High-Speed Rail Train Timetabling Problem: A Time-Space Network Based Method with an Improved Branch-and-Price Algorithm

Table 2

Solving Statistics for 9 instances.

#	Network	Period	Train numbers	CPU time (s)				Solution
				Cplex	RHA	GBAP	IBAP	Cplex	RHA	GBAP	IBAP
1	(10, 9)	5	40	331	175	302	241	62300	5923	5802	5451
2	(10, 9)	10	80	657	235	398	354	122501	11323	10689	9878
3	(10, 9)	17	140	—	422	525	467	—	24432	23490	23412
4	(23, 22)	5	40	—	446	464	347	—	14981	13821	13323
5	(23, 22)	10	80	—	876	678	543	—	25234	24723	24591
6	(23, 22)	17	140	—	1113	796	686	—	51234	50321	49943
7	(40, 39)	5	40	—	1042	987	826	—	25189	24890	23414
8	(40, 39)	10	80	—	2283	1531	953	—	46903	46667	45594
9	(40, 39)	17	140	—	3225	1825	1221	—	86443	85564	82432