IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v19y2021i4d10.1007_s10288-020-00460-z.html
   My bibliography  Save this article

Inductive linearization for binary quadratic programs with linear constraints

Author

Listed:
  • Sven Mallach

    (University of Bonn)

Abstract

A linearization technique for binary quadratic programs (BQPs) that comprise linear constraints is presented. The technique, called “inductive linearization”, extends concepts for BQPs with particular equation constraints, that have been referred to as “compact linearization” before, to the general case. Quadratic terms may occur in the objective function, in the set of constraints, or in both. For several relevant applications, the linear programming relaxations obtained from applying the technique are proven to be at least as strong as the one obtained with a well-known classical linearization. It is also shown how to obtain an inductive linearization automatically. This might be used, e.g., by general-purpose mixed-integer programming solvers.

Suggested Citation

  • Sven Mallach, 2021. "Inductive linearization for binary quadratic programs with linear constraints," 4OR, Springer, vol. 19(4), pages 549-570, December.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:4:d:10.1007_s10288-020-00460-z
    DOI: 10.1007/s10288-020-00460-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-020-00460-z
    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/s10288-020-00460-z?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. Fred Glover & Eugene Woolsey, 1973. "Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems," Operations Research, INFORMS, vol. 21(1), pages 156-161, February.
    2. Oral, Muhittin & Kettani, Ossama, 1992. "Reformulating nonlinear combinatorial optimization problems for higher computational efficiency," European Journal of Operational Research, Elsevier, vol. 58(2), pages 236-249, April.
    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    4. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
    5. Billionnet, Alain & Calmels, Frederic, 1996. "Linear programming for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 310-325, July.
    6. Sven Mallach, 2018. "Compact linearization for binary quadratic problems subject to assignment constraints," 4OR, Springer, vol. 16(3), pages 295-309, September.
    7. C. Helmberg & F. Rendl & R. Weismantel, 2000. "A Semidefinite Programming Approach to the Quadratic Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 197-215, 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. Sven Mallach, 2018. "Compact linearization for binary quadratic problems subject to assignment constraints," 4OR, Springer, vol. 16(3), pages 295-309, September.
    2. Rostami, Borzou & Malucelli, Federico & Belotti, Pietro & Gualandi, Stefano, 2016. "Lower bounding procedure for the asymmetric quadratic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 584-592.
    3. Caprara, Alberto, 2008. "Constrained 0-1 quadratic programming: Basic approaches and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1494-1503, June.
    4. de Meijer, Frank, 2023. "Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization," Other publications TiSEM b1f1088c-95fe-4b8a-9e15-c, Tilburg University, School of Economics and Management.
    5. Nihal Berktaş & Hande Yaman, 2021. "A Branch-and-Bound Algorithm for Team Formation on Social Networks," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1162-1176, July.
    6. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    7. Monique Guignard, 2020. "Strong RLT1 bounds from decomposable Lagrangean relaxation for some quadratic 0–1 optimization problems with linear constraints," Annals of Operations Research, Springer, vol. 286(1), pages 173-200, March.
    8. Fabio Furini & Emiliano Traversi, 2019. "Theoretical and computational study of several linearisation techniques for binary quadratic problems," Annals of Operations Research, Springer, vol. 279(1), pages 387-411, August.
    9. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.
    10. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    11. Buchheim, Christoph & Crama, Yves & Rodríguez-Heck, Elisabeth, 2019. "Berge-acyclic multilinear 0–1 optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 102-107.
    12. Alain Billionnet & Sourour Elloumi & Amélie Lambert, 2013. "An efficient compact quadratic convex reformulation for general integer quadratic programs," Computational Optimization and Applications, Springer, vol. 54(1), pages 141-162, January.
    13. Neves-Moreira, Fábio & Almada-Lobo, Bernardo & Guimarães, Luís & Amorim, Pedro, 2022. "The multi-product inventory-routing problem with pickups and deliveries: Mitigating fluctuating demand via rolling horizon heuristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    14. Furini, Fabio & Persiani, Carlo Alfredo & Toth, Paolo, 2016. "The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 38-55.
    15. Almoustafa, Samira & Hanafi, Said & Mladenović, Nenad, 2013. "New exact method for large asymmetric distance-constrained vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 226(3), pages 386-394.
    16. Tang, Lixin & Liu, Jiyin & Rong, Aiying & Yang, Zihou, 2000. "A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex," European Journal of Operational Research, Elsevier, vol. 124(2), pages 267-282, July.
    17. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    18. Santos, Lui­s & Coutinho-Rodrigues, João & Current, John R., 2008. "Implementing a multi-vehicle multi-route spatial decision support system for efficient trash collection in Portugal," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(6), pages 922-934, July.
    19. Rahma Lahyani & Leandro C. Coelho & Jacques Renaud, 2018. "Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 125-157, January.
    20. Anja Fischer & Frank Fischer, 2015. "An extended approach for lifting clique tree inequalities," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 489-519, October.

    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:aqjoor:v:19:y:2021:i:4:d:10.1007_s10288-020-00460-z. 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.