As noted earlier, we have used a simulated annealing based algorithm for improving the NNBH solutions
in large-sized problems. Thus, these problems are solved by proposed SA algorithm in Section 4.1
and the associated results are shown in Table 2. The SA solution is compared with the lower bound (LB) solution.
The LB solution is obtained by relaxing constraint (8). In other words, The LB solution is equal to the
number of vehicles that we need to serve all nodes with the maximum capacity utilization and without limitation
of service time. The SA parameters set in advance as follows: EL = 100, MTT = 100, a = 0.95 and
T0 = 5.