Exploring Further Advantages in an Alternative Formulation for the Set Covering Problem

Table 5

RPD metrics, average total execution time, and average number of evaluations obtained during the second study for ABC algorithm.

Instance		d-ABC					n-ABC
				(%)	(%)	(%)			(%)	(%)	(%)
4_1	429	125,808	485	0.82	0.23	0.93	124,122	447	0.23	0.23	0.23
4_2	512	9998	93	0.00	0.00	0.00	8194	76	0.00	0.00	0.00
4_3	516	56027	390	0.00	0.00	0.19	11,191	103	0.00	0.00	0.00
4_4	494	128,399	535	0.20	0.00	0.61	126,209	488	0.20	0.20	0.20
4_5	512	11,161	102	0.00	0.00	0.00	118,961	354	0.39	0.00	0.39
4_6	560	127,988	537	0.36	0.00	0.54	28,428	254	0.00	0.00	0.36
4_7	430	110,922	207	0.93	0.00	1.16	110,224	194	0.70	0.47	0.70
4_8	492	126,117	491	0.20	0.20	0.20	34,292	283	0.00	0.00	0.20
4_9	641	128,322	526	0.94	0.00	2.18	128,276	523	0.47	0.00	0.78
4_10	514	18,162	164	0.00	0.00	0.00	55,670	333	0.00	0.00	0.58
5_1	253	125,020	1797	0.40	0.00	1.58	123,792	1706	0.40	0.00	0.40
5_2	302	127,193	1956	1.99	1.66	2.98	125,859	1856	0.99	0.00	1.32
5_3	226	123,812	1713	1.33	1.33	1.33	123,627	1696	0.88	0.88	0.88
5_4	242	17,751	650	0.00	0.00	0.00	6760	239	0.00	0.00	0.00
5_5	211	14,945	521	0.00	0.00	0.00	7927	277	0.00	0.00	0.00
5_6	213	19,299	684	0.00	0.00	0.00	5575	200	0.00	0.00	0.00
5_7	293	126,401	1924	0.34	0.34	1.02	14,753	547	0.00	0.00	0.00
5_8	288	17,153	652	0.00	0.00	0.00	23,534	814	0.00	0.00	0.00
5_9	279	124,770	1754	0.36	0.36	0.36	8961	316	0.00	0.00	0.00
5_10	265	86,539	1149	0.19	0.00	1.13	12,431	407	0.00	0.00	0.00
6_1	138	124,417	1198	1.45	0.00	2.17	91,269	916	0.36	0.00	1.45
6_2	146	8784	217	0.00	0.00	0.00	6381	156	0.00	0.00	0.00
6_3	145	14,699	359	0.00	0.00	0.00	4776	115	0.00	0.00	0.00
6_4	131	16,928	400	0.00	0.00	0.00	3961	95	0.00	0.00	0.00
6_5	161	13,760	338	0.00	0.00	0.00	4377	106	0.00	0.00	0.00
a_1	253	123,573	5729	0.40	0.40	0.79	122,222	5381	0.40	0.40	0.40
a_2	252	126,016	6309	1.39	0.79	2.38	126,212	6346	0.79	0.00	1.19
a_3	232	126,103	6334	1.29	0.86	1.72	125,826	6189	0.43	0.00	0.86
a_4	234	125,908	6287	0.43	0.43	0.43	124,897	6004	0.43	0.43	0.43
a_5	236	124,785	5948	0.42	0.42	0.42	11,144	1346	0.00	0.00	0.00
b_1	69	120,832	13,012	1.45	0.00	1.45	3970	1228	0.00	0.00	0.00
b_2	76	6962	2054	0.00	0.00	0.00	3372	1043	0.00	0.00	0.00
b_3	80	4170	1296	0.00	0.00	0.00	3572	1106	0.00	0.00	0.00
b_4	79	6166	1932	0.00	0.00	0.00	3965	1227	0.00	0.00	0.00
b_5	72	3172	988	0.00	0.00	0.00	2774	857	0.00	0.00	0.00
c_1	227	121,978	12,589	0.88	0.44	1.76	116,551	9431	0.88	0.88	0.88
c_2	219	110,309	13,899	0.23	0.00	1.37	21,664	6492	0.00	0.00	0.00
c_3	243	126,728	15,246	1.65	0.41	2.47	126,018	14,881	0.82	0.00	2.06
c_4	219	126,196	14,951	0.46	0.00	1.83	28,355	7658	0.00	0.00	0.00
c_5	215	19,075	5434	0.00	0.00	0.00	14,546	4086	0.00	0.00	0.00
d_1	60	5970	4455	0.00	0.00	0.00	7572	5603	0.00	0.00	0.00
d_2	66	121,272	31,555	1.52	1.52	1.52	11,343	8371	0.00	0.00	0.00
d_3	72	122,829	34,063	1.39	1.39	2.78	18,808	13,510	0.00	0.00	0.00
d_4	62	121,976	32,383	1.61	1.61	1.61	4768	3510	0.00	0.00	0.00
d_5	61	109,457	14,077	1.64	1.64	1.64	5090	3690	0.00	0.00	0.00
nre_1	29	27,684	68,066	0.00	0.00	0.00	3479	9634	0.00	0.00	0.00
nre_2	30	119,319	111,213	6.67	6.67	6.67	18,666	51,982	0.00	0.00	3.33
nre_3	27	120,070	115,028	7.41	7.41	7.41	19,339	53,470	0.00	0.00	0.00
nre_4	28	119,063	109,812	10.71	3.57	14.29	10,559	30,055	0.00	0.00	0.00
nre_5	28	118,585	106,781	3.57	3.57	7.14	4053	11,203	0.00	0.00	0.00
nrf_1	14	119,200	230,417	14.29	14.29	14.29	2353	13,741	0.00	0.00	0.00
nrf_2	15	119,831	238,705	13.33	13.33	13.33	1950	11,337	0.00	0.00	0.00
nrf_3	14	119,332	236,611	14.29	14.29	21.43	3929	23,123	0.00	0.00	0.00
nrf_4	14	119,910	241,666	14.29	14.29	14.29	2746	16,074	0.00	0.00	0.00
nrf_5	13	106,580	79,141	15.38	15.38	23.08	120,731	248,033	7.69	7.69	7.69
nrg_1	176	128,776	257,664	2.84	2.27	3.41	126,471	235,636	1.14	0.57	1.70
nrg_2	154	128,678	253,564	3.25	2.60	3.90	126,160	233,168	1.95	1.30	2.60
nrg_3	166	134,516	243,567	3.61	3.01	4.22	124,477	217,781	2.41	1.81	3.01
nrg_4	168	135,789	223,456	3.57	2.98	4.17	125,268	224,757	1.79	1.19	2.38
nrg_5	168	126,782	227,346	4.17	3.57	4.76	126,077	232,047	2.38	2.38	2.98
nrh_1	63	126,421	228,326	3.17	3.17	4.76	145,678	253,467	1.59	1.59	3.17
nrh_2	63	134,282	217,456	3.17	4.76	4.76	155,671	243,457	1.59	1.59	3.17
nrh_3	59	123,481	237,222	3.39	5.08	5.08	132,451	233,245	1.69	1.69	3.39
nrh_4	58	143,562	242,456	3.45	3.45	5.17	142,457	231,002	1.72	1.72	3.45
nrh_5	55	134,612	232,216	3.64	3.64	3.64	143,417	224,452	1.82	1.82	3.64