Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

Table 2

Mixed integer knapsack problems with nonnegative coefficients.

Problem	,		Ratio	MILP time (s)	Certificate time (s)
mipkn1.mps	100, 100	8	0.04
mipkn2.mps	500, 500	28	0.028
mipkn3.mps	1000, 1000	91	0.0455
mipkn4.mps	5000, 5000	155	0.0155	29.97	0.01
mipkn5.mps	10000, 10000	998	0.0499	1944.64	0.01
mipkn6.mps	50000, 50000	5022	0.05022	2449.36	0.05