## 3 Manipulation of Swarms Positions and Space Solution Using Multi-Threaded Techniques
### Proposition II
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **GA** & **PSOA** & **FA** & **CSA** & **WSA** & **ACO** \\ \hline \(f_{1}\) & 0.00892 & 0.00913 & 0.00088 & 0.01001 & 0.00785 & 0.00339 \\ \(f_{2}\) & 0.06694 & 0.02898 & 0.00948 & 0.01298 & 0.0238 & 0.00539 \\ \(f_{3}\) & 0 & 0 & 0.0001 & 0.00044 & 0.00005 & 0.00001 \\ \(f_{4}\) & 0.00218 & 0.001 & 0.00012 & 0.00179 & 0.00019 & 0.00049 \\ \(f_{5}\) & \(-186.692\) & \(-186.699\) & \(-186.694\) & \(-186.698\) & \(-186.698\) & \(-187.1\) \\ \(f_{6}\) & 0 & 0 & 0 & 0.00002 & 0 & 0 \\ \(f_{7}\) & 0.00001 & 0 & 0.00001 & 0.0002 & 0.00001 & 0.00001 \\ \(f_{7}\) & 0.00105 & 0.00062 & 0.66179 & 0.00035 & 0.00025 & 0.00037 \\ \(f_{8}\) & \(-391.329\) & \(-391.58\) & \(-391.344\) & \(-391.746\) & \(-391.598\) & \(-391.594\) \\ \(f_{9}\) & 0.19899 & 0.07731 & 0.13266 & 0.07822 & 0.1328 & 0.09898 \\ \(f_{10}\) & 0.00103 & 0.00172 & 0.04368 & 0.33444 & 0.00103 & 0.00098 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Averaged solution values achieved by all algorithms for each test functions for proposition I. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **GA** & **PSOA** & **FA** & **CSA** & **WSA** & **ACO** \\ \hline \(f_{1}\) & 0.00892 & 0.00913 & 0.00088 & 0.01001 & 0.00785 & 0.00339 \\ \(f_{2}\) & 0.06694 & 0.02898 & 0.00948 & 0.01298 & 0.0238 & 0.00539 \\ \(f_{3}\) & 0 & 0 & 0.0001 & 0.00044 & 0.00005 & 0.00001 \\ \(f_{4}\) & 0.00218 & 0.001 & 0.00012 & 0.00179 & 0.00019 & 0.00049 \\ \(f_{5}\) & \(-186.692\) & \(-186.699\) & \(-186.694\) & \(-186.698\) & \(-186.698\) & \(-187.1\) \\ \(f_{6}\) & 0 & 0 & 0 & 0.00002 & 0 & 0 \\ \(f_{7}\) & 0.0



We also evaluated individual algorithms by assigning them ranks for each proposal--if the algorithm obtained the most accurate solution for a given function using a particular technique, it received one point. Results are presented in Figure 2, and it is easy to notice that depending on the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **GA** & **PSOA** & **FA** & **CSA** & **WSA** & **ACO** \\ \hline \(f_{1}\) & 1623.6 & 1349.25 & 1345.5 & 1367.25 & 1335.75 & 1401 \\ \(f_{2}\) & 2418.24 & 2286.75 & 2449.8 & 2399.76 & 2690.25 & 2650 \\ \(f_{3}\) & 788.48 & 756 & 673.5 & 678 & 672 & 673 \\ \(f_{4}\) & 1258.4 & 1060.5 & 1062.75 & 1061.25 & 1060.5 & 1064 \\ \(f_{5}\) & 4094.25 & 4091.25 & 4122.75 & 4001 & 4104 & 4005 \\ \(f_{6}\) & 483 & 567.6 & 488.25 & 491.25 & 486 & 473 \\ \(f_{7}\) & 584.32 & 495.75 & 545.75 & 497.25 & 496.5 & 491 \\ \(f_{8}\) & 2202 & 2121 & 2292 & 2160.75 & 2176.5 & 2189 \\ \(f_{9}\) & 718.96 & 601.5 & 703 & 597 & 635 & 606 \\ \(f_{10}\) & 2103 & 2014 & 2261 & 2127 & 2221 & 2134 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Running time values achieved by all algorithms for each test functions for original algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **GA** & **PSOA** & **FA** & **CSA** & **WSA** & **ACO** \\ \hline \(f_{1}\) & 1609.2 & 1784 & 1820 & 1802 & 1589 & 1673 \\ \(f_{2}\) & 2377.7 & 2409.44 & 2432.7 & 2400.3 & 2382.3 & 2401 \\ \(f_{3}\) & 812.7 & 822.6 & 808.2 & 815.4 & 806.4 & 812 \\ \(f_{4}\) & 1417 & 1282.5 & 1275.3 & 286.1 & 1276.2 & 1267 \\ \(f_{5}\) & 4868.1 & 4860 & 4932 & 4914 & 4908.6 & 4912 \\ \(f_{6}\) & 591.3 & 653 & 601.2 & 589.5 & 583.2 & 592.5 \\ \(f_{7}\) & 635.4 & 633.6 & 682.6 & 636.3 & 586.08 & 581.4 \\ \(f_{8}\) & 2301 & 2318 & 2529 & 2249 & 2492 & 2498 \\ \(f_{9}\) & 720 & 702.24 & 763.6 & 714.6 & 732.6 & 712 \\ \(f_{10}\) & 2048 & 2047 & 2234 & 2021 & 2089 & 2091 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Running time values achieved by all algorithms for each test functions for proposition I.