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

Table 1

Computational results comparison for Set 2 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	E-n22-k4-s6-17	2	417.07	417.07	0.00	417.07	0.00	0	417.07	0.00	417.07	0.00	0
2	E-n22-k4-s8-14	2	384.96	384.96	0.00	384.96	0.00	0	384.96	0.00	384.96	0.00	0
3	E-n22-k4-s9-19	2	470.60	470.60	0.00	470.60	0.00	0	470.60	0.00	470.60	0.00	0
4	E-n22-k4-s10-14	2	371.50	371.50	0.00	371.50	0.00	0	371.50	0.00	371.50	0.00	0
5	E-n22-k4-s11-12	2	427.22	427.22	0.00	427.22	0.00	0	427.22	0.00	427.22	0.00	0
6	E-n22-k4-s12-16	2	392.78	392.78	0.00	392.78	0.00	0	392.78	0.00	392.78	0.00	0
7	E-n33-k4-s1-9	2	730.16	730.16	0.00	730.16	0.00	0	730.16	0.00	730.16	0.00	0
8	E-n33-k4-s2-13	2	714.63	714.63	0.00	714.63	0.00	0	714.63	0.00	714.63	0.00	0
9	E-n33-k4-s3-17	2	707.48	707.48	0.00	707.48	0.00	0	707.48	0.00	707.48	0.00	0
10	E-n33-k4-s4-5	2	778.74	778.74	0.00	778.74	0.00	3	778.74	0.00	778.74	0.00	1
11	E-n33-k4-s7-25	2	756.85	756.85	0.00	756.85	0.00	0	756.85	0.00	756.85	0.00	0
12	E-n33-k4-s14-22	2	779.05	779.05	0.00	779.05	0.00	0	779.05	0.00	779.05	0.00	0
13	E-n51-k5-s2-17	2	597.49	597.49	0.00	597.49	0.00	7	597.49	0.00	597.49	0.00	1
14	E-n51-k5-s4-46	2	530.76	530.76	0.00	530.76	0.00	0	530.76	0.00	530.76	0.00	0
15	E-n51-k5-s6-12	2	554.81	554.81	0.00	554.81	0.00	2	554.81	0.00	554.81	0.00	2
16	E-n51-k5-s11-19	2	581.64	581.64	0.00	581.64	0.00	6	581.64	0.00	581.64	0.00	5
17	E-n51-k5-s27-47	2	538.22	538.22	0.00	538.22	0.00	1	538.22	0.00	538.22	0.00	1
18	E-n51-k5-s32-37	2	552.28	552.28	0.00	552.28	0.00	1	552.28	0.00	552.28	0.00	1
19	E-n51-k5-s2-4-17-46	4	530.76	530.76	0.00	530.76	0.00	1	530.76	0.00	530.76	0.00	1
20	E-n51-k5-s6-12-32-37	4	531.92	531.92	0.00	531.92	0.00	0	531.92	0.00	531.92	0.00	1
21	E-n51-k5-s11-19-27-47	4	527.63	527.63	0.00	527.63	0.00	1	527.63	0.00	527.63	0.00	1
Average			565.55	565.55	0.00	565.55	0.00	1	565.55	0.00	565.55	0.00	0.67