[Retracted] A Hybrid Algorithm of Ant Colony and Benders Decomposition for Large-Scale Mixed Integer Linear Programming

Table 4

Numerical results of medium-large scale numerical examples.

Parameters			Variable size		ADMM				ACA				Hybrid algorithm
S	D	K	x	y	UB	LB	CPU (s)	Gap (%)	UB	LB	CPU (s)	Gap (%)	UB	LB	CPU (s)	Gap (%)
2	5	3	147	15	590	531	0.39	8.2	602	527	0.40	10.6	586	537	0.35	4.0
5	10	5	1125	50	3302	3214	1.80	1.4	3314	3201	1.80	1.7	3298	3231	1.70	0.7
5	15	5	2000	75	4395	4287	2.50	1.9	4420	4239	2.60	2.4	4327	4306	2.40	0.3
5	20	5	3125	100	6890	6651	4.20	2.5	6999	6608	3.50	3.0	6814	6699	3.60	1.2
10	20	5	4500	100	7234	6901	3.90	6.2	7981	6681	3.90	8.3	7092	6990	3.80	0.5
5	20	10	6250	200	8016	7629	4.20	3.3	8210	7523	4.20	4.6	7901	7842	4.10	0.5
10	20	10	9000	200	8299	7893	5.20	4.6	8465	7768	5.60	5.7	8104	7962	4.90	1.2
10	25	10	12250	250	8207	8014	16.70	1.6	8287	7995	17.30	2.1	8186	8087	15.50	0.3
10	30	10	16000	300	11416	9960	21.30	8.4	11409	9893	20.30	10.6	10423	10167	19.70	1.4
15	30	15	30375	450	14590	13027	46.70	6.3	15409	12580	49.30	10.1	14407	13664	43.20	2.6