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Table 3 The average experimental results for MTRPD instances

From: A hybrid metaheuristic for solving asymmetric distance-constrained vehicle routing problem

Instances \(MD = 2 \times d_{{{{\text{max}}}}}\) \(MD = 2.5 \times d_{{{{\text{max}}}}}\) \(MD = 3 \times d_{{{{\text{max}}}}}\)
\(Gap_1\) Time \(Gap_1\) Time \(Gap_1\) Time
pr1002_30_x 0.00 0.25 0.00 0.23 0.00 0.24
brd14051_30_x 0.00 0.25 0.00 0.24 0.00 0.25
fnl4461_30_x 0.00 0.22 0.00 0.22 0.00 0.24
d15112_30_x 0.00 0.25 0.00 0.23 0.00 0.21
nrw1379_30_x 0.00 0.25 0.00 0.25 0.00 0.24
pr1002_40_x 0.00 0.45 0.00 0.44 0.00 0.41
brd14051_40_x 0.00 0.44 0.00 0.42 0.00 0.41
fnl4461_40_x 0.00 0.44 0.00 0.44 0.00 0.44
d15112_40_x 0.00 0.44 0.00 0.41 0.00 0.44
nrw1379_40_x 0.00 0.43 0.00 0.42 0.00 0.42
pr1002_50_x 0.00 0.85 0.00 0.84 0.00 0.82
brd14051_50_x 0.00 0.81 0.00 0.82 0.00 0.81
fnl4461_50_x 0.00 0.83 0.00 0.83 0.00 0.83
d15112_50_x 0.00 0.83 0.00 0.83 0.00 0.85
nrw1379_50_x 0.00 0.84 0.00 0.84 0.00 0.82
pr1002_60_x 0.55 1.12 0.48 1.45 0.34 1.45
brd14051_60_x 0.67 1.13 0.46 1.45 0.54 1.45
fnl4461_60_x 0.48 1.12 0.39 1.45 0.29 1.45
d15112_60_x 0.57 1.11 0.39 1.46 0.31 1.46
nrw1379_60_x 0.64 1.12 0.71 1.45 0.76 1.45
pr1002_70_x 0.89 1.48 0.83 1.97 0.93 1.97
brd14051_70_x 0.51 1.49 0.54 1.84 0.51 1.84
fnl4461_70_x 0.63 1.46 0.60 1.94 0.67 1.94
d15112_70_x 0.70 1.51 0.74 1.85 0.76 1.85
nrw1379_70_x 0.65 1.44 0.73 1.95 0.62 1.95
pr1002_80_x 0.69 3.58 0.74 4.66 0.66 4.66
brd14051_80_x 0.58 3.56 0.63 4.62 0.57 4.62
fnl4461_80_x 0.74 3.59 0.80 4.63 0.73 4.63
d15112_80_x 0.41 3.57 0.39 4.65 0.43 4.65
nrw1379_80_x 0.96 3.53 0.86 4.67 0.82 4.67
Average 0.32 0.30 0.30