Solving the Set Packing Problem via a Maximum Weighted Independent Set Heuristic

Table 2

Comparison of each algorithm on instances with 500 and 1000 variables.

Instance	Characteristics					CPLEX	GRASP			ACO			EA/G; C			DLSWC
	Var	Cnst	Density (%)	M_one	Weight	Opt	Best	Avrg	ATET	Best	Avrg	ATET	Best	Avrg	ATET	Best	Avrg	ATET	Hit
pb500rand01	500	2500	1.20	10	[1-20]	323	323	319.38	32.08	323	319.87	154.67	323	321.31	7.03	323	323	1.07	16
pb500rand02	500	2500	1.20	10	[1-1]	24	24	23.69	25.62	24	23.06	26.67	25	23.56	5.16	25	25	1.58	16
pb500rand03	500	2500	0.70	5	[1-20]	776	772	767.63	70.33	776	772.75	244.00	776	771.38	10.61	776	776	0.38	16
pb500rand04	500	2500	0.70	5	[1-1]	61	61	60.13	57.30	61	60.06	69.00	62	60.38	6.06	62	62	0.34	16
pb500rand05	500	2500	2.20	20	[1-20]	122	122	121.5	15.48	122	120.62	71.00	122	121.56	3.92	122	122	4.71	16
pb500rand06	500	2500	2.20	20	[1-1]	8	8	8	12.08	8	7.87	99.67	8	7.88	2.27	8	8	4.82	16
pb500rand07	500	500	1.20	10	[1-20]	1141	1141	1141	13.43	1141	1141	960.00	1141	1139.94	9.64	1141	1141	0.13	16
pb500rand08	500	500	1.20	10	[1-1]	89	89	88.25	15.80	89	88.12	21.67	89	88.94	4.75	89	89	0.08	16
pb500rand09	500	500	0.70	5	[1-20]	2236	2235	2235	23.44	2236	2234.43	84.33	2236	2232.81	12.49	2236	2236	0.16	16
pb500rand10	500	500	0.70	5	[1-1]	179	179	178.06	18.20	179	178.31	44.67	179	178.56	6.12	179	179	0.06	16
pb500rand11	500	500	2.30	20	[1-20]	424	423	419.31	19.25	424	418.25	37.33	424	421.56	7.92	424	424	1.00	16
pb500rand12	500	500	2.20	20	[1-1]	33	33	33	11.91	33	32.62	8.00	33	32.88	4.00	33	33	0.53	16
pb500rand13	500	1500	1.20	10	[1-20]	474	474	470	32.88	474	468	105.00	474	468.56	8.90	474	474	0.51	16
pb500rand14	500	1500	1.20	10	[1-1]	37	37	36.94	20.77	37	36.5	25.66	38	36.88	4.39	38	38	0.65	16
pb500rand15	500	1500	0.70	5	[1-20]	1196	1196	1186.9	59.36	1196	1190.93	161.67	1196	1185.62	10.68	1196	1196	0.15	16
pb500rand16	500	1500	0.70	5	[1-1]	88	88	86.63	36.31	88	86.12	60.67	88	87	5.12	88	88	0.15	16
pb500rand17	500	1500	2.20	20	[1-20]	192	192	191.75	18.38	192	188.31	57.00	192	191.38	5.55	192	192	2.64	16
pb500rand18	500	1500	2.20	20	[1-1]	13	13	13	12.03	13	12.43	9.00	13	12.81	2.85	13	13	2.66	16
pb1000rand1	1000	5000	2.60	50	[1-20]	67	67	65.5	53.50	67	64	117.67	67	67	10.64	67	67	129.66	16
pb1000rand2	1000	5000	2.59	50	[1-1]	4	4	3.15	39.30	4	3.81	15.00	4	3.44	3.58	4	4	131.08	16
pb1000rand3	1000	5000	0.60	10	[1-20]	661	649	639.5	221.20	661	640.5	700.67	661	642.81	32.92	661	661	6.41	16
pb1000rand4	1000	5000	0.60	10	[1-1]	48	48	46.83	149.70	47	45.06	108.33	48	46.5	18.12	48	48	6.29	16
pb1000rand5	1000	1000	2.60	50	[1-20]	222	222	217.98	64.80	222	219.62	85.67	222	217.88	23.11	222	222	46.62	16
pb1000rand6	1000	1000	2.65	50	[1-1]	15	14	13.68	41.40	15	13.37	8.00	15	14.06	12.03	15	15	59.52	16
pb1000rand7	1000	1000	0.58	10	[1-20]	2260	2222	2214.1	119.70	2248	2239.56	296.67	2253	2242.06	44.48	2260	2259	8.66	7
pb1000rand8	1000	1000	0.60	10	[1-1]	175	172	170.81	82.60	173	170.5	94.00	174	172.62	21.21	175	175	2.93	16
Avrg						418.00	415.69	413.53	48.73	417.42	414.45	141.00	417.81	414.98	10.91	418.12	418.06	15.88	15.65