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An Efficient Heuristic for the k-Partitioning Problem

Author

Listed:
  • Pawel Kalczynski

    (California State University-Fullerton)

  • Zvi Goldstein

    (California State University-Fullerton)

  • Zvi Drezner

    (California State University-Fullerton)

Abstract

We investigate the k-partitioning problem, in which a set of items is divided into mutually exclusive and collectively exhaustive non-empty groups (clusters). The number of groups is given, and the distances between items, which may include weights, are defined. The sum of the distances between all members of the same group is calculated for each group, and the objective is to find the partition of the set of items that minimizes the sum of these individual sums. Two formulations of the problem are proposed and solved. In the first problem, the number of items in each group is given. In the second problem, there is no restriction on the number of items in each group. We propose an optimal algorithm for each of these two problems and an efficient heuristic algorithm that found all confirmed optimal solutions and improved several best-known solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:4:d:10.1007_s43069-023-00249-w
    DOI: 10.1007/s43069-023-00249-w
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    References listed on IDEAS

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    1. A. Bagirov & B. Ordin & G. Ozturk & A. Xavier, 2015. "An incremental clustering algorithm based on hyperbolic smoothing," Computational Optimization and Applications, Springer, vol. 61(1), pages 219-241, May.
    2. Guillermo Durán & Mario Guajardo & Jaime Miranda & Denis Sauré & Sebastián Souyris & Andres Weintraub & Rodrigo Wolf, 2007. "Scheduling the Chilean Soccer League by Integer Programming," Interfaces, INFORMS, vol. 37(6), pages 539-552, December.
    3. 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.
    4. Zvi Drezner & Pawel Kalczynski, 2017. "The continuous grey pattern problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(5), pages 469-483, May.
    5. Zvi Drezner & Alfonsas Misevičius & Gintaras Palubeckis, 2015. "Exact algorithms for the solution of the grey pattern quadratic assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 85-105, August.
    6. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
    7. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
    8. Michael Brusco & Hans-Friedrich Köhn, 2009. "Clustering Qualitative Data Based on Binary Equivalence Relations: Neighborhood Search Heuristics for the Clique Partitioning Problem," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 685-703, December.
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