A polyhedral study on 0-1 knapsack problems with disjoint cardinality constraints: Strong valid inequalities by sequence-independent lifting

Authors:
Bo Zeng;Jean-Philippe P. Richard
Affiliations:
Department of Industrial and Management Systems Engineering, University of South Florida, Tampa, FL 33620, USA;Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
Venue:
Discrete Optimization
Year:
2011

Citing 10
Cited 1

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A polyhedral study on 0-1 knapsack problems with disjoint cardinality constraints: Facet-defining inequalities by sequential lifting

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Abstract

We study the set of 0-1 integer solutions to a single knapsack constraint and a set of non-overlapping cardinality constraints (MCKP), which generalizes the classical 0-1 knapsack polytope and the 0-1 knapsack polytope with generalized upper bounds. We derive strong valid inequalities for the convex hull of its feasible solutions using sequence-independent lifting. For problems with a single cardinality constraint, we derive two-dimensional superadditive lifting functions and prove that they are maximal and non-dominated under some mild conditions. We then show that these functions can be used to build strong valid inequalities for problems with multiple disjoint cardinality constraints. Finally, we present preliminary computational results aimed at evaluating the strength of the cuts obtained from sequence-independent lifting with respect to those obtained from sequential lifting.