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Review of Basic Local Searches for Solving the Minimum Sum-of-Squares Clustering Problem

In: Open Problems in Optimization and Data Analysis

Author

Listed:
  • Thiago Pereira

    (Universidade Federal do Rio Grande do Norte)

  • Daniel Aloise

    (Polytechnique Montréal)

  • Jack Brimberg

    (The Royal Military College of Canada)

  • Nenad Mladenović

    (Emirates College of Technologies
    Mathematical Institute)

Abstract

This paper presents a review of the well-known K-means, H-means, and J-means heuristics, and their variants, that are used to solve the minimum sum-of-squares clustering problem. We then develop two new local searches that combine these heuristics in a nested and sequential structure, also referred to as variable neighborhood descent. In order to show how these local searches can be implemented within a metaheuristic framework, we apply the new heuristics in the local improvement step of two variable neighborhood search (VNS) procedures. Computational experiments are carried out which suggest that this new and simple application of VNS is comparable to the state of the art. In addition, a very significant improvement (over 30%) in solution quality is obtained for the largest problem instance investigated containing 85,900 entities.

Suggested Citation

  • Thiago Pereira & Daniel Aloise & Jack Brimberg & Nenad Mladenović, 2018. "Review of Basic Local Searches for Solving the Minimum Sum-of-Squares Clustering Problem," Springer Optimization and Its Applications, in: Panos M. Pardalos & Athanasios Migdalas (ed.), Open Problems in Optimization and Data Analysis, pages 249-270, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-99142-9_13
    DOI: 10.1007/978-3-319-99142-9_13
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    Cited by:

    1. Pawel Kalczynski & Zvi Goldstein & Zvi Drezner, 2023. "An Efficient Heuristic for the k-Partitioning Problem," SN Operations Research Forum, Springer, vol. 4(4), pages 1-21, December.

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