## 4 Experimental Results
### Effect of Cooperating with Effective-Address
Even the slightest improvement in MS, which is 1, is very good, because what is sought with any optimization algorithm is to improve the bounds already known for big problems. The improved efficacy makes SACT competitive with the best algorithms reported in the literature, according to the results presented below. Table 2 summarizes the efficacy of SACT with cooperation and without _effective-address_ for YN problems in descending order. It can be observed that the efficacy of the algorithm SACT as a function of the number of threads depends on the problem being resolved. When there is both cooperation and _effective-address_, there is definite behavior for running threads, as can be seen in Figures 4b, 5b, 6b and 7b. Table 3 summarizes the efficacy of SACT with cooperation and with _effective-address_ for YN problems in descending order. It can be seen that the increased efficacy of the SACT algorithm, as a function of the number of threads, occurs when the number of threads is the largest (\(H48\)). The exception to this is the YN3 problem, in which case the number of threads is also great. In YN1 and YN4, the worst efficacy is obtained with \(H40\). According to Table 3, in order to define the number of threads needed to increase the efficacy in SACT, it would be necessary to start with \(H32\) threads, and slowly increase the threads, being careful to detect cases when SACT has a number of threads that presents a low efficacy, as in the case of YN1(\(H40\)) and YN4(\(H40\)). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{6}{c}{**Threads**} \\ \cline{2-7}  & & & _Best_\(\rightarrow\)_Worst_ & & \\ \hline YN1 & \(H40\)–\(H16\) & \(H16\) & \(H48\) & \(H8\) & \(H32\) & \(H1\) \\ YN2 & \(H40\)–\(H32\) & \(H32\) & \(H8\) & \(H48\) & \(H16\) & \(H1\) \\ YN3 & \(H32\) & \(H48\) & \(H40\) & \(H16\) & \(H8\) & \(H1\) \\ YN4 & \(H16\) & \(H32\) & \(H40\) & \(H48\) & \(H8\) & \(H1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Efficacy of SACT with cooperation and without effective-address procedure as a function of the threads executed. An evaluation of the Hamming distance presented in Figures 8-11 for the problems YN1, YN2, YN3, and YN4, respectively, with different numbers of threads, shows the degree of similarity in each solution with respect to the best solution in each iteration. The Hamming distance between \(S_{H\_c}\) and \(S_{best}\) is obtained by comparing the sequence of operations on each machine of JSSP. If the Hamming value of a solution \(S_{H\_c}\) is zero regarding \(S_{best}\), then the solution \(S_{H\_c}\) is the same as \(S_{best}\) and they have the same configuration. Conversely, if \(S_{H\_c}\), has a very large Hamming value e.g., 400 (maximum value for a solution of the problem YN), then \(S_{best}\) is totally different from \(S_{H\_c}\). The greater the Hamming distance in a set of solutions \(S=\{S_{H\_c}\), \(S_{H\_c}\), \(S_{H\_3}\_c}\),..., \(S_{H\_n\_c}\) with respect to an \(S_{best}\) solution, the greater the diversity in the set of solutions \(S\), where n is the number of running threads. Figures 8a, 9a, 10a and 11a, show that for cooperation without _effective-address_, more diversity exists than in the case of cooperation with _effective-address_. There is less diversity when movement follows a directed path via \(S_{best}\), as seen in Figures 8b, 9b, 10b and 11b. In Figures 8a, 9a, 10a and 11a, the Hamming distance without _effective-address_ is within a range of 250 to 380. This is the case in almost all the execution interval of SACT, with different numbers of threads, and for different problems. It is true for YN1, YN2 between 180 and 325, YN3 between 190 and 320, and YN4 between 200 and 325. Given that in this kind of cooperation there is no _effective-address_, the diversity behavior remains almost constant throughout the runtime of SACT, with the exception of the first 250 s. It is seen that \(H8\) and \(H16\) have less diversity than all the other YN problems.