## 3 Proposed Methodology
### Decoding the Customer Vector
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & & **SR1** & **SR2** & **PACO** & **DPSO** & **BLS-PSO** \\ \hline \multirow{4}{*}{F-n72-k4} & \multirow{2}{*}{237} & **237** & **237** & **237** & 244  & **1162** & 1170 & 1215  & **820** & **820** & 824  & 1036  & **1034** & 1040 \\  & & 88 & 89 & 80.62 & 1733.5 & 33.33 & \\  & & (0.68) & (0.19) & (0.00) & (0.39) & (0.00) & (0.58) \\ \hline \multirow{4}{*}{P-n76-k4} & \multirow{2}{*}{593} & 599 & 594 & 593 & 602  & 692 & 699 \\  & & 99 & 86 & 64.92 & 977.5 & 20.17 & \\  & & (0.73) & (0.29) & (0.29) & (1.91) & (1.62) & (2.64) \\ \hline \multirow{4}{*}{Average} & \multirow{4}{*}{47.81} & - & - & - & - & - & - \\  & & 47.81 & 60.63 & 55.78 & 517.325 & 13.25 & \\ \cline{1-1}  & & (0.62) & (0.066) & (0.1) & (0.97) & (0.25) & (1.49) \\ \hline \end{tabular}
\end{table} 
Table 11: _Cont._

Figure 7: Performances of different algorithms in solving selective instances. **(a)** gap (%); **(b)** Computational Time (s). Table 12 portrays the comparison of performance in handling CMT problem set instances. Here we have compared SR1, SR2 [44; 46], HybPSO [47] and PSCO [52] with the proposed BLS-PSO. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **SR1** & **SR2** & **PACO** & **HybPSO** & **BLS-PSO** \\ \hline \multirow{3}{*}{**Problem**} & \multirow{3}{*}{\(BKS\)} & _Cost_ & _Cost_ & _Cost_ & _Cost_ & _Cost_ & _AvgCost_ \\  & _BT_ & _BT_ & _BT_ & _BT_ & _AgT_ & _AvgT_ & \\  & (_gap_) & (_gap_) & (_gap_) & (_gap_) & (_gap_) & (_gap_) & (_SD_) \\ \hline \multirow{3}{*}{CMT1} & \multirow{3}{*}{524.61} & **524.61** & **524.61** & **524.61** & **524.61** & **524.61** & **524.61** & **524.61** \\  & & 21 & 24 & 32.3 & 3 & 2.19 & \\  & & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) \\ \hline \multirow{3}{*}{CMT2} & \multirow{3}{*}{835.26} & 849.58 & 844.42 & \multirow{3}{*}{**835.26**} & **835.26** & **835.26** & **835.26** & 840.39 \\  & & 39 & 57 & 108 & 13 & 8.44 & \\  & & (1.71) & (1.1) & (0.00) & (0.00) & (0.61) & \\ \hline \multirow{3}{*}{CMT3} & \multirow{3}{*}{826.14} & 835.8 a & 829.4 a & \multirow{3}{*}{826.14} & 829.92 & \multirow{3}{*}{826.14} & **826.14** & 836.44 \\  & & 61 & 101 & 142 & 19 & 10.58 & \\  & & (1.17) & (0.39) & (0.46) & (0.00) & (0.00) & (1.25) \\ \hline \multirow{3}{*}{CMT4} & \multirow{3}{*}{1028.42} & 1067.57 & 1048.89 & \multirow{3}{*}{1040.23} & \multirow{3}{*}{1029.54} & \multirow{3}{*}{1042.8} & \multirow{3}{*}{1059.13} \\  & & 3 & (1.99) & (1.15) & (0.11) & (1.4) & (2.99) \\ \hline \multirow{3}{*}{CMT5} & \multirow{3}{*}{1291.29} & 1345.84 & \multirow{3}{*}{1323.89} & \multirow{3}{*}{1348.73} & \multirow{3}{*}{1294.13} & \multirow{3}{*}{1324.01} & \multirow{3}{*}{1348.27} \\  & & 3 & & & & & \\  & & 188 & 413 & 1049 & 129 & 16.37 & \\  & & (4.21) & (2.51) & (4.44) & (0.22) & (2.53) & (4.41) \\ \hline \multirow{3}{*}{CMT6} & \multirow{3}{*}{555.43} & 555.68 & \multirow{3}{*}{**555.43**} & **555.43** & **555.43** & **555.43** & **555.43** \\  & & 3 & 21 & 30 & 28 & 3 & 9.11 & \\  & & (0.23) & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) \\ \hline \multirow{3}{*}{CMT7} & \multirow{3}{*}{909.68} & 952.77 & 917.68 & \multirow{3}{*}{**909.68**} & **909.68** & **909.68** & 917.94 \\  & & 3 & 3 & & & & \\  & & 3 & & & & & \\  & & 3 & & & & & \\  & & 3 & & & & & \\  & & 3 & & & & & \\  & & 3 & & & & & \\  & & 3 & & & & & \\  & & 3 & & & & &Figure 8 shows clearer comparative graphical representations of the performances of the PSO-based algorithms dealing instances in Set CMT. Here, BLS-PSO has obtained results equal to the best known results with an average gap of 0.64% whereas SR1, SR2, PACO and HybPSO have gap of 1.788%, 0.874%, 0.913% and 0.084% respectively. However, the average of the reported CPU times required by BLS-PSO is only 13.33 s to solve the instances in Set CMT whereas the average of the best times required by SR1, SR2, PACO and HybPSO are 84.1 s, 163.1 s, 302.58 s and 48.13 s, respectively.