Degree-Constrained -Minimum Spanning Tree Problem

Table 9

Numerical results obtained with VNS 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	46.86	0.80	254.76	48.27	6.06	13842	3.00	208.73	46.86	0.62	1620	0
2		20	113.97	0.73	266.68	118.53	22.80	7213	4.00	353.48	116.07	8.29	2796	1.84
3		30	204.35	1.67	338.03	206.35	46.51	3674	0.97	326.75	205.43	30.49	2503	0.52
4		50	459.09	1.00	463.14	463.14	0.08	1	0.88	463.14	463.14	0.08	1	0.88
5	100	25	115.44	1.79	352.14	115.44	115.10	23826	0	413.40	118.77	18.59	8854	2.88
6		50	263.95	6.43	564.30	269.18	61.89	2962	1.98	517.86	265.42	86.41	7382	0.55
7		75	454.44	5.04	600.65	465.48	197.61	2681	2.42	659.23	456.59	215.46	4098	0.47
8		100	749.75	22.56	749.87	749.87	0.25	1	0.01	749.87	749.87	0.24	1	0.01
9	200	50	162.55	10.39	555.42	179.98	1857.83	63640	10.72	463.99	169.38	477.84	18728	4.20
10		100	378.43	506.06	725.35	395.98	2928.53	12324	4.63	763.28	386.12	1657.52	9194	2.03
11		150	652.86	1663.29	883.28	721.07	1250.91	912	10.44	926.60	670.36	1130.82	872	2.68
12		200	1049.25	505.27	1056.34	1056.34	3.98	1	0.67	1056.34	1056.34	3.90	1	0.67
Input graphs with Euclidean distance costs
1	Berlin52	10	274.46	0.82	1976.48	274.46	1.41	5959	0	1645.70	274.46	0.09	470	0
2		20	926.77	2.15	3923.04	926.77	2.69	7382	0	3161.01	926.77	0.36	820	0
3		30	1935.71	2.31	4961.30	2104.32	5.29	5133	8.71	4484.23	2071.97	178.34	193048	7.03
4		52	6081.63	2	6081.63	6081.63	0.01	1	0	6081.63	6081.63	0.00	1	0
5	gr96	25	72.40	268.87	204.00	79.28	122.54	230336	9.50	247.07	74.14	271.89	508583	2.40
6		50	162.80	250.78	307.92	179.50	74.78	34094	10.25	260.74	163.70	2.74	1163	0.55
7		75	267.57	109.28	388.13	269.88	20.97	3049	0.86	372.46	267.57	141.16	21176	0
8		96	436.23	42.30	436.23	436.23	0.02	1	0	436.23	436.23	0.01	1	0
9	ch150	50	1567.77	921.27	3441.77	1716.09	348.67	154734	9.46	3290.91	1696.06	37.20	16107	8.18
10		80	2657.21	3600	4327.97	2792.69	115.65	13889	5.09	4480.37	2771.08	223.80	21675	4.28
11		100	3399.17	1009.76	4722.64	3527.70	408.36	15366	3.78	4745.73	3499.01	288.25	13858	2.93
12		150	5882.45	212.27	5882.45	5882.45	0.12	1	0	5882.45	5882.45	0.12	1	0