A polyhedral study on 0-1 knapsack problems with disjoint cardinality constraints: Facet-defining inequalities by sequential 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 14
Cited 1

Integer and combinatorial optimization

Integer and combinatorial optimization
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A computational study of a multiple-choice knapsack algorithm

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Solving Multiple Knapsack Problems by Cutting Planes

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Second-order cover inequalities

Mathematical Programming: Series A and B
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints

Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
A polyhedral study on 0-1 knapsack problems with disjoint cardinality constraints: Strong valid inequalities by sequence-independent lifting

Discrete Optimization
Higher-order cover cuts from zero-one knapsack constraints augmented by two-sided bounding inequalities

Discrete Optimization
A note of the knapsack problem with special ordered sets

Operations Research Letters
Lifted cover facets of the 0-1 knapsack polytope with GUB constraints

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

Discrete Optimization

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Abstract

In this paper, we study the polyhedral structure of the set of 0-1 integer solutions to a single knapsack constraint and multiple disjoint cardinality constraints (MCKP). This set is a generalization of the classical 0-1 knapsack polytope (KP) and the 0-1 knapsack polytope with generalized upper bounds (GUBKP). For MCKP, we extend the traditional concept of a cover to that of a generalized cover. We then introduce generalized cover inequalities and present a polynomial algorithm that can lift them into facet-defining inequalities of the convex hull of MCKP. For the case where the knapsack coefficients are non-negative, we derive strong bounds on the lifting coefficients and describe the maximal set of generalized cover inequalities. Finally, we show that the bound estimates we obtained strengthen or generalize the known results for KP and GUBKP.