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

Table 1

Pure integer knapsack problems with nonnegative coefficients.

Problem	Number of variables		Ratio	MILP time (s)	Certificate time (s)
ipkn1.mps	100	11	0.11
ipkn3.mps	500	62	0.124
ipkn4.mps	1000	104	0.104
ipkn5.mps	1000	24	0.024
ipkn6.mps	5000	109	0.0218	0.4	0.08
ipkn7.mps	10000	212	0.0212	3.42	0.04
ipkn8.mps	50000	2131	0.04262	14.23	0.29
ipkn9.mps	100000	2227	0.02227	72.83	0.16