Degree-Constrained -Minimum Spanning Tree Problem

Table 11

Numerical results obtained with ACO algorithms for random and Euclidean instances using .

#
			Best	Time (s)			Time (s)	#Iter				Time (s)	#Iter
Input graphs with random uniform costs
1	50	10	52.22	0.61	93.69	52.22	54.78	5576	0	259.26	52.22	89.89	2083	0
2		20	134.08	1.61	175.53	135.75	24.58	2551	1.24	955.85	135.75	126.17	2111	1.24
3		30	240.30	1.08	370.28	244.31	26.01	2648	1.66	435.68	245.24	234.25	4437	2.05
4		50	564.37	0.47	684.50	584.18	5.53	561	3.51	2486.65	588.31	48.69	803	4.24
5	100	25	123.71	2.95	163.55	123.71	2.06	67	0	1231.26	123.71	192.91	995	0
6		50	287.78	6.04	337.69	293.90	29.20	975	2.12	2546.91	298.88	339.66	1731	3.85
7		75	529.56	0.84	650.54	550.41	46.00	1533	3.93	3804.55	563.89	220.28	1164	6.48
8		100	915.29	3.34	1093.20	970.43	50.66	1699	6.02	5188.97	1021.63	239.28	1230	11.61
9	200	50	184.29	4.04	279.89	193.34	168.47	1626	4.91	2495.55	198.36	698.71	1093	7.63
10		100	437.08	30.84	546.76	467.76	68.13	657	7.01	4856.80	492.90	258.63	408	12.77
11		150	775.89	18.53	941.43	836.89	9.54	90	7.86	7444.72	870.56	273.53	460	12.20
12		200	1285.32	6.43	1734.02	1480.76	15.91	156	15.20	10277.04	1614.61	321.30	529	25.61
Input graphs with Euclidean distance costs
1	Berlin52	10	279.23	0.51	2195.31	279.23	389.57	42096	0	4581.09	279.23	21.44	351	0
2		20	1015.39	2.09	1270.76	1015.39	2.01	201	0	9757.74	1020.02	72.24	1189	0.45
3		30	2065.12	2.23	2757.23	2065.12	58.28	6258	0	12888.36	2069.90	32.44	535	0.23
4		52	6968.77	0.73	9738.24	7156.65	17.71	1895	2.69	22432.48	7234.27	6.47	106	3.80
5	gr96	25	73.56	621.64	112.78	74.59	144.67	5647	1.40	144.72	74.80	7.65	45	1.68
6		50	168.53	299.41	219.39	172.38	97.18	3811	2.28	546.20	180.29	161.80	984	6.97
7		75	283.14	96.28	379.18	292.20	24.97	966	3.19	609.61	302.66	50.22	302	6.89
8		96	474.95	17.58	619.16	497.06	66.02	2578	4.65	944.82	534.30	320.22	1956	12.49
9	ch150	50	1753.83	3600	2050.39	1678.93	38.58	672	−4.27	18522.68	1722.83	222.95	613	−1.76
10		80	2881.72	3600	3667.84	2843.87	169.47	2972	−1.31	27659.44	2929.44	141.14	394	1.65
11		100	3627.93	279.88	4833.86	3788.26	98.18	1718	4.41	35594.85	3773.76	325.01	908	4.01
12		150	6368.79	43.71	7566.16	6720.31	42.55	742	5.51	52740.44	7005.90	113.50	315	10.00