A Hybrid Demon Algorithm for the Two-Dimensional Orthogonal Strip Packing Problem

Table 8

Results obtained by GRASP, SVC, ISA, and HDA on Nice and Path.

Instance				meanh				Gap
			LB	GRASP	SVC	ISA	HDA	GRASP	SVC	ISA	HDA
Nice1	25	1000	1000	1034	1037	1040.7	1034.8	3.4	3.7	4.1	3.5
Nice2	50	1000	1001	1047	1038	1047.2	1037.7	4.6	3.7	4.6	3.7
Nice3	100	1000	1001	1041	1035	1036.5	1030.9	4.0	3.4	3.5	3.0
Nice4	200	1000	1001	1037	1026	1030.9	1023	3.6	2.5	2.9	2.2
Nice5	500	1000	1000	1024	1017	1015.0	1008	2.4	1.7	1.5	0.8
Nice6	1000	1000	999	1020	1014	1011.0	1004	2.1	1.5	1.2	0.5
Nice1t	1000	1000	1001	1026	1015	1011.0	1006	2.5	1.4	1.0	0.5
	1000	1000	1001	1022	1016	1010.0	1005	2.1	1.5	0.9	0.4
	1000	1000	1000	1020	1013	1011.0	1005	2.0	1.3	1.1	0.5
	1000	1000	1000	1019	1013	1010.0	1005	1.9	1.3	1.0	0.5
	1000	1000	1000	1022	1014	1010.0	1005	2.2	1.4	1.0	0.5
	1000	1000	1001	1020	1014	1010.0	1005	1.9	1.3	0.9	0.4
	1000	1000	1000	1022	1014	1010.0	1006	2.2	1.4	1.0	0.6
	1000	1000	1001	1021	1016	1012.0	1007	2.0	1.5	1.1	0.6
	1000	1000	1000	1022	1017	1012.0	1005	2.2	1.7	1.2	0.5
	1000	1000	1001	1027	1016	1012.0	1007	2.6	1.5	1.1	0.6
Nice2t	2000	1000	1001	1016	1008	1006.0	1004	1.5	0.7	0.5	0.3
	2000	1000	1001	1015	1011	1005.0	1005	1.4	1.0	0.4	0.4
	2000	1000	1000	1016	1008	1007.0	1005	1.6	0.8	0.7	0.5
	2000	1000	1000	1014	1007	1006.0	1003	1.4	0.7	0.6	0.3
	2000	1000	1000	1015	1008	1006.0	1003	1.5	0.8	0.6	0.3
	2000	1000	1000	1016	1002	1005.0	1004	1.6	0.2	0.5	0.4
	2000	1000	1001	1016	1007	1007.0	1004	1.5	0.6	0.6	0.3
	2000	1000	1001	1014	1006	1006.0	1003	1.3	0.5	0.5	0.2
	2000	1000	1001	1016	1008	1007.0	1006	1.5	0.7	0.6	0.5
	2000	1000	1001	1016	1009	1007.0	1005	1.5	0.8	0.6	0.4
Nice5t	5000	1000	1000	1010	1003	1003.0	1003	1.0	0.3	0.3	0.3
	5000	1000	1001	1011	1005	1003.0	1003	1.0	0.4	0.2	0.2
	5000	1000	1001	1010	1002	1003.0	1003	0.9	0.1	0.2	0.2
	5000	1000	1000	1009	1005	1002.0	1003	0.9	0.5	0.2	0.3
	5000	1000	1001	1011	1006	1003.0	1004	1.0	0.5	0.2	0.3
	5000	1000	1000	1009	1001	1002.0	1001	0.9	0.1	0.2	0.1
	5000	1000	1001	1011	1004	1003.0	1003	1.0	0.3	0.2	0.2
	5000	1000	1000	1011	1004	1002.0	1003	1.1	0.4	0.2	0.3
