Local and global lifted cover inequalities for the 0–1 multidimensional knapsack problem

The 0–1 multidimensional knapsack problem (0–1 MKP) is a well-known (and strongly NPNP-hard) combinatorial optimization problem with many applications. Up to now, the majority of upper bounding techniques for the 0–1 MKP have been based on Lagrangian or surrogate relaxation. We show that good upper bounds can be obtained by a cutting plane method based on lifted cover inequalities (LCIs). As well as using traditional LCIs, we use some new ‘global’ LCIs, which take the whole constraint matrix into account.