A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach

Table 2

Numerical results of VI approach and Weiszfeld-type method for Example 19.

𝑑1	VI approach				Weiszfeld-type method			Impro.	Freq.
	No. of Iter.0	No. of Iter.	CPU	Obj.	No. of Iter.	CPU	Obj.	percent	num.
1	25.11	59.96	0.015	15.4465	52.99	0.0117	15.5664	0.78	90
	25.04	58.97	0.015	15.1803	27.28	0.0055	15.2926	0.74	92
	25.35	60.89	0.015	15.3693	31.11	0.0070	15.4834	0.74	92
	25.24	59.80	0.015	15.0924	35.45	0.0080	15.1961	0.69	90
	23.61	55.13	0.014	14.6321	34.27	0.0069	14.7055	0.50	93
0.1	32.95	278.26	0.060	4.2157	28.59	0.0082	4.6791	10.99	63
	32.11	270.81	0.059	4.0864	60.38	0.0135	4.4318	8.45	66
	34.07	301.67	0.067	4.2248	36.63	0.0081	4.6001	8.88	63
	34.16	278.24	0.065	4.1189	34.03	0.0067	4.4854	8.89	63
	32.63	280.00	0.062	4.0842	38.20	0.0069	4.3619	6.80	64
0.01	33.11	427.34	0.089	3.0633	25.85	0.0063	3.8005	24.07	28
	35.28	407.61	0.086	3.0615	39.92	0.0087	3.7669	23.04	25
	39.26	382.82	0.080	3.1259	26.53	0.0064	3.6954	18.22	29
	35.46	425.33	0.089	2.9975	35.06	0.0077	3.6500	21.77	35
	32.96	437.24	0.091	3.0691	57.90	0.0130	3.6925	20.31	33
0.001	35.44	151.52	0.035	3.0477	18.88	0.0045	3.8310	25.70	15
	36.87	140.58	0.032	3.0224	17.20	0.0048	3.7128	22.84	14
	33.43	91.72	0.022	2.9797	17.53	0.0042	3.9617	32.96	17
	33.79	115.79	0.027	2.9600	15.20	0.0044	3.7221	25.75	19
	37.19	96.08	0.022	3.1936	16.47	0.0047	4.1362	29.52	18