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Local and Variable Neighborhood Searches for Solving the Capacitated Clustering Problem

In: Optimization Methods and Applications

Author

Listed:
  • Jack Brimberg

    (Royal Military College of Canada)

  • Nenad Mladenović

    (Mathematical Institute SANU)

  • Raca Todosijević

    (Mathematical Institute SANU)

  • Dragan Urošević

    (Mathematical Institute SANU)

Abstract

The capacitated clustering problem requires finding a partition of a given set of elements with associated positive weights into a specified number of groups (or clusters) so that the sum of diversities of the individual clusters is maximized and the sum of weights of the elements in each cluster is within some capacity limits. We examine here various neighborhood structures for conducting local search for this type of problem and then describe a powerful variable neighborhood descent (VND) that employs three of these neighborhoods in a deterministic fashion and has appeared recently in the literature as a stand-alone heuristic. We then examine some recently developed heuristics for solving the problem that are based on variable neighborhood search (VNS), including a new one that applies a recently proposed variant of VNS known as nested VNS. These heuristics all use the prescribed VND in their local improvement step. A summary is given of extensive computational tests that demonstrate the effectiveness of these VNS-based heuristics over the state of the art.

Suggested Citation

  • Jack Brimberg & Nenad Mladenović & Raca Todosijević & Dragan Urošević, 2017. "Local and Variable Neighborhood Searches for Solving the Capacitated Clustering Problem," Springer Optimization and Its Applications, in: Sergiy Butenko & Panos M. Pardalos & Volodymyr Shylo (ed.), Optimization Methods and Applications, pages 33-55, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-68640-0_3
    DOI: 10.1007/978-3-319-68640-0_3
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