Multivisit Drone-Vehicle Routing Problem with Simultaneous Pickup and Delivery considering No-Fly Zones

Table 6

Comparison experiment for determining the effectiveness of the algorithm considering no-fly zones.

Instance	Customer size	No-fly	Solver solution			Two-stage heuristic algorithm		Gap^1 (%)
			Obj_UB ($)	Obj_LB ($)	Time (s)	Obj ($)	Time (s)
1P1_1	5	1	25.96	25.96	1	25.96	25.3508	0.00
1P1_2	5	2	20.52	20.52	1	20.52	25.5584	0.00
1P1_3	5	3	21.76	21.76	1	21.76	25.2819	0.00
1P1_4	5	4	14.41	14.41	1	14.41	25.2415	0.00
1P1_5	5	5	14.16	14.16	1	14.16	25.0967	0.00
1P1_6	5	1, 2	27.06	27.06	1	27.06	25.2376	0.00
1P1_7	5	1, 3	31.31	31.31	1	31.31	25.2657	0.00
1P1_8	5	1, 4	26.05	26.05	1	26.05	25.0332	0.00
1P1_9	5	1, 5	25.96	25.96	1	25.96	25.0608	0.00
1P1_10	5	2, 3	25.03	25.03	1	25.03	27.5985	0.00
1P1_11	5	2, 4	20.62	20.62	1	20.62	25.0996	0.00
1P1_12	5	2, 5	20.52	20.52	1	20.52	25.0662	0.00
1P1_13	5	3, 4	22.08	22.08	1	22.08	25.1485	0.00
1P1_14	5	3, 5	21.76	21.76	1	21.76	25.0723	0.00
1P1_15	5	4, 5	20.42	20.42	1	20.42	25.5597	0.00
1P1_16	5	1, 2, 3	31.31	31.31	1	31.31	25.1711	0.00
1P1_17	5	1, 2, 4	27.15	27.15	1	27.15	25.1168	0.00
1P1_18	5	1, 2, 5	27.06	27.06	1	27.06	25.1320	0.00
1P1_19	5	1, 3, 4	31.31	31.31	1	31.31	25.2537	0.00
1P1_20	5	1, 3, 5	31.31	31.31	1	31.31	25.2396	0.00
1P1_21	5	1, 4, 5	27.07	27.07	1	27.07	25.2176	0.00
1P1_22	5	2, 3, 4	25.18	25.18	1	25.18	25.4017	0.00
1P1_23	5	2, 3, 5	25.03	25.03	1	25.03	25.0857	0.00
1P1_24	5	2, 4, 5	25.09	25.09	1	25.09	25.4050	0.00
1P1_25	5	3, 4, 5	24.77	24.77	1	24.77	25.2607	0.00
Avg.					1		25.3182	0
6P1_1	10	2	31.62	31.62	3505	33.80	30.8478	6.89
6P1_2	10	2, 5	31.72	31.72	3811	34.18	33.9215	7.76
6P1_3	10	1	31.98	31.98	3900	33.81	26.0616	5.72
6P1_4	10	1, 2, 5	32.09	32.09	3242	34.28	25.9153	6.82
Avg.					3615		29.1866	6.80
11P1_1	16	2, 5	70.23	56.81	7200	79.85	28.7801	13.70
11P1_2	16	1, 2, 5	70.33	59.65	7200	81.15	26.9204	15.38
Avg.					7200		27.8503	14.54
11P1_3	18	2, 5	75.75	37.98	7200	93.21	28.1936	23.05
11P1_4	18	1, 2, 5	77.08	39.08	7200	92.58	27.0675	20.11
Avg.					7200		27.6306	21.58
11P1_5	20	2, 5	77.79	48.12	7200	94.09	28.1038	20.95
11P1_6	20	1, 2, 5	90.81	50.04	7200	93.35	27.9111	2.80
Avg.					7200		28.0075	11.88
11P1_7	25	2, 5, 10	—	—	—	95.49	28.3291	—
11P1_8	25	1, 5, 10, 15, 20	—	—	—	95.79	27.5383	—
Avg.							27.9337
16P1_1	50	2, 5, 10	—	—	—	103.21	29.1527	—
16P1_2	50	1, 5, 10, 15, 20	—	—	—	103.16	28.8346	—
Avg.							28.9937
20P1_1	100	1, 5, 15	—	—	—	171.78	31.3569	—
20P1_2	100	1, 5, 15, 25, 35	—	—	—	172.10	31.2769	—
Avg.							31.3169

The optimal solution cannot be obtained within a time limit of 2 h.