IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v83y2022i2d10.1007_s10589-022-00406-7.html
   My bibliography  Save this article

Minimum cost b-matching problems with neighborhoods

Author

Listed:
  • I. Espejo

    (Universidad de Cádiz)

  • R. Páez

    (Universidad de Cádiz)

  • J. Puerto

    (Universidad de Sevilla
    Universidad de Sevilla)

  • A. M. Rodríguez-Chía

    (Universidad de Cádiz)

Abstract

In this paper, we deal with minimum cost b-matching problems on graphs where the nodes are assumed to belong to non-necessarily convex regions called neighborhoods, and the costs are given by the distances between points of the neighborhoods. The goal in the proposed problems is twofold: (i) finding a b-matching in the graph and (ii) determining a point in each neighborhood to be the connection point among the edges defining the b-matching. Different variants of the minimum cost b-matching problem are considered depending on the criteria to match neighborhoods: perfect, maximum cardinality, maximal and the a–b-matching problems. The theoretical complexity of solving each one of these problems is analyzed. Different mixed integer non-linear programming formulations are proposed for each one of the considered problems and then reformulated as Second Order Cone formulations. An extensive computational experience shows the efficiency of the proposed formulations to solve the problems under study.

Suggested Citation

  • I. Espejo & R. Páez & J. Puerto & A. M. Rodríguez-Chía, 2022. "Minimum cost b-matching problems with neighborhoods," Computational Optimization and Applications, Springer, vol. 83(2), pages 525-553, November.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:2:d:10.1007_s10589-022-00406-7
    DOI: 10.1007/s10589-022-00406-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-022-00406-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-022-00406-7?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Dong, Lijun & Kang, Xiaojun & Pan, Mengqi & Zhao, Man & Zhang, Feng & Yao, Hong, 2020. "B-matching-based optimization model for energy allocation in sea surface monitoring," Energy, Elsevier, vol. 192(C).
    2. Blanco, Víctor & Fernández, Elena & Puerto, Justo, 2017. "Minimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods," European Journal of Operational Research, Elsevier, vol. 262(3), pages 863-878.
    3. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, April.
    4. Donald L. Miller, 1995. "A Matching Based Exact Algorithm for Capacitated Vehicle Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 1-9, February.
    5. Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, 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. 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.
    2. Puerto, Justo & Valverde, Carlos, 2022. "Routing for unmanned aerial vehicles: Touring dimensional sets," European Journal of Operational Research, Elsevier, vol. 298(1), pages 118-136.
    3. Li, Xin & Wang, Tianqi & Xu, Weihan & Li, Huaiyue & Yuan, Yun, 2022. "A novel model and algorithm for designing an eco-oriented demand responsive transit (DRT) system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    4. Shahmohammadi, Ali & Sioshansi, Ramteen & Conejo, Antonio J. & Afsharnia, Saeed, 2018. "Market equilibria and interactions between strategic generation, wind, and storage," Applied Energy, Elsevier, vol. 220(C), pages 876-892.
    5. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    6. Arthur Medeiros & Thales Ramos & José Tavares de Oliveira & Manoel F. Medeiros Júnior, 2020. "Direct Voltage Control of a Doubly Fed Induction Generator by Means of Optimal Strategy," Energies, MDPI, vol. 13(3), pages 1-28, February.
    7. Ivorra, Benjamin & Mohammadi, Bijan & Manuel Ramos, Angel, 2015. "A multi-layer line search method to improve the initialization of optimization algorithms," European Journal of Operational Research, Elsevier, vol. 247(3), pages 711-720.
    8. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    9. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    10. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    11. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    12. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    13. Csaba I. Fábián, 2021. "Gaining traction: on the convergence of an inner approximation scheme for probability maximization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 491-519, June.
    14. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    15. Bouslah, B. & Gharbi, A. & Pellerin, R., 2016. "Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint," Omega, Elsevier, vol. 61(C), pages 110-126.
    16. Rafał Wiśniowski & Krzysztof Skrzypaszek & Tomasz Małachowski, 2020. "Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods," Energies, MDPI, vol. 13(12), pages 1-17, June.
    17. Martins Barros, Rafael & Guimarães Lage, Guilherme & de Andrade Lira Rabêlo, Ricardo, 2022. "Sequencing paths of optimal control adjustments determined by the optimal reactive dispatch via Lagrange multiplier sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 301(1), pages 373-385.
    18. Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
    19. Enrique I. Acuña & Ian S. Lowndes, 2014. "A Review of Primary Mine Ventilation System Optimization," Interfaces, INFORMS, vol. 44(2), pages 163-175, April.
    20. Nadia Demarteau & Thomas Breuer & Baudouin Standaert, 2012. "Selecting a Mix of Prevention Strategies against Cervical Cancer for Maximum Efficiency with an Optimization Program," PharmacoEconomics, Springer, vol. 30(4), pages 337-353, April.

    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:spr:coopap:v:83:y:2022:i:2:d:10.1007_s10589-022-00406-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.