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Multilevel Refinement for Combinatorial Optimisation: Boosting Metaheuristic Performance

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Hybrid Metaheuristics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 114))

The multilevel paradigm as applied to combinatorial optimisation problems is a simple one, which at its most basic involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found, usually at the coarsest level, and then iteratively refined at each level, coarsest to finest, typically by using some kind of heuristic optimisation algorithm (either a problem-specific local search scheme or a metaheuristic). Solution extension (or projection) operators can transfer the solution from one level to another. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (for example multigrid techniques can be viewed as a prime example of the paradigm). Overview papers such as [39] attest to its efficacy. However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial problems and in this chapter we discuss recent developments. In this chapter we survey the use of multilevel combinatorial techniques and consider their ability to boost the performance of (meta)heuristic optimisation algorithms.

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Authors and Affiliations

  1. Computing and Mathematical Sciences, University of Greenwich, London, UK

    Chris Walshaw

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  1. Chris Walshaw
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Editors and Affiliations

  1. Dept. Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Jordi Girona 1-3 Omega 112, E-08034, Barcelona, Spain

    Christian Blum

  2. Dept. Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Jordi Girona 1-3 Omega 213, E-08034, Barcelona, Spain

    Maria José Blesa Aguilera

  3. Università di Bologna, Via Venezia 52, I-47023, Cesena, Italy

    Andrea Roli

  4. Université Libre de Bruxelles, Avenue Franklin Roosevelt 50, B-1050, Brussels, Belgium

    Michael Sampels

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Walshaw, C. (2008). Multilevel Refinement for Combinatorial Optimisation: Boosting Metaheuristic Performance. In: Blum, C., Aguilera, M.J.B., Roli, A., Sampels, M. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78295-7_9

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  • DOI: https://doi.org/10.1007/978-3-540-78295-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78294-0

  • Online ISBN: 978-3-540-78295-7

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