## 3 Proposed Methodology
### Decoding the Customer Vector
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problems** & **BKS** & \(\textit{Cost}_{\textit{BLS-PSO}}\) & _gap_ & _AvgT_ & \(\textit{k}_{2}\) & \(\textit{k}_{3}\)_ \\ \hline P-n16-k8 & 450 & 450 & 0.00 & 0.11 & 0.1 & 0.9 \\ P-n19-k2 & 212 & 212 & 0.00 & 0.1 & 0.9 & 0.0 \\ P-n20-k2 & 216 & 216 & 0.00 & 0.35 & 0.1 & 0.1 \\ P-n21-k2 & 211 & 211 & 0.00 & 0.32 & 0.1 & 0.1 \\ P-n22-k2 & 216 & 216 & 0.00 & 0.71 & 0.1 & 0.7 \\ P-n22-k8 & 603 & 603 & 0.00 & 0.83 & 0.4 & 0.2 \\ P-n23-k8 & 529 & 529 & 0.00 & 1.02 & 0.5 & 0.8 \\ P-n40-k5 & 458 & 458 & 0.00 & 1.33 & 0.5 & 0.2 \\ P-n45-k5 & 510 & 510 & 0.00 & 1.45 & 1.0 & 0.3 \\ P-n50-k7 & 554 & 554 & 0.00 & 1.48 & 0.7 & 0.9 \\ P-n50-k8 & 631 & 631 & 0.00 & 1.05 & 1.0 & 0.1 \\ P-n50-k10 & 696 & 696 & 0.00 & 2.23 & 0.3 & 0.5 \\ P-n51-k10 & 741 & 741 & 0.00 & 3.38 & 0.3 & 0.6 \\ P-n55-k7 & 568 & 568 & 0.00 & 4.32 & 1.0 & 0.1 \\ P-n55-k10 & 694 & 694 & 0.00 & 4.94 & 0.6 & 1.0 \\ P-n55-k15 & 989 & 989 & 0.00 & 4.29 & 1.0 & 0.3 \\ P-n60-k10 & 744 & 744 & 0.00 & 5.83 & 0.8 & 0.1 \\ P-n60-k15 & 968 & 968 & 0.00 & 5.37 & 0.0 & 0.7 \\ P-n65-k10 & 792 & 792 & 0.00 & 6.44 & 0.0 & 0.8 \\ P-n70-k10 & 827 & 833 & 0.73 & 9.24 & 0.8 & 1.0 \\ P-n76-k4 & 593 & 598 & 0.84 & 16.11 & 0.4 & 1.0 \\ P-n76-k5 & 627 & 636 & 1.44 & 15.85 & 0.6 & 0.4 \\ P-n101-k4 & 681 & 692 & 1.62 & 20.17 & 0.5 & 0.7 \\ \hline \multicolumn{2}{c}{Average} & 0.2 & 4.72 & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance of BLS-PSO in solving the benchmark problems in Set P.

BLS-PSO has not met the best-known results for some instances. The main reason behind this may be the small population size or the lower value of the maximum number of iterations. Increasing them are expected to attain better solutions. ### Comparative Performance of PSO-Based Approaches

To portray the comparison of the performance of our proposed algorithm with other PSO-based algorithms in the literature, we have taken the same instances used by other researchers [41; 44; 47; 52]. Table 11 contains the results for 16 instances from the Sets A, B, E, F, M and P, and Table 12 lists results for all the 14 instances of Set CMT. Here, PSO-based algorithms DPSO [41], SR1, SR2 [44; 46] and PSCO [52] are compared with proposed BLS-PSO. Here, _Cost_ is the result obtained by respective algorithms and a value is in boldface font when it is equal to the best-known result reported in the literature. The superscript \"_a_\" indicates that the cost is inferior to what is achieved by the proposed BLS-PSO. \(BT\) refers to the computational time in seconds to reach the corresponding result. For the proposed algorithm, we have reported the _AvgT_ as mentioned earlier. As mentioned above there are no convergence of solution for specific \(k_{2}\) and \(k_{3}\) value, we have mentioned _AvgCost_ as the average of all the solutions obtained by BLS-PSO for different \(k_{2}\) and \(k_{3}\). The deviation of the _AvgCost_ with the best-known solutions is mentioned as \(SD\) in Table 11. It is evident that even the average time taken by the proposed method is far better, let alone the shortest time, than the shortest time of other approaches for each of the problem instances under consideration.