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

Author

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  • Vicky Mak

    (Deakin University)

  • Tommy Thomadsen

    (Technical University of Denmark)

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.

Suggested Citation

  • Vicky Mak & Tommy Thomadsen, 2006. "Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem," Journal of Combinatorial Optimization, Springer, vol. 11(4), pages 421-434, June.
    • Handle: RePEc:spr:jcomop:v:11:y:2006:i:4:d:10.1007_s10878-006-8462-5
    DOI: 10.1007/s10878-006-8462-5
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    References listed on IDEAS

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    Cited by:

    1. Zhang Yang & Jiacheng Li & Lei Li, 2020. "Time-Dependent Theme Park Routing Problem by Partheno-Genetic Algorithm," Mathematics, MDPI, vol. 8(12), pages 1-20, December.

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