## 5 Testing the Proposed Algorithm
### Performance of the Proposed Algorithm and Comparison to the State-of-the Art Algorithms
Especially in the case of instance 7, which was the most difficult \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Instance**} & \multirow{3}{*}{**Score**} & \multirow{3}{*}{**Exec. Time**} & \multirow{3}{*}{**Score**} & \multirow{3}{*}{**Exec. Time**} \\  & & & **(min-s)** & & \\ \hline \multirow{4}{*}{1} & best & \(11\) & 32 min 39 s & **7** & 37 min 17 s \\  & worst & 21 & 39 min 15 s & 20 & 40 min 42 s \\  & Ave. & 16 & 36 min 36 s & 12.97 & 38 min 2 s \\  & STD & 2.5 & 3 min 24 s & 2.35 & 2 min \\  & CV & 15.6\% & 9.3\% & 18.1\% & 5.25\% \\ \hline \multirow{4}{*}{2} & best & 18 & 46 min 57 s & **13** & 44 min 3 s \\  & worst & 28 & 48 min 30 s & 21 & 48 min 11 s \\  & Ave. & 22.1 & 47 min 48 s & 17.3 & 45 min 10 s \\  & STD & 2.5 & 48 s & 1.65 & 1 min 5 s \\  & CV & 11.3\% & 1.7\% & 9.5\% & 2.2\% \\ \hline \multirow{4}{*}{3} & best & 5 & 3 min 30 s & **4** & 1 min 20 s \\  & worst & 9 & 4 min 17 s & 10 & 1 min 50 s \\  & Ave. & 7.4 & 3 min 54 s & 8.3 & 1 min 40 s \\  & STD & 0.8 & 24 s & 1.7 & 15 s \\  & CV & 10.8\% & 10.3\% & 20.5\% & 15\% \\ \hline \multirow{4}{*}{4} & best & 5 & 13 min 4 s & **3** & 6 min 45 s \\  & worst & 13 & 13 min 26 s & 10 & 10 min 15 s \\  & Ave. & 8.8 & 13 min 12 s & 7.25 & 9 min 10 s \\  & STD & 2.2 & 18 s & 1.6 & 47 s \\  & CV & 25\% & 2.3\% & 22\% & 7.5\% \\ \hline \multirow{4}{*}{5} & best & 0 & 2 min 50 s & 0 & 1 min 10 s \\  & worst & 0 & 3 min 10 s & 3 & 1 min 40 s \\  & Ave. & 0 & 3 min & 0.88 & 1 min 20 s \\  & STD & 0 & 6 s & 0.99 & 12 s \\  & CV & 0\% & 3.3\% & – & 15\% \\ \hline \multirow{4}{*}{7} & best & 23 & 57 min 36 s & **6** & 67 min 19 s \\  & worst & 49 & 58 min 22 s & 26 & 68 min 30 s \\  & Ave. & 35.8 & 57 min 54 s & 18.6 & 67 min 45 s \\  & STD & 6.8 & 24 s & **4** & 15 s \\  & CV & 19\% & 0.7\% & 21.5\% & 0.37\% \\ \hline \multirow{4}{*}{8} & best & 11 & 1 min 47 s & 11 & 40 s \\  & worst & 11 & 1 min 48 s & 12 & 50 s \\  & Ave. & 11 & 1 min 48 s & 11.2 & 46 s \\  & STD & 0 & 0 s & 0.39 & 3 s \\  & CV & 0\% & 0\% & 3.5\% & 6.5\% \\ \hline \multirow{4}{*}{9} & best & 2 & 4 min 21 s & 2 & 1 min 53 s \\  & worst & 3 & 4 min 28 s & 4 & 2 min 10 s \\  & Ave. & 2.1 & 4 min 24 s & 2.5 & 2 min 1 s \\  & STD & 0.3 & 6 s & 0.74 & 10 s \\  & CV & 14.3\% & 2.3\% & – & 8.3\% \\ \hline \multirow{4}{*}{10} & best & 10 & 3 min 42 s & 10 & 1 min 29 s \\  & worst & 12 & 3 min 42 s & 13 & 1 min 40 s \\  & Ave. & 10.3 & 3 min 42 s & 11.4 & 1 min 34 s \\  & STD & 0.6 & 0 s & 0.97 & 7 s \\  & CV & 5,8\% & 0\% & 8.5\% & 7.4\% \\ \hline \multirow{4}{*}{11} & best & 19 & 7 min 7 s & 19 & 2 min 57 s \\  & worst & 21 & 7 min 50 s & 23 & 3 min 15 s \\  & Ave. & 20.3 & 7 min 24 s & 20.5 & 3 min 5 s \\  & STD & 0.6 & 24 s & 1.63 & 13 s \\  & CV & 3\% & 5.4\% & 7.9\% & 7.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Global-based PSO [8] versus local-based PSO (The best score between the two algorithms is indicated by bold). among all instances, the difference was remarkable. Additionally, in terms of the execution times, the proposed algorithm took less time to run in almost all cases, despite using one additional refining schema. Furthermore, analyzing the performance and the behavior of the proposed algorithm, it could be said that the sample of the scores and the sample of execution times was rather homogeneous, since most of the corresponding CV values were below 10%. The corresponding box plots of total cost and execution times per instance are presented in Figures 3 and 4, respectively. However, it may be observed that some instance execution times were higher than those of the global version of PSO, a fact which may be attributed to the use of two refining procedures. To keep the corresponding computational cost to a minimum, the algorithm was run for approximately half the number of iterations compared to its global version. This approach, albeit efficient in terms of the best solution attained, resulted in slightly inferior average results compared to the global version of PSO.