Table III. Comparison of the developed...

Table III.

Comparison of the developed algorithms for the small-size instances

Inst.	BC	\|V\|	BARON		MA-DPC		MA		EA		SA		VNS
Inst.	BC	\|V\|	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s
S1	[BC1]	6	3.815	5.22	3.815	38.97	3.815	34.43	3.815	33.71	3.815	7.29	3.815	25.51
S2	[BC1]	8	5.596	62.33	5.596	41.50	5.596	36.43	5.596	35.45	5.596	7.81	5.596	27.11
S3	[BC1]	10	7.518	148.80	7.518	43.70	7.518	38.47	7.518	37.28	7.518	8.19	7.518	28.62
S4	[BC1]	12	9.689	342.14	9.689	45.77	9.695	40.71	9.695	39.29	9.695	8.58	9.695	30.15
S5	[BC1]	14	11.468	595.01	11.468	47.80	11.502	42.35	11.521	41.05	11.554	9.04	11.554	31.56
S6	[BC1]	16	12.892	995.47	12.892	50.66	12.958	44.46	13.020	43.08	13.037	9.46	13.020	33.12
S7	[BC2]	6	3.689	15.29	3.689	42.47	3.689	37.70	3.689	36.56	3.689	7.81	3.689	27.89
S8	[BC2]	8	5.343	185.89	5.343	44.61	5.343	39.79	5.343	38.83	5.343	8.29	5.343	29.16
S9	[BC2]	10	7.031	499.86	7.031	47.29	7.031	41.63	7.031	41.08	7.031	8.91	7.031	31.00
S10	[BC2]	12	8.896	1205.18	8.896	49.80	8.918	43.73	9.043	43.11	9.053	9.34	9.046	32.63
S11	[BC2]	14	10.404	2331.02	10.424	51.97	10.461	45.84	10.593	44.94	10.640	10.01	10.593	34.12
S12	[BC2]	16	12.055	7201.49	11.585	55.88	11.643	48.25	11.846	46.79	11.857	10.40	11.796	35.50
S13	[BC3]	6	3.627	32.22	3.627	45.77	3.627	39.75	3.627	38.80	3.627	8.52	3.627	29.45
S14	[BC3]	8	5.220	342.44	5.220	48.00	5.220	41.98	5.220	41.39	5.220	8.95	5.220	31.17
S15	[BC3]	10	6.810	784.84	6.810	50.55	6.810	44.39	6.810	43.43	6.810	9.55	6.810	33.41
S16	[BC3]	12	8.578	1857.84	8.578	53.25	8.628	46.31	8.728	45.47	8.748	10.15	8.732	34.54
S17	[BC3]	14	9.953	3249.19	9.999	55.64	10.025	48.90	10.146	47.22	10.191	10.69	10.150	36.15
S18	[BC3]	16	11.504	7202.12	11.023	57.51	11.090	52.08	11.236	49.91	11.274	11.08	11.219	38.84
Average:			8.005	1503.13	7.956	48.40	7.976	42.62	8.027	41.52	8.039	9.11	8.025	31.66

Inst.	BC	\|V\|	BARON		MA-DPC		MA		EA		SA		VNS
Inst.	BC	\|V\|	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s	Z, 10⁶ US$	CPU, s
S1	[BC1]	6	3.815	5.22	3.815	38.97	3.815	34.43	3.815	33.71	3.815	7.29	3.815	25.51
S2	[BC1]	8	5.596	62.33	5.596	41.50	5.596	36.43	5.596	35.45	5.596	7.81	5.596	27.11
S3	[BC1]	10	7.518	148.80	7.518	43.70	7.518	38.47	7.518	37.28	7.518	8.19	7.518	28.62
S4	[BC1]	12	9.689	342.14	9.689	45.77	9.695	40.71	9.695	39.29	9.695	8.58	9.695	30.15
S5	[BC1]	14	11.468	595.01	11.468	47.80	11.502	42.35	11.521	41.05	11.554	9.04	11.554	31.56
S6	[BC1]	16	12.892	995.47	12.892	50.66	12.958	44.46	13.020	43.08	13.037	9.46	13.020	33.12
S7	[BC2]	6	3.689	15.29	3.689	42.47	3.689	37.70	3.689	36.56	3.689	7.81	3.689	27.89
S8	[BC2]	8	5.343	185.89	5.343	44.61	5.343	39.79	5.343	38.83	5.343	8.29	5.343	29.16
S9	[BC2]	10	7.031	499.86	7.031	47.29	7.031	41.63	7.031	41.08	7.031	8.91	7.031	31.00
S10	[BC2]	12	8.896	1205.18	8.896	49.80	8.918	43.73	9.043	43.11	9.053	9.34	9.046	32.63
S11	[BC2]	14	10.404	2331.02	10.424	51.97	10.461	45.84	10.593	44.94	10.640	10.01	10.593	34.12
S12	[BC2]	16	12.055	7201.49	11.585	55.88	11.643	48.25	11.846	46.79	11.857	10.40	11.796	35.50
S13	[BC3]	6	3.627	32.22	3.627	45.77	3.627	39.75	3.627	38.80	3.627	8.52	3.627	29.45
S14	[BC3]	8	5.220	342.44	5.220	48.00	5.220	41.98	5.220	41.39	5.220	8.95	5.220	31.17
S15	[BC3]	10	6.810	784.84	6.810	50.55	6.810	44.39	6.810	43.43	6.810	9.55	6.810	33.41
S16	[BC3]	12	8.578	1857.84	8.578	53.25	8.628	46.31	8.728	45.47	8.748	10.15	8.732	34.54
S17	[BC3]	14	9.953	3249.19	9.999	55.64	10.025	48.90	10.146	47.22	10.191	10.69	10.150	36.15
S18	[BC3]	16	11.504	7202.12	11.023	57.51	11.090	52.08	11.236	49.91	11.274	11.08	11.219	38.84
Average:			8.005	1503.13	7.956	48.40	7.976	42.62	8.027	41.52	8.039	9.11	8.025	31.66

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