A Hybrid GRASP+VND Heuristic for the Two-Echelon Vehicle Routing Problem Arising in City Logistics

Table 3

Computational results comparison for Set 4 for the 2E-VRP.

Number	Instance name	𝑛𝑠	BKS [7]	ALNS					GRASP+VND
				Best	% dev.	Average	% dev.	Time (s)	Best	% dev.	Average	% dev.	Time (s)
1	Instance50-s2-01	2	1569.42	1569.42	0.00	1569.42	0.00	6	1569.42	0.00	1569.42	0.00	2
2	Instance50-s2-02	2	1438.33	1438.33	0.00	1441.02	0.19	43	1438.33	0.00	1438.33	0.00	53
3	Instance50-s2-03	2	1570.43	1570.43	0.00	1570.43	0.00	3	1570.43	0.00	1570.43	0.00	2
4	Instance50-s2-04	2	1424.04	1424.04	0.00	1424.04	0.00	11	1424.04	0.00	1429.04	0.35	98
5	Instance50-s2-05	2	2193.52	2194.11	0.03	2194.11	0.03	63	2193.52	0.00	2193.95	0.02	46
6	Instance50-s2-06	2	1279.87	1279.87	0.00	1279.87	0.00	2	1279.87	0.00	1279.87	0.00	1
7	Instance50-s2-07	2	1408.57	1458.63	3.55	1458.63	3.55	6	1408.57	0.00	1408.57	0.00	22
8	Instance50-s2-08	2	1360.32	1360.32	0.00	1360.32	0.00	5	1360.32	0.00	1360.32	0.00	5
9	Instance50-s2-09	2	1403.53	1450.27	3.33	1450.27	3.33	46	1403.53	0.00	1403.53	0.00	6
10	Instance50-s2-10	2	1360.56	1360.56	0.00	1360.56	0.00	1	1360.56	0.00	1360.56	0.00	2
11	Instance50-s2-11	2	2047.46	2059.88	0.61	2059.88	0.61	101	2059.41	0.58	2059.41	0.58	5
12	Instance50-s2-12	2	1209.42	1209.42	0.00	1209.42	0.00	44	1209.42	0.00	1209.42	0.00	8
13	Instance50-s2-13	2	1450.93	1481.83	2.13	1481.83	2.13	25	1450.93	0.00	1450.93	0.00	3
14	Instance50-s2-14	2	1393.61	1393.61	0.00	1393.61	0.00	6	1393.61	0.00	1393.61	0.00	2
15	Instance50-s2-15	2	1466.83	1489.94	1.58	1489.94	1.58	9	1466.83	0.00	1466.83	0.00	1
16	Instance50-s2-16	2	1387.83	1387.83	0.00	1387.83	0.00	6	1387.83	0.00	1387.83	0.00	8
17	Instance50-s2-17	2	2088.49	2088.49	0.00	2088.49	0.00	165	2088.49	0.00	2088.49	0.00	36
18	Instance50-s2-18	2	1227.61	1227.61	0.00	1227.61	0.00	3	1227.61	0.00	1227.61	0.00	2
19	Instance50-s3-19	3	1546.28	1546.28	0.00	1546.28	0.00	25	1546.28	0.00	1546.28	0.00	34
20	Instance50-s3-20	3	1272.97	1272.97	0.00	1272.97	0.00	12	1272.97	0.00	1272.97	0.00	76
21	Instance50-s3-21	3	1577.82	1577.82	0.00	1577.82	0.00	61	1577.82	0.00	1577.82	0.00	25
22	Instance50-s3-22	3	1281.83	1281.83	0.00	1281.83	0.00	2	1281.83	0.00	1281.83	0.00	37
23	Instance50-s3-23	3	1652.98	1652.98	0.00	1652.98	0.00	5	1652.98	0.00	1652.98	0.00	4
24	Instance50-s3-24	3	1282.68	1282.68	0.00	1282.68	0.00	2	1282.68	0.00	1282.68	0.00	2
25	Instance50-s3-25	3	1408.57	1440.68	2.28	1440.84	2.29	53	1408.57	0.00	1408.57	0.00	23
26	Instance50-s3-26	3	1167.46	1167.46	0.00	1167.46	0.00	0	1167.46	0.00	1167.46	0.00	9
