Table 6 The test results of the algorithms on benchmark DIMACS graphs.

From: An efficient swarm evolution algorithm with probability learning for the black and white coloring problem

Instance	\|V\|	b	Swarm-E-1			Swarm-E-2			VNS1			VNS2
Instance	\|V\|	b	best	avg	time(s)	best	avg	time(s)	best	avg	time(s)	best	avg	time(s)
anna.col	138	10	*127*	127	54.54	*127*	127	4.49	126	124	1296.60	126	124	970.73
david.col	87	5	81	81	20.13	81	81	< *0.01*	81	81	0.42	81	81	0.27
DSJC125.1.col	125	12	72	72	*1.03*	69	68	744.68	62	60	853.67	63	61	644.72
DSJC125.5.col	125	12	7	6	799.64	5	4	459.08	4	3	836.85	4	3	928.93
DSJC125.9.col	125	3	4	4	*0.07*	4	3	603.95	4	4	2.07	4	4	2.91
fpsol2.i.1.col	496	20	*476*	429	34.29	*476*	476	*0.11*	*476*	464	789.68	*476*	468	613.54
fpsol2.i.2.col	451	20	*431*	422	348.52	*431*	431	*0.11*	401	396	769.30	399	396	500.71
fpsol2.i.3.col	425	20	*405*	394	457.41	*405*	405	*0.10*	373	368	563.29	369	366	969.02
games120.col	120	10	*106*	106	59.88	*106*	106	4.87	97	90	742.78	95	89	1209.73
homer.col	561	25	534	529	88.11	*535*	535	*251.65*	519	516	737.72	520	516	65.27
huck.col	74	5	69	68	713.78	69	69	85.74	69	69	65.96	69	69	89.89
inithx.i.1.col	864	30	*834*	791	502.56	*834*	834	*0.62*	797	779	1517.17	798	777	1340.81
inithx.i.2.col	645	30	*615*	584	258.18	*615*	615	*0.33*	550	542	1199.43	549	543	983.57
inithx.i.3.col	621	30	*591*	564	509.48	*591*	591	*0.29*	520	515	1769.25	523	516	102.15
jean.col	80	6	73	73	72.62	73	73	< *0.01*	73	73	3.45	73	73	9.39
latin_square_10.col	900	5	*126*	85	824.31	*126*	120	436.94	90	90	193.05	*126*	93	702.97
le450_5a.col	450	25	*262*	255	*152.35*	204	200	854.54	168	157	1042.90	168	157	516.66
le450_5b.col	450	25	*262*	251	*18.28*	202	190	967.89	159	155	388.96	164	156	1576.90
le450_5c.col	450	25	*214*	205	*91.52*	98	91	1403.28	91	81	494.93	95	83	1751.55
le450_5d.col	450	25	*218*	208	*170.73*	113	104	587.48	91	83	502.14	94	86	1101.46
le450_15b.col	450	25	*315*	312	*219.47*	304	301	1319.66	161	153	1777.96	163	152	1701.85
le450_15c.col	450	25	*121*	118	*160.54*	65	63	823.56	39	36	1169.35	40	36	1166.79
le450_15d.col	450	25	*115*	110	*21.92*	68	66	1143.43	39	36	950.02	40	36	1.14
le450_25a.col	450	25	*363*	356	*292.63*	358	356	934.74	209	196	1448.50	207	195	554.57
le450_25b.col	450	25	348	317	242.11	344	344	0.44	200	188	1332.89	199	187	617.28
le450_25c.col	450	25	*182*	178	179.82	132	128	833.76	59	51	743.86	61	52	359.77
le450_25d.col	450	25	*174*	169	*239.22*	118	113	145.92	53	48	243.52	51	47	1039.16
miles250.col	128	8	*120*	120	34.91	*120*	120	60.79	118	116	813.57	118	116	663.35
