## 3 Proposed Methodology
### Decoding the Customer Vector
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & & **SR1** & **SR2** & **PACO** & **DPSO** & **BLS-PSO** \\ \hline \multirow{2}{*}{**Problem**} & \multirow{2}{*}{_BKS_} & \(Cost\) & \(Cost\) & \(Cost\) & \(Cost\) & \(Cost\) & \(Cost\) \\  & & \(BT\) & \(BT\) & \(BT\) & \(BT\) & \(AvgT\) & \\  & & (gap) & (gap) & (gap) & (gap) & (gap) & (gap) & (SD) \\ \hline \multirow{3}{*}{A-n33-k5} & \multirow{3}{*}{661} & **661** & **661** & **661** & **661** & **661** \\  & & 11 & 13 & 0.87 & 32.3 & 0.15 & \\  & & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) \\ \hline \multirow{3}{*}{A-n46-k7} & \multirow{3}{*}{914} & **914** & **914** & **914** & **914** & **914** & **914** \\  & & 18 & 23 & 6.02 & 128.9 & 1.29 & \\  & & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) \\ \hline \multirow{3}{*}{A-n60-k9} & \multirow{3}{*}{1354} & 1366 \({}^{\text{a}}\) & 1355 \({}^{\text{a}}\) & **1354** & **1354** & **1354** & 1362 \\  & & 28 & 40 & 52.88 & 308.8 & 8.78 & \\  & & (0.89) & (0.07) & (0.00) & (0.00) & (0.00) & (0.59) \\ \hline \multirow{3}{*}{B-n35-k5} & \multirow{3}{*}{955} & **955** & **955** & **955** & **955** & **955** & **955** \\  & & 12 & 14 & 2.65 & 37.6 & 1.12 & \\  & & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) \\ \hline \multirow{3}{*}{B-n45-k5} & \multirow{3}{*}{751} & **751** & **751** & **751** & **751** & **751** & 757 \\  & & 17 & 20 & 5.85 & 134.2 & 2.04 & \\  & & (0.00) & (0.00) & (0.00) & (0.00) & (0.8) & \\ \hline \multirow{3}{*}{B-n68-k9} & \multirow{3}{*}{1272} & 1278 \({}^{\text{a}}\) & 1274 \({}^{\text{a}}\) & 1275 \({}^{\text{a}}\) & **1272** & **1272** & 1289 \\  & & 33 & 50 & 62.97 & 344.3 & 6.19 & \\  & & (0.47) & (0.16) & (0.24) & (0.00) & (0.00) & (1.34) \\ \hline \multirow{3}{*}{B-n78-k10} & \multirow{3}{*}{1221} & 1239 \({}^{\text{a}}\) & 1223 \({}^{\text{a}}\) & **1221** & 1239 \({}^{\text{a}}\) & **1221** & 1243 \\  & & 41 & 64 & 98.78 & 429.4 & 9.71 & \\  & & (1.47) & (0.16) & (0.00) & (1.47) & (0.00) & (1.8) \\ \hline \multirow{3}{*}{E-n30-k3} & \multirow{3}{*}{534} & 541 \({}^{\text{a}}\) & **534** & **534** & **534** & **534** & 534 \\  & & 11 & 16 & 4.38 & 28.4 & 0.3 & \\  & & (1.31) & (0.00) & (0.00) & (0.00) & (0.00) & (0.00) \\ \hline \multirow{3}{*}{E-n51-k5} & \multirow{3}{*}{521} & **521** & **521** & **521** & 528 \({}^{\text{a}}\) & **521** & 531 \\  & & 21 & 22 & 19.46 & 30.5 & 2.81 & \\ \cline{1-1}  & & (0.00) & (0.00) & (0.00) & (0.34) & (1.34) & (0.00) & (1.92) \\ \hline \multirow{3}{*}{E-n76-k7} & \multirow{3}{*}{682} & 691 \({}^{\text{a}}\) & 682 & 685 & 688 \({}^{\text{a}}\) & 687 & 696 \\ \cline{1-1}  & & 38 & 60 & 46.85 & 526.5 & 13.55 & \\ \cline{1-1}  & & (1.32) & (0.00) & (0.44) & (0.88) & (0.73) & (2.05) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Performance comparison of BLS-PSO with respect to other PSO-based approaches for solving some selected instances. The overall results are also graphically represented in Figure 7 to show the comparative performances more comprehensively. The negative gap in Figure 7a corresponds to the problem instance, for which the BLS-PSO has obtained a new optimal result. Figure 7b demonstrates that time consumed by BLS-PSO is significantly less than the other approaches, where the plot is almost touching the horizontal axis for all the instances.