Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

Vicky Mak () and Tommy Thomadsen ()
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Vicky Mak: Deakin University
Tommy Thomadsen: Technical University of Denmark

Journal of Combinatorial Optimization, 2006, vol. 11, issue 4, No 6, 434 pages

Abstract: Abstract This paper considers the Cardinality Constrained Quadratic Knapsack Problem (QKP) and the Quadratic Selective Travelling Salesman Problem (QSTSP). The QKP is a generalization of the Knapsack Problem and the QSTSP is a generalization of the Travelling Salesman Problem. Thus, both problems are NP hard. The QSTSP and the QKP can be solved using branch-and-cut methods. Good bounds can be obtained if strong constraints are used. Hence it is important to identify strong or even facet-defining constraints. This paper studies the polyhedral combinatorics of the QSTSP and the QKP, i.e. amongst others we identify facet-defining constraints for the QSTSP and the QKP, and provide mathematical proofs that they do indeed define facets.

Keywords: Quadratic knapsack; Quadratic selective travelling salesman; Polyhedral analysis; Facets (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10878-006-8462-5

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