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

Table 3

Pure integer knapsack problems.

Problem	Number of variables		Ratio	MILP time (s)	Certificate time (s)
nipkn1.mps	200	15	0.13
nipkn2.mps	1000	40	0.077
nipkn3.mps	2000	45	0.044
nipkn4.mps	10000	1006	0.19	0.23	0.19
nipkn5.mps	20000	1974	0.193	0.95	0.56
nipkn6.mps	50000	1136	0.04	3.19	0.79