Kaparis, Konstantinos and Letchford, A N (2008) Local and global lifted cover inequalities for the multidimensional knapsack problem. European Journal of Operational Research, 186 (1). pp. 91-103. ISSN 0377-2217
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The 0-1 Multidimensional Knapsack Problem (0-1 MKP) is a well-known (and strongly NP-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.
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