## 4 Experimental Results
### Effect of Cooperating with Effective-Address
Since there is not a directed path through the best solution \(S_{best}\), the Hamming distance does not present a significant decrease over time. The behavior does differ in relation to the number of threads, as can be observed in Figures 8a, 9a, 10a and 11a. In Figure 8a for YN1, the Hamming distance is greatest for \(H40\) and least for \(H8\). The other Hamming distances have almost the same average behavior (\(H16\), \(H32\), and \(H48\)). In Figures 8a, 9a, 10a and 11a, for YN2, YN3, and YN4, respectively, Hamming distance has the same average performance for \(H16\), \(H32\), \(H40\), and \(H48\). For \(H8\), the Hamming distance is smaller. The behavior of the Hamming distance based on the number of threads is due to each thread involving a solution of SA. Because of this, if a larger number of solutions are compared to \(S_{best}\), there could be a wider diversity. This is not always true because \(S_{best}\) has no relationship with most of the solutions generated by the thread. An example of this can be seen in Figure 8a, Hamming (\(H48\)) \(<\) Hamming (\(H40\)). In Figures 8b, 9b, 10b and 11b, the Hamming distance with _effective-address_ at the beginning of SACT has a diversity of Hamming values up to 350. This is then reduced considerably as the execution progresses, and SACT has values in the range of 70 to 150. Because there is such cooperation with _effective-address_, the diversity is reduced because the search in the solution directs itself toward \(S_{best}\) solutions. The behavior of the Hamming distance based on the number of threads is due to each thread involving a solution of SA. Because of this, if a larger number of solutions are compared to \(S_{best}\), there could be a wider diversity. However, as the time of implementation of _effective-address_, is reduced, solutions are directed toward a single path. This could be debatable. It can be observed in Figures 8b, 9b, 10b and 11b and Figures 4b, 5b, 6b and 7b, that applying cooperation threads with a directed path toward the best solution, a greater number of threads find better solutions. Since the greater diversity \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{6}{c}{**Threads**} \\ \cline{2-7}  & \multicolumn{6}{c}{**Best \(\rightarrow\)Worst**} \\ \hline YN1 & \(H48\) & \(H32\) & \(H16\) & \(H8\) & \(H40\) & \(H1\) \\ YN2 & \(H48\)–\(H40\) & \(H40\) & \(H32\) & \(H16\) & \(H8\) & \(H1\) \\ YN3 & \(H40\)–\(H48\) & \(H48\) & \(H32\) & \(H16\) & \(H8\) & \(H1\) \\ YN4 & \(H48\) & \(H32\) & \(H8\) & \(H16\) & \(H40\) & \(H1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Efficacy of SACT with cooperation and with effective-address procedure as a function of the threads executed. of the solutions is achieved with a greater number of threads, this avoids a hasty convergence prior to finding good solutions. Figure 8: YN1-\(20\times 20\). Solution diversity with different number of threads. Average of 30 tests. (**a**) Without _effective-address_. (**b**) With _effective-address_. Figure 9: YN2-\(20\times 20\). Solution diversity with different number of threads. Average of 30 tests. (**a**) Without _effective-address_. (**b**) With _effective-address_. Figure 10: YN3-20 \(\times\) 20. Solution diversity with different number of threads. Average of 30 tests. (**a**) Without _effective-address._ (**b**) With _effective-address._  
Figure 12 presents YN1 with \(H32\) threads, with a long execution time of close to 2 h. It can be seen that the _effective-address_ procedure still does not make the Hamming distance converge in SACT. What can be seen is that if SACT is left running an extremely long time, the Hamming distance will tend to zero. Figure 11: YN4-20 \(\times\) 20. Solution diversity with different number of threads. Average of 30 tests. (**a**) Without _effective-address_. (**b**) With _effective-address_.