Solving a Large-Scale Multi-Depot Vehicle Scheduling Problem in Urban Bus Systems

Table 1

Computational results for test instances with different number of timetabled trips.

Test Number	Number of timetabled; trips	Total Cost (RMB)		Quality Gap ()	Computational Time(min)		Efficiency Ratio
		LNS(Cl)	BP(Cb)		LNS(Tl)	BP(Tb)
NO. 1	500	151327	150844	0.32	6.0	17.7	2.95
	1000	306801	305670	0.37	36.8	111.1	3.02
	1500	463116	460629	0.54	104.4	380.0	3.64
	2000	605876	600516	0.89	153.1	597.1	3.90
NO. 2	500	167877	167408	0.28	6.7	19.3	2.88
	1000	325414	324021	0.43	36.7	110.8	3.02
	1500	468142	465026	0.67	101.9	379.1	3.72
	2000	588228	582392	1.00	151.8	567.7	3.74
NO. 3	500	159752	159274	0.30	7.4	20.8	2.81
	1000	335644	334573	0.32	35.6	104.0	2.92
	1500	448323	445457	0.64	104.9	377.6	3.60
	2000	631646	625950	0.91	150.4	562.5	3.74
NO. 4	500	161611	160999	0.38	7.8	23.4	3.00
	1000	306715	305493	0.40	34.5	102.1	2.96
	1500	426785	423881	0.69	108.4	396.7	3.66
	2000	619895	614609	0.86	162.8	613.8	3.77
NO. 5	500	165670	164944	0.44	6.5	18.9	2.91
	1000	309025	307641	0.45	38.2	114.2	2.99
	1500	466090	463218	0.62	114.7	410.6	3.58
	2000	664978	658492	0.98	154.2	573.6	3.72
NO. 6	500	149889	149381	0.34	6.9	19.5	2.83
	1000	318111	317160	0.30	35.0	103.6	2.96
	1500	414619	411818	0.68	104.7	383.2	3.66
	2000	629447	623647	0.93	152.6	567.7	3.72
NO. 7	500	167467	166717	0.45	7.6	21.9	2.88
	1000	314987	313701	0.41	36.8	109.3	2.97
	1500	459879	456909	0.65	117.0	437.6	3.74
	2000	673854	668001	0.88	166.3	623.6	3.75
NO. 8	500	156926	156441	0.31	7.0	19.9	2.84
	1000	313965	312652	0.42	40.5	123.1	3.04
	1500	458466	455279	0.70	110.3	401.5	3.64
	2000	630643	624708	0.95	164.2	635.5	3.87
NO. 9	500	157143	156642	0.32	7.0	20.6	2.94
	1000	318107	317092	0.32	39.4	117.8	2.99
	1500	467748	465143	0.56	103.6	371.9	3.59
	2000	623549	617987	0.90	161.2	617.4	3.83
NO. 10	500	162175	161658	0.32	5.9	16.8	2.85
	1000	310107	308995	0.36	36.1	105.4	2.92
	1500	474581	471985	0.55	111.8	413.7	3.7
	2000	629727	623369	1.02	160.6	611.9	3.81