Mathematical Problems in Engineering

Research Article

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

Table 6

Comparisons of the optimization results of test example 2 with 22 customers.


Algorithms	Vehicle path	Fuel consumption/kg	Waiting time/min	Distance/km	Average computing time/min

T-NSGA-II	0-1-4-7-11-19-13-2-6-22-0 0-18-14-21-5-9-20-0 0-15-3-16-12-8-10-17-0	702.56	109.37	708.43	2.5
	0-4-15-7-11-19-2-13-6-22-0 0-18-14-21-5-9-16-0 0-1-3-20-12-8-10-17-0	654.17	125.09	676.71
	0-4-15-7-11-19-2-13-6-22-0 0-18-14-21-5-9-16-0 0-1-20-3-12-8-10-17-0	652.72	141.55	678.08
	0-4-15-11-7-19-2-13-6-22-0 0-18-14-21-5-9-16-0 0-1-3-20-12-8-10-17-0	650.68	150.43	680.65
	0-4-15-11-19-1-13-2-6-22-0 0-18-14-21-5-9-20-0 0-3-7-16-12-8-10-17-0	698.33	96.99	712.65
	0-4-15-19-11-1-13-2-6-22-0 0-18-14-21-5-9-20-0 0-3-7-16-12-8-10-17-0	695.59	122.56	714.06
	0-4-15-19-11-7-2-13-6-22-0 0-18-14-21-5-9-16-0 0-1-3-20-12-8-10-17-0	644.90	161.72	676.88
	0-4-15-19-11-7-2-13-6-22-0 0-18-14-21-5-9-16-0 0-1-20-3-12-8-10-17-0	643.45	178.18	678.25
	0-4-15-19-11-7-2-13-6-22-0 0-18-14-21-9-5-16-0 0-1-3-20-12-8-10-17-0	644.72	168.08	683.36
	0-4-15-19-11-7-2-13-6-22-0 0-18-14-21-9-5-16-0 0-1-20-3-12-8-10-17-0	643.26	184.54	684.73
W-BEG-NSGA-II	0-3-8-12-17-9-13-21-0 0-4-7-11-19-20-16-0 0-1-5-14-10-2-6-22-15-18-0	597.48	70.17	591.05	1.6
	0-3-8-12-17-9-13-21-0 0-4-7-11-19-20-16-0 0-1-14-5-10-2-6-22-15-18-0	631.29	66.56	620.02
	0-3-8-12-17-9-13-21-0 0-4-11-7-19-16-20-0 0-1-5-14-10-2-6-22-15-18-0	590.77	70.17	593.94
	0-3-8-12-17-9-13-21-0 0-4-11-7-19-16-20-0 0-1-14-5-10-2-6-22-15-18-0	624.58	66.56	622.91
	0-3-8-12-17-9-13-21-0 0-4-19-7-11-16-20-0 0-1-5-14-10-2-6-22-15-18-0	599.79	73.82	588.29
	0-3-8-12-17-9-13-21-0 0-4-19-11-7-16-20-0 0-1-5-14-10-2-6-22-15-18-0	585.67	75.06	589.56
	0-3-8-12-17-9-13-21-0 0-4-19-11-7-20-16-0 0-1-5-14-10-2-6-22-15-18-0	585.60	82.61	588.27
	0-4-11-7-19-16-20-0 0-3-8-12-17-9-13-21-0 0-1-5-14-10-2-6-22-15-18-0	590.77	70.17	593.94
	0-4-11-7-19-16-20-0 0-3-8-12-17-9-13-21-0 0-1-14-5-10-2-6-22-15-18-0	624.58	66.56	622.91
	0-4-19-7-11-20-16-0 0-3-8-12-17-9-13-21-0 0-1-5-14-10-2-6-22-15-18-0	599.76	80.99	586.63
	0-4-19-11-7-16-20-0 0-3-8-12-17-9-13-21-0 0-1-5-14-10-2-6-22-15-18-0	585.67	75.06	589.56
	0-4-19-11-7-16-20-0 0-3-12-8-17-9-13-21-0 0-1-5-14-10-2-6-22-15-18-0	585.60	81.80	594.75
BEG-NSGA-II	0-4-15-2-10-6-22-18-14-0 0-1-17-16-3-11-19-0 0-9-13-21-5-12-8-7-20-0	544.83	147.38	569.64	0.9
	0-4-15-2-10-6-22-18-14-0 0-9-17-3-16-11-19-0 0-1-13-21-5-12-8-7-20-0	543.80	147.15	570.21
	0-4-15-2-10-6-22-18-14-0 0-9-17-16-3-11-19-0 0-1-13-21-5-12-8-7-20-0	540.38	159.78	569.18
	0-4-15-2-10-6-22-18-14-0 0-17-9-16-3-11-19-0 0-1-13-21-5-12-8-7-20-0	537.94	164.41	572.82
	0-4-15-2-10-14-6-22-18-0 0-1-17-3-16-11-19-0 0-9-13-21-5-12-8-7-20-0	546.79	47.91	572.21
	0-4-15-2-10-14-6-22-18-0 0-1-17-16-3-11-19-0 0-9-13-21-5-12-8-7-20-0	543.37	60.54	571.17
	0-4-15-2-10-14-6-22-18-0 0-3-9-17-16-11-19-0 0-1-13-21-5-12-8-7-20-0	542.87	0	583.29
	0-4-15-2-10-14-6-22-18-0 0-3-16-17-9-11-19-0 0-1-13-21-5-12-8-7-20-0	539.74	0	584.11
	0-4-15-2-10-14-6-22-18-0 0-3-17-9-16-11-19-0 0-1-13-21-5-12-8-7-20-0	537.20	0	584.27
	0-4-15-2-10-14-6-22-18-0 0-9-17-3-16-11-19-0 0-1-13-21-5-12-8-7-20-0	542.34	60.31	571.75

Note: (a) “” meant that the marked result dominates the results of T-NSGA-II.
(b) “” meant that the marked result dominates the results of W-BEG-NSGA-II.
(c) “” meant that the marked result dominates the results of T-NSGA-II and W-BEG-NSGA-II simultaneously.