27	Instance50-s3-27	3	1444.51	1444.51	0.00	1447.79	0.23	12	1444.51	0.00	1454.63	0.70	52
28	Instance50-s3-28	3	1210.44	1210.44	0.00	1210.44	0.00	7	1210.44	0.00	1210.44	0.00	3
29	Instance50-s3-29	3	1552.66	1559.82	0.46	1561.81	0.59	102	1552.66	0.00	1555.56	0.19	40
30	Instance50-s3-30	3	1211.59	1211.59	0.00	1211.59	0.00	5	1211.59	0.00	1211.59	0.00	2
31	Instance50-s3-31	3	1440.86	1440.86	0.00	1440.86	0.00	37	1440.86	0.00	1441.07	0.01	39
32	Instance50-s3-32	3	1199.00	1199.00	0.00	1199.00	0.00	11	1199.00	0.00	1199.00	0.00	13
33	Instance50-s3-33	3	1478.86	1478.86	0.00	1478.86	0.00	16	1478.86	0.00	1478.86	0.00	19
34	Instance50-s3-34	3	1233.92	1233.92	0.00	1233.92	0.00	4	1233.92	0.00	1233.92	0.00	15
35	Instance50-s3-35	3	1570.72	1570.72	0.00	1570.80	0.01	116	1570.72	0.00	1570.72	0.00	6
36	Instance50-s3-36	3	1228.89	1228.89	0.00	1228.89	0.00	6	1228.89	0.00	1228.89	0.00	3
37	Instance50-s5-37	5	1528.73	1528.73	0.00	1528.81	0.01	55	1528.73	0.00	1528.98	0.02	58
38	Instance50-s5-38	5	1163.07	1163.07	0.00	1163.07	0.00	15	1163.07	0.00	1163.07	0.00	2
39	Instance50-s5-39	5	1520.92	1520.92	0.00	1520.92	0.00	33	1520.92	0.00	1520.92	0.00	21
40	Instance50-s5-40	5	1163.04	1163.04	0.00	1165.24	0.19	20	1163.04	0.00	1163.04	0.00	9
41	Instance50-s5-41	5	1652.98	1652.98	0.00	1652.98	0.00	12	1652.98	0.00	1652.98	0.00	12
42	Instance50-s5-42	5	1190.17	1190.17	0.00	1190.17	0.00	31	1190.17	0.00	1190.17	0.00	95
43	Instance50-s5-43	5	1406.11	1406.11	0.00	1408.95	0.20	60	1406.11	0.00	1406.11	0.00	32
44	Instance50-s5-44	5	1035.03	1035.03	0.00	1035.32	0.03	30	1035.03	0.00	1035.03	0.00	9
45	Instance50-s5-45	5	1401.87	1403.10	0.09	1406.43	0.33	104	1402.03	0.01	1402.03	0.01	36
46	Instance50-s5-46	5	1058.11	1058.11	0.00	1058.97	0.08	17	1058.11	0.00	1058.11	0.00	9
47	Instance50-s5-47	5	1552.66	1559.82	0.46	1564.41	0.76	103	1552.66	0.00	1557.04	0.28	33
48	Instance50-s5-48	5	1074.50	1074.50	0.00	1074.50	0.00	2	1074.50	0.00	1074.50	0.00	1
49	Instance50-s5-49	5	1434.88	1434.88	0.00	1435.28	0.03	81	1434.88	0.00	1434.88	0.00	51
50	Instance50-s5-50	5	1065.25	1065.25	0.00	1065.25	0.00	16	1065.25	0.00	1065.25	0.00	3
51	Instance50-s5-51	5	1387.51	1387.51	0.00	1387.72	0.02	46	1387.51	0.00	1387.51	0.00	4
52	Instance50-s5-52	5	1103.42	1103.42	0.00	1103.76	0.03	47	1103.42	0.00	1103.42	0.00	30
53	Instance50-s5-53	5	1545.73	1545.73	0.00	1545.73	0.00	37	1545.73	0.00	1545.73	0.00	6
54	Instance50-s5-54	5	1113.62	1113.62	0.00	1113.62	0.00	2	1113.62	0.00	1113.62	0.00	16
Average			1397.04	1400.96	0.28	1401.39	0.31	32	1397.27	0.02	1397.70	0.05	21