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New Hybrid Matheuristics for Solving the Multidimensional Knapsack Problem

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Hybrid Metaheuristics (HM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6373))

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Abstract

In this paper we propose new hybrid methods for solving the multidimensional knapsack problem. They can be viewed as matheuristics that combine mathematical programming with the variable neighbourhood decomposition search heuristic. In each iteration a relaxation of the problem is solved to guide the generation of the neighbourhoods. Then the problem is enriched with a pseudo-cut to produce a sequence of not only lower, but also upper bounds of the problem, so that integrality gap is reduced. The results obtained on two sets of the large scale multidimensional knapsack problem instances are comparable with the current state-of-the-art heuristics. Moreover, a few best known results are reported for some large, long-studied instances.

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Author information

Authors and Affiliations

  1. Univ Lille Nord de France, F-59000, Lille, France

    Saïd Hanafi, Christophe Wilbaut & Igor Crévits

  2. UVHC, LAMIH, F-59313, Valenciennes, France

    Saïd Hanafi, Christophe Wilbaut & Igor Crévits

  3. CNRS, FRE 3304, F-59313, Valenciennes, France

    Saïd Hanafi, Christophe Wilbaut & Igor Crévits

  4. Brunel University, West London, UB8 3PH, UK

    Jasmina Lazić & Nenad Mladenović

  5. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Jasmina Lazić & Nenad Mladenović

Authors
  1. Saïd Hanafi
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  2. Jasmina Lazić
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  3. Nenad Mladenović
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  4. Christophe Wilbaut
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  5. Igor Crévits
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Editor information

Editors and Affiliations

  1. Universitat Politècnica de Catalunya, Omega 213 Campus Nord Jordi Girona 1-3, 08034, Barcelona, Spain

    María J. Blesa

  2. ALBCOM Research Group, Universitat Politècnica de Catalunya, Omega 112, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Christian Blum

  3. Institute of Computer Graphics and Algorithms, Vienna University of Technology, Favoritenstraße 9–11/1861, 1040, Vienna, Austria

    Günther Raidl

  4. Università di Bologna, Sede di Cesena, Via Venezia 52, 47521, Cesena, Italy

    Andrea Roli

  5. Université Libre de Bruxelles, IRIDIA CP 194/6, Avenue Franklin D. Roosevelt 50, 1050, Bruxelles, Belgium

    Michael Sampels

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Hanafi, S., Lazić, J., Mladenović, N., Wilbaut, C., Crévits, I. (2010). New Hybrid Matheuristics for Solving the Multidimensional Knapsack Problem. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds) Hybrid Metaheuristics. HM 2010. Lecture Notes in Computer Science, vol 6373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16054-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-16054-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16053-0

  • Online ISBN: 978-3-642-16054-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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