IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v39y2017i2d10.1007_s00291-016-0463-x.html
   My bibliography  Save this article

Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities

Author

Listed:
  • Timo Gschwind

    (Johannes Gutenberg University Mainz)

  • Stefan Irnich

    (Johannes Gutenberg University Mainz)

Abstract

We present two new methods to stabilize column-generation algorithms for the temporal knapsack problem (TKP). Caprara et al. (INFORMS J Comp 25(3):560–571, 2013] were the first to suggest the use of branch-and-price algorithms for Dantzig–Wolfe reformulations of the TKP. Herein, the respective pricing problems are smaller-sized TKP that can be solved with a general-purpose MIP solver or by dynamic programming. Our stabilization methods are tailored to the TKP as they use (deep) dual-optimal inequalities, that is, inequalities known to be fulfilled by all (at least some) optimal dual solutions to the linear relaxation. Extensive computational tests reveal that both new stabilization techniques are helpful. Several previously unsolved instances are now solved to proven optimality.

Suggested Citation

  • Timo Gschwind & Stefan Irnich, 2017. "Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 541-556, March.
    • Handle: RePEc:spr:orspec:v:39:y:2017:i:2:d:10.1007_s00291-016-0463-x
    DOI: 10.1007/s00291-016-0463-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-016-0463-x
    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/s00291-016-0463-x?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. Alberto Caprara & Fabio Furini & Enrico Malaguti, 2013. "Uncommon Dantzig-Wolfe Reformulation for the Temporal Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 560-571, August.
    2. Desrosiers, Jacques & Gauthier, Jean Bertrand & Lübbecke, Marco E., 2014. "Row-reduced column generation for degenerate master problems," European Journal of Operational Research, Elsevier, vol. 236(2), pages 453-460.
    3. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    4. François Vanderbeck, 2005. "Implementing Mixed Integer Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 331-358, Springer.
    5. Hatem Ben Amor & Jacques Desrosiers & José Manuel Valério de Carvalho, 2006. "Dual-Optimal Inequalities for Stabilized Column Generation," Operations Research, INFORMS, vol. 54(3), pages 454-463, June.
    6. R. E. Marsten & W. W. Hogan & J. W. Blankenship, 1975. "The B oxstep Method for Large-Scale Optimization," Operations Research, INFORMS, vol. 23(3), pages 389-405, June.
    7. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    8. Jean Bertrand Gauthier & Jacques Desrosiers & Marco E. Lübbecke, 2016. "Tools for primal degenerate linear programs: IPS, DCA, and PE," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(2), pages 161-204, June.
    9. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    10. Alberto Caprara & Enrico Malaguti & Paolo Toth, 2011. "A Freight Service Design Problem for a Railway Corridor," Transportation Science, INFORMS, vol. 45(2), pages 147-162, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martinovic, J. & Strasdat, N. & Valério de Carvalho, J. & Furini, F., 2023. "A combinatorial flow-based formulation for temporal bin packing problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 554-574.
    2. Park, Jongyoon & Han, Jinil & Lee, Kyungsik, 2024. "Integer optimization models and algorithms for the multi-period non-shareable resource allocation problem," European Journal of Operational Research, Elsevier, vol. 317(1), pages 43-59.
    3. Clautiaux, F. & Detienne, B. & Guillot, G., 2021. "An iterative dynamic programming approach for the temporal knapsack problem," European Journal of Operational Research, Elsevier, vol. 293(2), pages 442-456.
    4. Sebastian Kraul & Markus Seizinger & Jens O. Brunner, 2023. "Machine Learning–Supported Prediction of Dual Variables for the Cutting Stock Problem with an Application in Stabilized Column Generation," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 692-709, May.

    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. Timo Gschwind & Stefan Irnich, 2014. "Stabilized Column Generation for the Temporal Knapsack Problem using Dual- Optimal Inequalities," Working Papers 1413, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 13 Nov 2014.
    2. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    3. Timo Gschwind & Stefan Irnich, 2014. "Dual Inequalities for Stabilized Column Generation Revisited," Working Papers 1407, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 23 Jul 2014.
    4. Sebastian Kraul & Markus Seizinger & Jens O. Brunner, 2023. "Machine Learning–Supported Prediction of Dual Variables for the Cutting Stock Problem with an Application in Stabilized Column Generation," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 692-709, May.
    5. Katrin Heßler & Stefan Irnich & Tobias Kreiter & Ulrich Pferschy, 2020. "Lexicographic Bin-Packing Optimization for Loading Trucks in a Direct-Shipping System," Working Papers 2009, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    6. Katrin Heßler & Timo Gschwind & Stefan Irnich, 2017. "Stabilized Branch-and-Price Algorithms for Vector Packing Problems," Working Papers 1713, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    7. Ioannis Fragkos & Zeger Degraeve & Bert De Reyck, 2016. "A Horizon Decomposition Approach for the Capacitated Lot-Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 465-482, August.
    8. Heßler, Katrin & Gschwind, Timo & Irnich, Stefan, 2018. "Stabilized branch-and-price algorithms for vector packing problems," European Journal of Operational Research, Elsevier, vol. 271(2), pages 401-419.
    9. Luciano Costa & Claudio Contardo & Guy Desaulniers & Julian Yarkony, 2022. "Stabilized Column Generation Via the Dynamic Separation of Aggregated Rows," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1141-1156, March.
    10. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    11. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    12. Ann-Kathrin Rothenbächer & Michael Drexl & Stefan Irnich, 2018. "Branch-and-Price-and-Cut for the Truck-and-Trailer Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 52(5), pages 1174-1190, October.
    13. Ann-Kathrin Rothenbächer & Michael Drexl & Stefan Irnich, 2016. "Branch-and-Price-and-Cut for the Truck-andTrailer Routing Problem with Time Windows," Working Papers 1617, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    14. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    15. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    16. Gschwind, Timo & Bianchessi, Nicola & Irnich, Stefan, 2019. "Stabilized branch-price-and-cut for the commodity-constrained split delivery vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 91-104.
    17. Daniel Porumbel & François Clautiaux, 2017. "Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 170-184, February.
    18. Paul A. Chircop & Timothy J. Surendonk & Menkes H. L. van den Briel & Toby Walsh, 2022. "On routing and scheduling a fleet of resource-constrained vessels to provide ongoing continuous patrol coverage," Annals of Operations Research, Springer, vol. 312(2), pages 723-760, May.
    19. Ibrahim Muter & Jean-François Cordeau & Gilbert Laporte, 2014. "A Branch-and-Price Algorithm for the Multidepot Vehicle Routing Problem with Interdepot Routes," Transportation Science, INFORMS, vol. 48(3), pages 425-441, August.
    20. Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.

    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:orspec:v:39:y:2017:i:2:d:10.1007_s00291-016-0463-x. 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.