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Exact Solution Methods for the k-Item Quadratic Knapsack Problem

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Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

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Abstract

The purpose of this paper is to solve the 0–1 k-item quadratic knapsack problem (kQKP), a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.

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Author information

Authors and Affiliations

  1. Université Paris 13, Sorbonne Paris Cité, LIPN, CNRS, (UMR 7030), 93430, Villetaneuse, France

    Lucas Létocart

  2. Alpen-Adria-Universität Klagenfurt, 9020, Klagenfurt am Wörthersee, Austria

    Angelika Wiegele

Authors
  1. Lucas Létocart
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  2. Angelika Wiegele
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Corresponding author

Correspondence to Angelika Wiegele .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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Létocart, L., Wiegele, A. (2016). Exact Solution Methods for the k-Item Quadratic Knapsack Problem. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_15

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

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