	5000	1000	1001	1010	1004	1003.0	1003	0.9	0.3	0.2	0.2
	5000	1000	1000	1010	1005	1003.0	1003	1.0	0.5	0.3	0.3
Path1	25	1000	1001	1042	1042	1042.0	1041.8	4.1	4.1	4.1	4.1
Path2	50	1000	1000	1019	1014	1014.7	1011.9	1.9	1.4	1.5	1.2
Path3	100	1000	1000	1027	1022	1022.6	1025.1	2.7	2.2	2.3	2.5
Path4	200	1000	1002	1023	1018	1017.7	1013	2.1	1.6	1.6	1.1
Path5	500	1000	1000	1034	1022	1020.0	1016	3.4	2.2	2.0	1.6
Path6	1000	1000	1002	1026	1018	1011.0	1010	2.4	1.6	0.9	0.8
Path1t	1000	1000	999	1019	1011	1007.0	1003	2.0	1.2	0.8	0.4
	1000	1000	1001	1018	1010	1006.0	1005	1.7	0.9	0.5	0.4
	1000	1000	1001	1018	1013	1008.0	1006	1.7	1.2	0.7	0.5
	1000	1000	1000	1016	1009	1006.0	1003	1.6	0.9	0.6	0.3
	1000	1000	1003	1024	1017	1010.0	1010	2.1	1.4	0.7	0.7
	1000	1000	1002	1018	1013	1010.0	1005	1.6	1.1	0.8	0.3
	1000	1000	999	1019	1012	1008.0	1004	2.0	1.3	0.9	0.5
	1000	1000	1000	1020	1012	1008.0	1006	2.0	1.2	0.8	0.6
	1000	1000	999	1019	1012	1006.0	1003	2.0	1.3	0.7	0.4
	1000	1000	1002	1018	1011	1008.0	1006	1.6	0.9	0.6	0.4
Path2t	2000	1000	1000	1015	1009	1006.0	1002	1.5	0.9	0.6	0.2
	2000	1000	1002	1016	1010	1007.0	1004	1.4	0.8	0.5	0.2
	2000	1000	1000	1015	1011	1006.0	1003	1.5	1.1	0.6	0.3
	2000	1000	999	1014	1007	1003.0	1000	1.5	0.8	0.4	0.1
	2000	1000	1002	1018	1012	1008.0	1006	1.6	1.0	0.6	0.4
	2000	1000	1002	1016	1011	1007.0	1003	1.4	0.9	0.5	0.1
	2000	1000	998	1011	1007	1004.0	1001	1.3	0.9	0.6	0.3
	2000	1000	998	1014	1010	1004.0	1003	1.6	1.2	0.6	0.5
	2000	1000	1001	1017	1010	1008.0	1003	1.6	0.9	0.7	0.2
	2000	1000	1003	1018	1009	1009.0	1005	1.5	0.6	0.6	0.2
Path5t	5000	1000	1000	1010	1002	1003.0	1001	1.0	0.2	0.3	0.1
	5000	1000	998	1009	1003	1001.0	1001	1.1	0.5	0.3	0.3
	5000	1000	1000	1011	1002	1003.0	1002	1.1	0.2	0.3	0.2
	5000	1000	995	1006	998	997.0	997	1.1	0.3	0.2	0.2
	5000	1000	1004	1016	1005	1006.0	1006	1.2	0.1	0.2	0.2
	5000	1000	1000	1009	1003	1002.0	1001	0.9	0.3	0.2	0.1
	5000	1000	998	1009	1001	1001.0	1000	1.1	0.3	0.3	0.2
	5000	1000	996	1007	998	999.0	998	1.1	0.2	0.3	0.2
	5000	1000	997	1007	999	999.0	998	1.0	0.2	0.2	0.1
	5000	1000	1002	1013	1004	1004.0	1005	1.1	0.2	0.2	0.3
Average				1016.63	1009.75	1007.36	1006.57	1.65	0.96	0.72	0.63