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

Table 3

Numerical results of medium-large scale numerical examples.

Parameters			Variable size		CPLEX				GUROBI				Benders decomposition
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	544	544	1.58	0	544	544	1.21	0	544	544	32.3	0
5	10	5	1125	50	3257	3257	3.20	0	3257	3257	2.81	0	3257	3257	102	0
5	15	5	2000	75	4313	4313	4.60	0	4313	4313	3.98	0	4313	4313	134.0	0
5	20	5	3125	100	6777	6777	5.66	0	6777	6777	4.23	0	6777	6777	156.0	0
10	20	5	4500	100	7051	7051	6.05	0	7051	7051	5.58	0	7051	7051	196.0	0
5	20	10	6250	200	7886	7886	6.84	0	7886	7886	5.92	0	7886	7886	275.0	0
10	20	10	9000	200	8008	8008	7.32	0	8008	8008	6.59	0	8008	8008	365.0	0
10	25	10	12250	250	8117	8117	351	0	8117	8117	235	0	8117	8117	1221.0	0
10	30	10	16000	300	10307	10307	2524	0	10307	10307	2012	0	14270	10001	3600.0	38
15	30	15	30375	450	—	—	—	—	—	—	—	—	34407	9853	3600.0	145