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A branch-and-price procedure for clustering data that are graph connected

Author

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  • Benati, Stefano
  • Ponce, Diego
  • Puerto, Justo
  • Rodríguez-Chía, Antonio M.

Abstract

This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. This problem, introduced by Benati, Puerto, and Rodríguez-Chía (2017) under the name of Connected Partitioning Problem, shows that the combination of the two data types improves the clustering quality in comparison with other methodologies. Nevertheless, the resulting optimization problem is difficult to solve; only small-sized instances can be solved exactly, large-sized instances require the application of heuristic algorithms. In this paper we improve the exact and the heuristic algorithms previously proposed. Here, we provide a new Integer Linear Programming (ILP) formulation, that solves larger instances, but at the cost of using an exponential number of variables. In order to limit the number of variables necessary to calculate the optimum, the new ILP formulation is solved implementing a branch-and-price (B&P) algorithm. The resulting pricing problem is itself a new combinatorial model: the Maximum-weighted Graph-Connected Single-Clique problem (MGCSC), that we solve testing various Mixed Integer Linear Programming (MILP) formulations and proposing a new fast “random shrink” heuristic. In this way, we are able to improve the previous algorithms: The B&P method outperforms the computational times of the previous MILP algorithms and the new random shrink heuristic, when applied to GCCP, is both faster and more accurate than the previous heuristic methods. Moreover, the combination of column generation and random shrink is itself a new MILP-relaxed matheuristic that can be applied to large instances too. Its main advantage is that all heuristic local optima are combined together in a restricted MILP, consisting in the application of the exact B&P method but solving heuristically the pricing problem.

Suggested Citation

  • Benati, Stefano & Ponce, Diego & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "A branch-and-price procedure for clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 297(3), pages 817-830.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:3:p:817-830
    DOI: 10.1016/j.ejor.2021.05.043
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    References listed on IDEAS

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    1. Raidl, Günther R., 2015. "Decomposition based hybrid metaheuristics," European Journal of Operational Research, Elsevier, vol. 244(1), pages 66-76.
    2. Laporte, Gilbert, 1992. "The traveling salesman problem: An overview of exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 59(2), pages 231-247, June.
    3. Egon Balas & Vašek Chvátal & Jaroslav Nešetřil, 1987. "On the Maximum Weight Clique Problem," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 522-535, August.
    4. Jacques Desrosiers & Marco E. Lübbecke, 2005. "A Primer in Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 1-32, Springer.
    5. Sato, Keisuke & Fukumura, Naoto, 2012. "Real-time freight locomotive rescheduling and uncovered train detection during disruption," European Journal of Operational Research, Elsevier, vol. 221(3), pages 636-648.
    6. Benati, Stefano & Puerto, Justo & Rodríguez-Chía, Antonio M., 2017. "Clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 261(1), pages 43-53.
    7. Samuel Deleplanque & Martine Labbé & Diego Ponce & Justo Puerto, 2020. "A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 582-599, July.
    8. Stefano Gualandi & Federico Malucelli, 2013. "Constraint Programming-based Column Generation," Annals of Operations Research, Springer, vol. 204(1), pages 11-32, April.
    9. Bektaş, Tolga & Gouveia, Luis, 2014. "Requiem for the Miller–Tucker–Zemlin subtour elimination constraints?," European Journal of Operational Research, Elsevier, vol. 236(3), pages 820-832.
    10. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    11. Bothorel, Cecile & Cruz, Juan David & Magnani, Matteo & Micenkovã , Barbora, 2015. "Clustering attributed graphs: Models, measures and methods," Network Science, Cambridge University Press, vol. 3(3), pages 408-444, September.
    12. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.
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    1. Calvino, José J. & López-Haro, Miguel & Muñoz-Ocaña, Juan M. & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "Segmentation of scanning-transmission electron microscopy images using the ordered median problem," European Journal of Operational Research, Elsevier, vol. 302(2), pages 671-687.
    2. Healy, Patrick & Jozefowiez, Nicolas & Laroche, Pierre & Marchetti, Franc & Martin, Sébastien & Róka, Zsuzsanna, 2024. "A branch-and-cut algorithm for the connected max-k-cut problem," European Journal of Operational Research, Elsevier, vol. 312(1), pages 117-124.
    3. Blanco, Víctor & Gázquez, Ricardo & Ponce, Diego & Puerto, Justo, 2023. "A branch-and-price approach for the continuous multifacility monotone ordered median problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 105-126.

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