## 4 Experimental Results
### Comparision of SACT with Other Algorithms  
Table 7, presents the results for the FT (Fisher and Thompson) and LA (Lawrence) benchmarks. SACT and BRK-GA (Biased Random-Key Genetic Algorithm) algorithms find the best results reported in the literature. Both algorithms obtained the optimal value for LA40. With regard to the execution time, it shows that SACT is competitive for most benchmarks. Table A2, in Appendix A, shows the software/hardware environment used for the execution of the algorithms presented in Table 7.  
Table 8, presents results for ORB, ABZ, TA, DMU, and YN benchmarks in [33]. SACT obtains the best results reported in the literature for most of the benchmarks. The relative error (RE) for ORB, ABZ, TA, YN, and DMU (06-10) benchmark is RE \(<\) 0.95%. For DMU (47-50,) benchmark is RE \(<\) 3.03%. This shows that SACT is competitive with respect to the other algorithms presented. In [36] the researchers report a new UB = 904 for the problem YN2; previously the known UB was 907. SACT finds a UB = 906. Although this is not the new value reported by [36], it was able to improve the UB known before 2014. In efficiency, SACT is competitive with the ACOFT-MWR (Ant Colony Optimization with Fast Taboo - Most Work Remaining). The exception can be seen with BRK-GA algorithm for the DMU benchmarks, SACT is, 0.12 \(<\) RE \(<\) 3.04 and BRK-GA is, 0 \(\leq\) RE \(<\) 0.49. Table A2, in Appendix A, shows the software/hardware environment used for the execution of the algorithms presented in Table 8.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Prob**} & \multirow{2}{*}{**Op**} & \multirow{2}{*}{**ST**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**BG**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**SG**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**AM**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**TA**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**SG**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**TGA**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**TS/PR**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**UP**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**HO**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**GT**} & \multirow{2}{*}{**AG**} \\  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multirow{2}{*}{**Op/UB**} & \multirow{2}{*}{**ST**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**BG**} & \multirow{2}{*}{**t Sec**} & \multirow{2}{*}{**AM**  
Table 9, presents the relative error of algorithms with threads/processes for the FT, LA, ORB, TA, DMU, and YN benchmarks. SACT has better performance with respect to the other algorithms, except DMU09. SACT has a relative error in the range of \(0\leq\text{RE}\leq 0.94\%\), PPSO (Parallel Particle Swarm Optimization) has a relative error in the range of \(29\leq\text{RE}\leq 68\%\), CGA-PR (Coarse-Grained Genetic Algorithm with Path-Relinking) has a relative error in the range of \(0\leq\text{RE}\leq 2.49\%\), PaGA (Parallel Agent-Based Genetic Algorithm) has a relative error in the range of \(0\leq\text{RE}\leq 12.4\%\), HGAPSA (Hybridization of Genetic Algorithm with Parallel Implementation of Simulated Annealing) presents a relative error of \(0.79\leq\text{RE}\leq 1.92\%\), HIMGA presents \(0\leq\text{RE}\leq 1.01\%\), NIMGA presents \(0\leq\text{RE}\leq 3.01\%\), IIMMA presents \(0\leq\text{RE}\leq 0.55\%\) and AGS presents \(0\leq\text{RE}\leq 1.76\%\). Concerning the HGACC distributed algorithm, SACT offers a better performance for YN benchmarks. It reaches the same effectiveness for \(10\times 10\) and \(15\times 15\) size benchmarks. Thus, it is best for the DMU06 benchmark and is competitive for the other DMU benchmarks. Table 2, in Appendix A, shows the software/hardware environment used for the execution of the algorithms presented in Table 9.