## 4 Experimental Results
### Effect of Cooperating with Effective-Address  
In this paper, two different types of cooperation are utilized. In the first type of cooperation, SACT uses an _effective-address_ procedure between two solutions with the best global solution \(S_{best}\) obtained from all threads. The best solution in the running thread is \(S_{Hi\_c}\), i.e., \(S_{Hi}\) = _effective-address_ (\(S_{Hi\_c}\), \(S_{best}\)). With solution \(S_{Hi}\) obtained in each thread \(Hi\), SA is restarted in each thread \(Hi\). The second type of cooperation does not use _effective-address_ in the SACT procedure for restarting SA in each thread \(Hi\). Instead, \(S_{Hi}=S_{Hi\_c}\) is used. In addition, in each iteration of SACT, the best solution \(S_{best}\) is saved. Cooperation occurs because the n threads working in parallel to find a solution at different points in the solution space always keep the best solution found in \(S_{best}\). In both types of cooperation, the best global solution \(S_{best}\) is obtained for each iteration of SACT because the best solution found in all threads for each SA is compared with the current best global solution, and the best solution \(S_{best}\) is saved. The SACT algorithm was executed with several different numbers of threads and with a maximum value of 2500 Maxiter SA, which corresponds to about an hour of runtime for a number of threads SA \(\geq\) 8. Figures 4-12 (Maxiter vs. \(S_{best}\)), present respectively the performance of the cooperation of threads in SA for the problems YN1, YN2, YN3, and YN4. These figures present the execution of SACT for 8, 16, 32, 40, and 48 threads. Figures 4, 5, 6 and 7 show the relationship with efficacy. When there is cooperation without using the _effective-address_ procedure, it can be observed that the best result obtained when Maxiter reaches 2500 SA does not depend on the number of threads in execution in SACT. The value of the makespan is very similar for any number of threads. This may be because there is no direct way to arrive at the same solution. Figures 4, 5, 6 and 7 show the relationship with efficacy. It can be observed that the best result obtained within the Maxiter = 2500 SA, using the _effective-address_ procedure, was when SACT used 48 threads. Figure 6 shows that in YN3, 48 threads compete with 40 threads to find the best solution. This indicates that with a greater number of threads, on average, better solutions may be obtained. This effect is seen because the larger group of threads (\(H\)48) has the same directed pathway toward the same \(S_{best}\) solution. This is due to the greater number of _effective-address_ applied to the n threads with the best solution \(S_{best}\). The result is that a greater number of threads lead to a directed path through the best solution \(S_{best}\). The Hamming distance becomes smaller between the set of threads with respect to \(S_{best}\). This can be seen in Figures 8, 9, 10 and 11. It is generally observed in all cases that on average, the Hamming distance decreases with an increasing number of threads. Interestingly, with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Problem** & \(C_{o}\) & \(C_{f}\) & \(\alpha\) & \(MC\) & _UB = f(5)_ \\ \hline \multicolumn{5}{c}{Size \(6\times 6\)} \\ \hline FT06 & 800 & 1.0 & 0.98 & 30 & 80 \\ \hline \multicolumn{5}{c}{Size \(10\times 10\)} \\ \hline FT10 & 25 & 1.0 & 0.98 & 1000 & 2500 \\ ORB and ABZ & 64,000 & 1.0 & 0.98 & 1000 & 2500 \\ \hline \multicolumn{5}{c}{Size \(15\times 15\)} \\ \hline LA16 to LA20 & 64,000 & 1.0 & 0.98 & 1000 & 2500 \\ LA36 to LA40 & 2 & \(1\times 10^{-6}\) & 0.99 & 300 & 2500 \\ TA01 to TA10 & 25 & 1.0 & 0.98 & 800 & 2500 \\ \hline \multicolumn{5}{c}{Size \(20\times 20\)} \\ \hline TA21 to TA30 & 2 & \(1\times 10^{-6}\) & 0.99 & 300 & 3500 \\ YN & 2 & \(1\times 10^{-6}\) & 0.99 & 300 & 2000 \\ DMU06 to DMU10 & 2 & \(5\times 10^{-6}\) & 0.99 & 300 & 9000 \\ DMU46 to DMU50 & 100 & 0.05 & 0.99 & 6000 & 9500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tuned parameters of simulated annealing.