miles500.col	128	8	*117*	117	276.13	113	111	772.76	112	109	803.82	112	109	908.16
miles750.col	128	8	*110*	109	785.45	108	108	0.02	106	104	741.84	105	103	862.90
miles1000.col	128	8	*102*	102	194.73	101	101	0.01	101	100	1013.15	101	99	753.85
miles1500.col	128	8	93	83	590.51	93	92	585.08	91	87	246.72	92	84	1231.09
mulsol.i.1.col	197	11	*186*	186	1.31	*186*	186	*0.01*	*186*	186	35.30	*186*	186	50.01
mulsol.i.2.col	188	11	*177*	177	70.01	*177*	177	*0.01*	154	149	1279.01	153	148	91.62
mulsol.i.3.col	184	11	*155*	155	18.94	*155*	155	*0.02*	145	142	1735.00	149	143	1734.25
mulsol.i.4.col	185	11	*156*	156	53.68	*156*	156	*0.01*	148	143	783.76	148	143	158.61
mulsol.i.5.col	186	11	*157*	157	11.18	*157*	157	*0.01*	150	145	958.93	148	144	1109.69
myciel3.col	11	2	5	5	< *0.01*	5	5	< *0.01*	5	5	< *0.01*	5	5	< *0.01*
myciel4.col	23	2	16	16	< *0.01*	16	16	< *0.01*	16	16	< *0.01*	16	16	< *0.01*
myciel5.col	47	2	39	39	< *0.01*	39	39	< *0.01*	39	39	< *0.01*	39	39	< *0.01*
myciel6.col	95	2	86	86	< *0.01*	86	86	< *0.01*	86	86	< *0.01*	86	86	< *0.01*
myciel7.col	191	5	*176*	176	0.05	*176*	176	*0.01*	*176*	174	696.41	*176*	173	193.96
queen5_5.col	25	2	7	7	< *0.01*	7	7	< *0.01*	7	7	< *0.01*	7	7	< *0.01*
queen6_6.col	36	2	13	13	< *0.01*	13	13	< *0.01*	13	13	< *0.01*	13	13	< *0.01*
queen7_7.col	49	2	21	21	< *0.01*	21	21	< *0.01*	21	21	< *0.01*	21	21	< *0.01*
queen8_8.col	64	2	31	31	< *0.01*	31	31	< *0.01*	31	31	< *0.01*	31	31	< *0.01*
queen8_12.col	96	2	58	58	22.65	58	58	104.78	58	58	< *0.01*	58	58	< *0.01*
queen9_9.col	81	2	43	43	< *0.01*	43	43	< *0.01*	43	43	< *0.01*	43	43	< *0.01*
queen10_10.col	100	5	37	37	*0.05*	37	36	887.24	37	37	95.07	37	37	117.08
queen11_11.col	121	5	51	51	*0.36*	51	50	827.10	51	51	143.44	51	51	135.04
queen12_12.col	144	5	65	65	*0.11*	64	63	640.15	65	64	471.63	65	64	650.10
queen13_13.col	169	5	83	83	*1.48*	83	80	1071.78	83	82	337.44	83	82	599.33
queen14_14.col	196	5	*101*	101	*0.31*	100	97	989.88	*101*	100	1035.30	*101*	100	850.70
queen15_15.col	225	5	*123*	123	*13.03*	*123*	116	888.20	*123*	122	681.90	*123*	121	523.89
queen16_16.col	256	5	*145*	145	*0.74*	144	135	630.27	144	143	575.01	*145*	144	589.45
school1.col	385	7	*377*	377	46.90	*377*	377	*0.04*	366	339	413.20	363	342	1226.57
school1_nsh.col	352	7	*344*	344	3.68	*344*	344	*0.03*	334	309	447.73	331	301	15.29
zeroin.i.1.col	211	7	*204*	204	117.53	*204*	204	*0.01*	*204*	204	0.03	*204*	204	0.03
zeroin.i.2.col	211	7	*204*	204	39.11	*204*	204	*0.01*	*204*	204	0.37	*204*	204	0.36
zeroin.i.3.col	206	7	*199*	199	54.87	*199*	199	*0.01*	*199*	199	0.56	*199*	199	0.42

