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The linear ordering problem with clusters: a new partial ranking

Author

Listed:
  • Javier Alcaraz

    (University of Alicante)

  • Eva M. García-Nové

    (University of Alicante)

  • Mercedes Landete

    (University of Alicante)

  • Juan F. Monge

    (University of Alicante)

Abstract

The linear ordering problem is among core problems in combinatorial optimization. There is a squared non-negative matrix and the goal is to find the permutation of rows and columns which maximizes the sum of superdiagonal values. In this paper, we consider that columns of the matrix belong to different clusters and that the goal is to order the clusters. We introduce a new approach for the case when exactly one representative is chosen from each cluster. The new problem is called the linear ordering problem with clusters and consists of both choosing a representative for each cluster and a permutation of these representatives, so that the sum of superdiagonal values of the sub-matrix induced by the representatives is maximized. A combinatorial linear model for the linear ordering problem with clusters is given, and eventually, a hybrid metaheuristic is carefully designed and developed. Computational results illustrate the performance of the model as well as the effectiveness of the metaheuristic.

Suggested Citation

  • Javier Alcaraz & Eva M. García-Nové & Mercedes Landete & Juan F. Monge, 2020. "The linear ordering problem with clusters: a new partial ranking," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 646-671, October.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:3:d:10.1007_s11750-020-00552-3
    DOI: 10.1007/s11750-020-00552-3
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    References listed on IDEAS

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    1. Kai Puolamäki & Mikael Fortelius & Heikki Mannila, 2006. "Seriation in Paleontological Data Using Markov Chain Monte Carlo Methods," PLOS Computational Biology, Public Library of Science, vol. 2(2), pages 1-9, February.
    2. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F., 2012. "Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 54-64.
    3. Halekoh, U. & Vach, W., 2004. "A Bayesian approach to seriation problems in archaeology," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 651-673, April.
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    Cited by:

    1. Jessica Rodríguez-Pereira & Gilbert Laporte, 2022. "The target visitation arc routing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 60-76, April.
    2. Labbé, Martine & Landete, Mercedes & Monge, Juan F., 2023. "Bilevel integer linear models for ranking items and sets," Operations Research Perspectives, Elsevier, vol. 10(C).

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