# Combining Parallel Stochastic Methods and Mixed Termination Rules in Optimization
## 2 Adopted Algorithms
### The Method Multistart
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Problems** & **1 \(\times\) 500** & **2 \(\times\) 250** & **5 \(\times\) 100** & **10 \(\times\) 50** \\ \hline BF1 & 49,714 & 41,284 & 41,089 & 19,596 \\ BF2 & 58,272 & 46,270 & 41,324 & 15,878 \\ BRANIN & 45,165 & 45,665 & 44,894 & 7268 \\ CAMEL & 54,786 & 54,989 & 54,651 & 10,295 \\ CIGAR10 & 63,026 & 62,206 & 60,277 & 27,217 \\ CM4 & 60,796 & 60,333 & 40,072 & 12,977 \\ DISCUS10 & 50,988 & 50,690 & 36,151 & 14,040 \\ EASOM & 40,376 & 34,178 & 21,355 & 7377 \\ ELP10 & 50,397 & 16,787 & 9334 & 7809 \\ EXP4 & 54,749 & 54,445 & 29,812 & 11,024 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Experiments using the proposed optimization technique and the mean—fitness stopping rule. Numbers in cells denote average function calls. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Problems** & **1 \(\times\) 500** & **2 \(\times\) 250** & **5 \(\times\) 100** & **10 \(\times\) 50** \\ \hline BF1 & 9270 & 6253 & 6497 & 6089 \\ BF2 & 9838 & 6249 & 6078 & 5853 \\ BRANIN & 5787 & 5022 & 4991 & 4989 \\ CAMEL & 12,204 & 5882 & 5765 & 5399 \\ CIGAR10 & 7631 & 6482 & 6350 & 6420 \\ CM4 & 16,222 & 5037 & 7422 & 6366 \\ DISCUS10 & 5997 & 7364 & 4906 & 5037 \\ EASOM & 4701 & 4752 & 4653 & 4668 \\ ELP10 & 6230 & 5223 & 5407 & 5314 \\ EXP4 & 10,277 & 5675 & 5638 & 5526 \\ EXP16 & 9577 & 5575 & 5471 & 5470 \\ GKLS250 & 13,328 & 5864 & 5323 & 4993 \\ GKLS350 & 10,131 & 4998 & 5442 & 4919 \\ GRIEWANK2 & 8504 & 7345 & 6108 & 5876 \\ GRIEWANK10 & 8535 & 7704 & 7771 & 7126 \\ POTENTIAL3 & 11,338 & 5726 & 5471 & 5699 \\ PONTENTIAL5 & 12,414 & 7192 & 6977 & 7070 \\ PONTENTIAL6 & 14,760 & 8480 & 7210 & 7511 \\ PONTENTIAL10 & 17,729 & 12,218 & 10,217 & 9439 \\ HANSEN & 8379 & 5945 & 5023 & 4972 \\ HARTMAN3 & 10,674 & 5613 & 5703 & 5163 \\ HARTMAN6 & 10,841 & 5541 & 5485 & 5536 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Experiments using the proposed optimization technique and the best—fitness stopping rule. Numbers in cells denote average function calls. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Problems** & **1 \(\times\) 500** & **2 \(\times\) 250** & **5 \(\times\) 100** & **10 \(\times\) 50** \\ \hline EXP16 & 52,768 & 51,233 & 24,782 & 10,722 \\ GKLS250 & 51,980 & 50,333 & 37,696 & 9641 \\ GKLS350 & 48,577 & 48,442 & 28,420 & 9337 \\ GRIEWANK2 & 56,767 & 40,471 & 30,632 & 12,356 \\ GRIEWANK10 & 68,439 & 58,410 & 53,818 & 30,317 \\ POTENTIAL3 & 49,418 & 49,328 & 33,657 & 10,140 \\ POTENTIAL5 & 59,827 & 58,259 & 34,436 & 11,515 \\ POTENTIAL6 & 62,720 & 62,715 & 34,158 & 14,417 \\ POTENTIAL10 & 72,899 & 72,800 & 64,964 & 16,780 \\ HANSEN & 45,064 & 45,582 & 32,013 & 9318 \\ HARTMAN3 & 47,307 & 47,983 & 31,033 & 8899 \\ HARTMAN6 & 49,370 & 47,983 & 27,884 & 9602 \\ RASTRIGIN & 54,637 & 53,551 & 33,095 & 10,169 \\ ROSENBROCK8 & 67,885 & 57,314 & 46,961 & 25,383 \\ ROSENBROCK16 & 77,207 & 66,172 & 59,098 & 41,461 \\ SHEKEL5 & 50,631 & 49,800 & 32,025 & 10,389 \\ SHEKEL7 & 51,212 & 50,630 & 29,136 & 11,193 \\ SHEKEL10 & 51,741 & 50,321 & 33,462 & 11,200 \\ SINU4 & 48,140 & 52,788 & 32,412 & 9721 \\ SINU8 & 48,761 & 55,864 & 32,685 & 10,410 \\ TEST2N4 & 48,904 & 48,800 & 28,959 & 8643 \\ TEST2N9 & 48,838 & 47,001 & 36,281 & 8085 \\ TEST30N3 & 51,514 & 50,100 & 39,828 & 11,699 \\ TEST30N4 & 48,992 & 46,875 & 42,564 & 11,954 \\
**Total** & **1,841,867** & **1,729,602** & **1,258,958** & **456,832** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _Cont._