Instance	\|V\|	b	SA			Greedy_One			Greedy_Two
Instance	\|V\|	b	best	avg	time(s)	best	avg	time(s)	best	avg	time(s)
anna.col	138	10	*127*	127	14.13	118	116	1045.85	*127*	127	*0.02*
david.col	87	5	81	81	0.14	76	76	20.33	81	81	< *0.01*
DSJC125.1.col	125	12	72	72	28.68	42	42	165.61	62	62	0.02
DSJC125.5.col	125	12	7	7	*433.39*	2	1	664.17	0	0	–
DSJC125.9.col	125	3	4	4	2.56	1	1	0.11	0	0	–
fpsol2.i.1.col	496	20	*476*	476	17.06	448	426	557.55	*476*	476	7.38
fpsol2.i.2.col	451	20	*431*	431	71.12	407	406	1031.18	*431*	431	4.19
fpsol2.i.3.col	425	20	*405*	405	158.46	381	380	437.35	*405*	405	3.79
games120.col	120	10	*106*	106	*4.76*	65	65	64.82	71	71	0.01
homer.col	561	25	534	533	520.94	500	494	96.78	534	534	1.15
huck.col	74	5	69	69	*0.84*	61	61	47.25	66	66	< 0.01
inithx.i.1.col	864	30	*834*	834	69.13	803	797	249.45	*834*	834	29.16
inithx.i.2.col	645	30	*615*	611	776.12	588	586	766.88	*615*	615	14.68
inithx.i.3.col	621	30	*591*	572	931.52	564	563	796.85	*591*	591	13.93
jean.col	80	6	73	73	0.42	64	64	14.76	73	73	< *0.01*
latin_square_10.col	900	5	*126*	126	*14.22*	*126*	91	612.73	0	0	–
le450_5a.col	450	25	*262*	261	1238.75	146	142	619.58	194	194	3.11
le450_5b.col	450	25	*262*	260	930.88	131	124	263.85	176	176	3.10
le450_5c.col	450	25	*214*	212	802.30	64	59	917.93	80	80	5.99
le450_5d.col	450	25	*218*	216	739.85	81	75	1101.01	71	71	5.99
le450_15b.col	450	25	*315*	314	380.38	107	92	1382.70	288	288	5.19
le450_15c.col	450	25	*121*	120	824.66	21	18	1494.23	50	50	12.87
le450_15d.col	450	25	113	110	1280.44	21	18	918.43	56	56	12.98
le450_25a.col	450	25	*363*	363	316.00	164	152	580.62	333	333	5.51
le450_25b.col	450	25	*352*	351	*1130.93*	142	137	1199.34	314	314	5.44
le450_25c.col	450	25	*182*	179	*417.01*	39	32	1769.07	124	124	14.44
le450_25d.col	450	25	*174*	172	391.39	34	30	898.71	108	108	14.33
miles250.col	128	8	*120*	120	*5.62*	98	98	65.96	114	114	< 0.01
miles500.col	128	8	*117*	117	*49.33*	83	80	933.12	94	94	0.02
miles750.col	128	8	*110*	110	*49.49*	57	54	844.27	80	80	0.14
miles1000.col	128	8	*102*	102	*14.81*	35	32	1428.63	40	40	0.28
miles1500.col	128	8	93	93	*116.23*	3	3	248.48	91	91	0.39
mulsol.i.1.col	197	11	*186*	186	6.97	*186*	156	1107.68	*186*	186	0.47
mulsol.i.2.col	188	11	*177*	177	41.94	147	147	106.01	*177*	177	0.41
mulsol.i.3.col	184	11	*155*	155	21.12	143	142	406.22	*155*	155	0.38
mulsol.i.4.col	185	11	*156*	156	23.52	144	144	532.82	*156*	156	0.39
mulsol.i.5.col	186	11	*157*	157	28.02	145	144	644.59	*157*	157	0.41
myciel3.col	11	2	5	5	1.86	5	5	< *0.01*	4	4	< 0.01
myciel4.col	23	2	16	16	< *0.01*	16	16	< *0.01*	15	15	< 0.01
myciel5.col	47	2	39	39	< *0.01*	39	39	< *0.01*	38	38	< 0.01
myciel6.col	95	2	86	86	< *0.01*	86	86	0.02	85	85	< 0.01
myciel7.col	191	5	*176*	176	2.03	172	172	1.45	*176*	176	0.11
queen5_5.col	25	2	7	7	41.97	7	7	0.01	6	6	< 0.01
queen6_6.col	36	2	13	13	< *0.01*	13	13	0.02	10	10	< 0.01
queen7_7.col	49	2	21	21	16.36	21	21	0.06	18	18	< 0.01
queen8_8.col	64	2	31	31	< *0.01*	31	31	0.07	27	27	< 0.01
queen8_12.col	96	2	58	58	< *0.01*	58	58	0.02	56	56	< 0.01
queen9_9.col	81	2	43	43	56.90	43	43	0.18	40	40	< 0.01
queen10_10.col	100	5	37	37	6.28	31	31	36.78	24	24	0.02
queen11_11.col	121	5	51	51	26.53	43	43	69.24	33	33	0.03
queen12_12.col	144	5	65	65	12.08	57	57	102.02	43	43	0.06
queen13_13.col	169	5	83	83	72.57	73	73	162.75	64	64	0.10
queen14_14.col	196	5	*101*	101	29.31	91	91	196.82	73	73	0.15
queen15_15.col	225	5	*123*	123	214.86	111	111	256.45	93	93	0.24
queen16_16.col	256	5	*145*	145	30.17	133	133	171.35	111	111	0.27
school1.col	385	7	*377*	377	43.33	293	293	27.27	314	314	1.42
school1_nsh.col	352	7	*344*	344	24.66	271	271	20.31	278	278	0.97
zeroin.i.1.col	211	7	*204*	204	0.02	*204*	204	3.44	*204*	204	0.13
zeroin.i.2.col	211	7	*204*	204	0.36	*204*	204	4.64	*204*	204	0.10
zeroin.i.3.col	206	7	*199*	199	0.36	*199*	199	7.56	*199*	199	0.09

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Table 6 The test results of the algorithms on benchmark DIMACS graphs.

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