \\ \hline EXP4 & 766 & 803 & 1049 \\ \hline EXP16 & 912 & 1009 & 1303 \\ \hline EXP64 & 968 & 1070 & 1359 \\ \hline GRIEWANK2 & 2409 (0.53) & 1641 (0.40) & 2069 (0.57) \\ \hline GRIEWANK10 & 2607 (0.97) & 2609 & 2902 (0.93) \\ \hline POTENTIAL3 & 1211 & 1297 & 1613 \\ \hline POTENTIAL5 & 2414 & 2521 & 2835 \\ \hline HANSEN & 6079 (0.87) & 4785 (0.83) & 6504 (0.77) \\ \hline HARTMAN3 & 729 & 830 & 1143 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results for the proposed method with N = 20. \begin{table}
\begin{tabular}{c c c c} \hline
**FUNCTION** & **ISAMPLES = 100** & **ISAMPLES = 200** & **ISAMPLES = 500** \\ \hline BF1 & 1093 & 1175 & 1527 \\ \hline BF2 & 943 & 1022 & 1319 \\ \hline BRANIN & 502 (0.97) & 594 & 900 \\ \hline CAMEL & 642 & 729 & 1046 \\ \hline CIGAR & 3527 & 3228 & 6729 \\ \hline CM4 & 1491 (0.87) & 1884 (0.90) & 1799 (0.97) \\ \hline DISCUS & 828 & 1365 & 1215 \\ \hline EASOM & 2320 & 398 & 723 \\ \hline EXP4 & 766 & 827 & 1050 \\ \hline EXP16 & 912 & 1007 & 1298 \\ \hline EXP64 & 983 & 1064 & 1358 \\ \hline GRIEWANK2 & 1788 (0.50) & 1762 (0.43) & 2345 (0.50) \\ \hline GRIEWANK10 & 2505 & 2677 & 2868 \\ \hline POTENTIAL3 & 1244 & 1313 & 1609 \\ \hline POTENTIAL5 & 2420 & 2502 & 2795 \\ \hline HANSEN & 6711 (0.70) & 4278 (0.70) & 7264 (0.67) \\ \hline HARTMAN3 & 728 & 830 & 1144 \\ \hline HARTMAN6 & 1027 (0.93) & 1202 (0.93) & 1492 \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental results for the proposed method with N = 50. \begin{table}
\begin{tabular}{c c c c} \hline HARTMAN6 & 1111 (0.90) & 1290 (0.93) & 1525 (0.97) \\ \hline HIGHELLIPTIC & 2618 & 2671 & 3098 \\ \hline RASTRIGIN & 1727 (0.57) & 1043 (0.87) & 1386 \\ \hline ROSENBROCK4 & 4111 & 2672 & 4357 \\ \hline ROSENBROCK8 & 5417 & 6253 & 5609 \\ \hline SHEKEL5 & 1751 (0.73) & 2152 (0.90) & 1245 (0.90) \\ \hline SHEKEL7 & 1667 (0.87) & 1627 (0.83) & 1676 (0.93) \\ \hline SHEKEL10 & 2329 (0.80) & 2946 (0.73) & 3678 (0.77) \\ \hline SINU4 & 938 & 991 & 1227 \\ \hline SINU8 & 1194 & 1360 & 1479 \\ \hline SINU16 & 14,305 (0.87) & 32,647 (0.97) & 21,363 (0.97) \\ \hline TEST2N4 & 904 (0.57) & 936 (0.73) & 1227 \\ \hline TEST2N5 & 1881 (0.80) & 1218 & 1351 \\ \hline TEST2N6 & 1092 (0.67) & 1224 (0.87) & 1435 (0.97) \\ \hline TEST2N7 & 1452 (0.70) & 1397 (0.80) & 1477 (0.90) \\ \hline TEST30N3 & 1244 & 2054 & 2584 \\ \hline TEST30N4 & 2027 & 2644 & 2638 \\ \hline
**TOTAL** & **74,103 (0.902)** & **91,780 (0.932)** & **89,834 (0.958)** \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._