IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v327y2025i1p42-57.html

Formulations and branch-and-cut algorithms for cycle covers with up to p cycles

Author

Listed:
  • Canas, Francisco
  • Gouveia, Luís

Abstract

Given a positive integer p and a weighted undirected graph G=(V,E), we study a problem in which the objective is to find a minimum weight set of up to p elementary cycles partitioning the vertices of G. We study several exponentially sized formulations including (i) edge variables only; (ii) edge and depot variables only; (iii) edge, depot and node-depot assignment (NDA) variables only; (iv) edge, depot, NDA and edge-depot assignment (EDA) variables. New flow formulations are also introduced, and relations between all the formulations are established. Branch-and-cut algorithms based on many of these formulations are proposed, and computational experiments are conducted to compare the performance of the different algorithms. The computational testing reveals that some of the formulations including edge, depot and NDA or EDA variables produce the best initial lower bounds and that the best computational times are obtained with the algorithms based on formulations including edge and depot variables only. The best performing algorithm (in terms of computational times) is capable of solving several instances with up to 442 nodes for different values of p.

Suggested Citation

  • Canas, Francisco & Gouveia, Luís, 2025. "Formulations and branch-and-cut algorithms for cycle covers with up to p cycles," European Journal of Operational Research, Elsevier, vol. 327(1), pages 42-57.
    • Handle: RePEc:eee:ejores:v:327:y:2025:i:1:p:42-57
    DOI: 10.1016/j.ejor.2025.04.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725003467
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.04.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Bektaş, Tolga & Gouveia, Luís & Santos, Daniel, 2019. "Revisiting the Hamiltonian p-median problem: A new formulation on directed graphs and a branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 276(1), pages 40-64.
    2. Olivier Goldschmidt & Dorit S. Hochbaum, 1994. "A Polynomial Algorithm for the k-cut Problem for Fixed k," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 24-37, February.
    3. Gilbert Laporte & Yves Nobert & Serge Taillefer, 1988. "Solving a Family of Multi-Depot Vehicle Routing and Location-Routing Problems," Transportation Science, INFORMS, vol. 22(3), pages 161-172, August.
    4. Laporte, Gilbert & Nobert, Yves & Pelletier, Paul, 1983. "Hamiltonian location problems," European Journal of Operational Research, Elsevier, vol. 12(1), pages 82-89, January.
    5. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    6. Branco, I. M. & Coelho, J. D., 1990. "The hamiltonian p-median problem," European Journal of Operational Research, Elsevier, vol. 47(1), pages 86-95, July.
    7. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    8. Letchford, Adam N. & Salazar-González, Juan-José, 2015. "Stronger multi-commodity flow formulations of the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 730-738.
    9. Prodhon, Caroline & Prins, Christian, 2014. "A survey of recent research on location-routing problems," European Journal of Operational Research, Elsevier, vol. 238(1), pages 1-17.
    10. Erdoğan, Güneş & Laporte, Gilbert & Rodríguez Chía, Antonio M., 2016. "Exact and heuristic algorithms for the Hamiltonian p-median problem," European Journal of Operational Research, Elsevier, vol. 253(2), pages 280-289.
    11. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    12. Bernardino, Raquel & Paias, Ana, 2018. "Solving the family traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 267(2), pages 453-466.
    13. Mark S. Daskin & Kayse Lee Maass, 2015. "The p-Median Problem," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 21-45, Springer.
    14. Barbato, Michele & Gouveia, Luís, 2024. "The Hamiltonian p-median problem: Polyhedral results and branch-and-cut algorithms," European Journal of Operational Research, Elsevier, vol. 316(2), pages 473-487.
    15. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    2. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Barbato, Michele & Gouveia, Luís, 2024. "The Hamiltonian p-median problem: Polyhedral results and branch-and-cut algorithms," European Journal of Operational Research, Elsevier, vol. 316(2), pages 473-487.
    4. F. Antonio Medrano, 2020. "The complete vertex p-center problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 327-343, October.
    5. S Salhi & A Al-Khedhairi, 2010. "Integrating heuristic information into exact methods: The case of the vertex p-centre problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1619-1631, November.
    6. R. Baldacci & E. Hadjiconstantinou & A. Mingozzi, 2004. "An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation," Operations Research, INFORMS, vol. 52(5), pages 723-738, October.
    7. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.
    8. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    9. Duran-Mateluna, Cristian & Ales, Zacharie & Elloumi, Sourour, 2023. "An efficient benders decomposition for the p-median problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 84-96.
    10. R. Baldacci & M. Dell'Amico & J. Salazar González, 2007. "The Capacitated m -Ring-Star Problem," Operations Research, INFORMS, vol. 55(6), pages 1147-1162, December.
    11. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.
    12. Jesus Garcia-Diaz & Jairo Sanchez-Hernandez & Ricardo Menchaca-Mendez & Rolando Menchaca-Mendez, 2017. "When a worse approximation factor gives better performance: a 3-approximation algorithm for the vertex k-center problem," Journal of Heuristics, Springer, vol. 23(5), pages 349-366, October.
    13. Bektaş, Tolga & Gouveia, Luís & Santos, Daniel, 2019. "Revisiting the Hamiltonian p-median problem: A new formulation on directed graphs and a branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 276(1), pages 40-64.
    14. Ponboon, Sattrawut & Qureshi, Ali Gul & Taniguchi, Eiichi, 2016. "Branch-and-price algorithm for the location-routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 1-19.
    15. Manuel Iori & Juan-José Salazar-González & Daniele Vigo, 2007. "An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints," Transportation Science, INFORMS, vol. 41(2), pages 253-264, May.
    16. Zhou, Fangting & Lischka, Attila & Kulcsár, Balázs & Wu, Jiaming & Haghir Chehreghani, Morteza & Laporte, Gilbert, 2025. "Learning for routing: A guided review of recent developments and future directions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 202(C).
    17. Chou, Xiaochen & Dell’Amico, Mauro & Jamal, Jafar & Montemanni, Roberto, 2023. "Precedence-Constrained arborescences," European Journal of Operational Research, Elsevier, vol. 307(2), pages 575-589.
    18. Gaar, Elisabeth & Sinnl, Markus, 2022. "A scaleable projection‐based branch‐and‐cut algorithm for the p‐center problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 78-98.
    19. Antiopi Panteli & Basilis Boutsinas & Ioannis Giannikos, 2021. "On solving the multiple p-median problem based on biclustering," Operational Research, Springer, vol. 21(1), pages 775-799, March.
    20. Daoqin Tong & Alan T. Murray, 2009. "Maximising coverage of spatial demand for service," Papers in Regional Science, Wiley Blackwell, vol. 88(1), pages 85-97, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:327:y:2025:i:1:p:42-57. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.