A Bee Evolutionary Algorithm for Multiobjective Vehicle Routing Problem with Simultaneous Pickup and Delivery

Table 9

Computational results for Dethloff’s benchmark.

Instance	Best so far know solution in		ACSEVNS			BEG-NSGA-II
	the literature
	Ref.	BKS	Best	Avg.	T	Best	Avg.	T	Fuel
SCA3-0	PILS, VLBR, HPSO, ACS	635.62	635.62	635.62	4.77	732.12	745.36	10.21	684.23
SCA3-1	PILS, VLBR, HPSO, ACS	697.84	697.84	697.84	5.24	821.13	838.39	11.32	761.96
SCA3-2	PILS, VLBR, HPSO, ACS	659.34	659.34	659.34	7.47	659.34	659.34	12.65	612.62
SCA3-3	PILS, VLBR, HPSO, ACS	680.04	680.04	680.34	5.20	762.36	776.61	9.69	715.37
SCA3-4	PILS, VLBR, HPSO, ACS	690.50	690.50	690.50	4.96	765.58	770.67	13.52	726.27
SCA3-5	PILS, VLBR, HPSO, ACS	659.91	659.91	659.91	5.18	675.69	680.21	12.38	606.39
SCA3-6	PILS, VLBR, HPSO, ACS	651.09	651.09	651.11	4.68	651.09	651.09	14.32	610.92
SCA3-7	PILS, VLBR, HPSO, ACS	659.17	659.17	659.17	6.06	763.47	773.6	12.21	723.26
SCA3-8	PILS, VLBR, HPSO, ACS	719.48	719.48	719.56	4.51	768.36	782.65	10.36	716.28
SCA3-9	PILS, VLBR, HPSO, ACS	681.00	681.00	681.00	7.08	681.00	681.00	9.36	621.23
SCA8-0	PILS, VLBR, HPSO, ACS	961.50	961.50	961.50	5.33	1012.38	1026.54	15.63	973.62
SCA8-1	PILS, VLBR, HPSO, ACS	1049.65	1049.65	1049.65	5.62	1099.63	1129.78	16.22	1038.53
SCA8-2	PILS, VLBR, HPSO, ACS	1039.64	1039.64	1041.62	6.05	1126.53	1139.25	16.37	1079.92
SCA8-3	PILS, VLBR, HPSO, ACS	983.34	983.34	983.34	8.39	1016.29	1035.69	13.23	968.37
SCA8-4	PILS, VLBR, HPSO, ACS	1065.49	1065.49	1065.49	6.07	1065.49	1065.49	11.32	1016.27
SCA8-5	PILS, VLBR, HPSO, ACS	1027.08	1027.08	1027.14	6.96	1089.36	1096.75	10.63	1023.63
SCA8-6	PILS, VLBR, HPSO, ACS	971.82	971.82	971.82	7.76	985.78	996.34	9.89	928.56
SCA8-7	PILS, VLBR, HPSO, ACS	1051.28	1051.28	1051.28	8.14	1156.36	1173.95	12.35	1103.93
SCA8-8	PILS, VLBR, HPSO, ACS	1071.18	1071.18	1071.22	7.06	1210.35	1242.25	18.69	1129.46
SCA8-9	PILS, VLBR, HPSO, ACS	1060.50	1060.50	1060.50	5.29	1126.52	1153.34	19.99	1086.95
CON3-0	PILS, VLBR, HPSO, ACS	616.52	616.52	616.52	6.80	712.45	732.32	15.36	672.97
CON3-1	PILS, VLBR, HPSO, ACS	554.47	554.47	554.47	5.01	589.76	593.67	11.25	521.36
CON3-2	PILS, VLBR, HPSO, ACS	518.00	518.00	518.00	7.55	562.98	583.53	16.87	512.39
CON3-3	PILS, VLBR, HPSO, ACS	591.19	591.19	591.19	5.75	591.19	591.19	13.63	538.13
CON3-4	PILS, VLBR, HPSO, ACS	588.79	588.79	588.79	3.90	623.82	643.78	9.36	579.24
CON3-5	PILS, VLBR, HPSO, ACS	563.70	563.70	563.70	6.86	563.70	563.70	12.36	513.21
CON3-6	PILS, VLBR, HPSO, ACS	499.05	499.05	499.05	8.54	499.05	499.05	12.21	432.63
CON3-7	PILS, VLBR, HPSO, ACS	576.48	576.48	576.48	4.26	596.35	601.28	10.86	536.52
CON3-8	PILS, VLBR, HPSO, ACS	523.05	523.05	523.05	3.89	556.31	571.36	10.35	506.37
CON3-9	PILS, VLBR, HPSO, ACS	578.25	578.25	578.25	6.33	623.67	635.73	13.62	576.23
CON8-0	PILS, VLBR, HPSO, ACS	857.17	857.17	857.17	5.40	926.46	942.39	15.36	876.56
CON8-1	PILS, VLBR, HPSO, ACS	740.85	740.85	740.85	8.46	740.85	740.85	15.78	695.35
CON8-2	PILS, VLBR, HPSO, ACS	712.89	712.89	712.89	4.79	763.56	781.22	10.36	713.69
CON8-3	PILS, VLBR, HPSO, ACS	811.07	811.07	811.07	7.21	862.35	873.68	14.36	812.38
CON8-4	PILS, VLBR, HPSO, ACS	772.25	772.25	772.25	6.70	812.65	832.47	15.69	756.24
CON8-5	PILS, VLBR, HPSO, ACS	754.88	754.88	754.88	5.74	754.88	754.88	12.63	703.63
CON8-6	PILS, VLBR, HPSO, ACS	678.92	678.92	678.92	4.36	723.52	736.61	12.53	676.29
CON8-7	PILS, VLBR, HPSO, ACS	811.96	811.96	813.46	8.38	866.76	873.69	20.32	813.53
CON8-8	PILS, VLBR, HPSO, ACS	767.53	767.53	767.53	6.16	813.65	826.63	12.36	763.96
CON8-9	PILS, VLBR, HPSO, ACS	809.00	809.00	809.00	7.19	901.23	923.57	14.23	863.24
G. Avg.					6.13			13.25
BKS found		40	40			9

Note: the best solution of each problem instance is highlighted in bold.
BKS: the best known solution. Ref.: the best solution reference. Best: the best solution in 10 replications.
Avg.: average solution over 10 replications. T: average computation time. G. Avg.: average of 40 instances.
BKS found: number of best solutions found.