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

Computational Social Networks

Table 3 The average experimental results for MTRPD instances

Instances	\(MD = 2 \times d_{{{{\text{max}}}}}\)		\(MD = 2.5 \times d_{{{{\text{max}}}}}\)		\(MD = 3 \times d_{{{{\text{max}}}}}\)
Instances	\(Gap_1\)	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	–