IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v35y2023i3p578-592.html
   My bibliography  Save this article

Optimization Problems in Graphs with Locational Uncertainty

Author

Listed:
  • Marin Bougeret

    (Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier, Centre National de la Recherche Scientifique, 34095 Montpellier, France)

  • Jérémy Omer

    (Institut de Recherche Mathématique de Rennes, Institut National des Sciences Appliquées, 35700 Rennes, France)

  • Michael Poss

    (Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier, Centre National de la Recherche Scientifique, 34095 Montpellier, France)

Abstract

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances of the chosen set of edges for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are N P -hard even when the feasible sets consist either of all spanning trees or of all s – t paths. Given this hardness, we propose an exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose a conservative approximation and show its equivalence to the affine decision rule approximation in the context of Euclidean distances. We compare our algorithms to three deterministic reformulations on instances inspired by the scientific literature for the Steiner tree problem and a facility location problem.

Suggested Citation

  • Marin Bougeret & Jérémy Omer & Michael Poss, 2023. "Optimization Problems in Graphs with Locational Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 578-592, May.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:3:p:578-592
    DOI: 10.1287/ijoc.2023.1276
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2023.1276
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2023.1276?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
    ---><---

    References listed on IDEAS

    as
    1. Joe Naoum-Sawaya & Christoph Buchheim, 2016. "Robust Critical Node Selection by Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 162-174, February.
    2. Isabel Correia & Francisco Saldanha Gama, 2015. "Facility Location Under Uncertainty," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 177-203, Springer.
    3. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    4. Krzysztof Postek & Dick den Hertog, 2016. "Multistage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty Set," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 553-574, August.
    5. Dimitris Bertsimas & Iain Dunning, 2016. "Multistage Robust Mixed-Integer Optimization with Adaptive Partitions," Operations Research, INFORMS, vol. 64(4), pages 980-998, August.
    6. Josette Ayoub & Michael Poss, 2016. "Decomposition for adjustable robust linear optimization subject to uncertainty polytope," Computational Management Science, Springer, vol. 13(2), pages 219-239, April.
    7. Christoph Buchheim & Jannis Kurtz, 2018. "Robust combinatorial optimization under convex and discrete cost uncertainty," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 211-238, September.
    8. Jannis Kurtz, 2018. "Robust combinatorial optimization under budgeted–ellipsoidal uncertainty," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 315-337, December.
    9. Grani A. Hanasusanto & Daniel Kuhn & Wolfram Wiesemann, 2015. "K -Adaptability in Two-Stage Robust Binary Programming," Operations Research, INFORMS, vol. 63(4), pages 877-891, August.
    10. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    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. Christoph Buchheim & Jannis Kurtz, 2018. "Robust combinatorial optimization under convex and discrete cost uncertainty," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 211-238, September.
    2. Nicolas Kämmerling & Jannis Kurtz, 2020. "Oracle-based algorithms for binary two-stage robust optimization," Computational Optimization and Applications, Springer, vol. 77(2), pages 539-569, November.
    3. Cohen, Izack & Postek, Krzysztof & Shtern, Shimrit, 2023. "An adaptive robust optimization model for parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 306(1), pages 83-104.
    4. Yanıkoğlu, İhsan & Gorissen, Bram L. & den Hertog, Dick, 2019. "A survey of adjustable robust optimization," European Journal of Operational Research, Elsevier, vol. 277(3), pages 799-813.
    5. Ayşe N. Arslan & Michael Poss & Marco Silva, 2022. "Min-Sup-Min Robust Combinatorial Optimization with Few Recourse Solutions," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2212-2228, July.
    6. Angelos Georghiou & Angelos Tsoukalas & Wolfram Wiesemann, 2020. "A Primal–Dual Lifting Scheme for Two-Stage Robust Optimization," Operations Research, INFORMS, vol. 68(2), pages 572-590, March.
    7. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    8. Detienne, Boris & Lefebvre, Henri & Malaguti, Enrico & Monaci, Michele, 2024. "Adjustable robust optimization with objective uncertainty," European Journal of Operational Research, Elsevier, vol. 312(1), pages 373-384.
    9. Borumand, Ali & Marandi, Ahmadreza & Nookabadi, Ali S. & Atan, Zümbül, 2024. "An oracle-based algorithm for robust planning of production routing problems in closed-loop supply chains of beverage glass bottles," Omega, Elsevier, vol. 122(C).
    10. Arkajyoti Roy & Shaunak S. Dabadghao & Ahmadreza Marandi, 2024. "Value of intermediate imaging in adaptive robust radiotherapy planning to manage radioresistance," Annals of Operations Research, Springer, vol. 339(3), pages 1307-1328, August.
    11. Jianzhe Zhen & Ahmadreza Marandi & Danique de Moor & Dick den Hertog & Lieven Vandenberghe, 2022. "Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2410-2427, September.
    12. Anirudh Subramanyam & Frank Mufalli & José M. Lí?nez-Aguirre & Jose M. Pinto & Chrysanthos E. Gounaris, 2021. "Robust Multiperiod Vehicle Routing Under Customer Order Uncertainty," Operations Research, INFORMS, vol. 69(1), pages 30-60, January.
    13. Farough Motamed Nasab & Zukui Li, 2023. "Multistage Adaptive Robust Binary Optimization: Uncertainty Set Lifting versus Partitioning through Breakpoints Optimization," Mathematics, MDPI, vol. 11(18), pages 1-24, September.
    14. Lee, Junhyeok & Moon, Ilkyeong, 2024. "A decomposition approach for robust omnichannel retail operations considering the third-party platform channel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    15. Sergey S. Ketkov, 2023. "On the Multistage Shortest Path Problem Under Distributional Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 277-308, April.
    16. Chassein, André & Goerigk, Marc & Kurtz, Jannis & Poss, Michael, 2019. "Faster algorithms for min-max-min robustness for combinatorial problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 279(2), pages 308-319.
    17. Marc Goerigk & Adam Kasperski & Paweł Zieliński, 2022. "Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 497-527, April.
    18. Jiu, Song, 2022. "Robust omnichannel retail operations with the implementation of ship-from-store," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    19. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    20. Ayşe N. Arslan & Boris Detienne, 2022. "Decomposition-Based Approaches for a Class of Two-Stage Robust Binary Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 857-871, March.

    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:inm:orijoc:v:35:y:2023:i:3:p:578-592. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.