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Decomposition Techniques as Metaheuristic Frameworks

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Matheuristics

Part of the book series: Annals of Information Systems ((AOIS,volume 10))

Abstract

Decomposition techniques are well-known as a means for obtaining tight lower bounds for combinatorial optimization problems, and thus as a component for solution methods. Moreover a long-established research literature uses them for defining problem-specific heuristics. More recently it has been observed that they can be the basis also for designing metaheuristics. This tutorial elaborates this last point, showing how the three main decomposition techniques, namely Dantzig-Wolfe, Lagrangean and Benders decompositions, can be turned into model-based, dual-aware metaheuristics. A well known combinatorial optimization problem, the Single Source Capacitated Facility Location Problem, is then chosen for validation, and the implemented codes of the proposed algorithms are benchmarked on standard instances from literature.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Bologna, Italy

    Marco Boschetti

  2. Department of Computer Science, University of Bologna, Bologna, Italy

    Vittorio Maniezzo & Matteo Roffilli

Authors
  1. Marco Boschetti
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  2. Vittorio Maniezzo
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  3. Matteo Roffilli
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Corresponding author

Correspondence to Marco Boschetti .

Editor information

Editors and Affiliations

  1. Dipto. Scienze dell‘Informazione, Universitá di Bologna, Contrada Sacchi 3, Cesena, 47023, Italy

    Vittorio Maniezzo

  2. Avenue Franklin Roosevelt 50, Bruxelles, 1050, Belgium

    Thomas Stützle

  3. Dept. Wirtschaftswissenschaften, Inst. Wirtschaftsinformatik, Universität Hamburg, Von-Melle-Park 5, Hamburg, 20146, Germany

    Stefan Voß

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Boschetti, M., Maniezzo, V., Roffilli, M. (2009). Decomposition Techniques as Metaheuristic Frameworks. In: Maniezzo, V., Stützle, T., Voß, S. (eds) Matheuristics. Annals of Information Systems, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1306-7_5

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