IDEAS home Printed from https://ideas.repec.org/p/ags/eureia/272158.html

Branching From The Largest Upper Bound: Folklore And Facts

Author

Listed:
  • Fox, B. L.
  • Lenstra, J. K.
  • Rinnooy Kan, A. H. G.
  • Schrage, L. E.

Abstract

Branch-and-bound algorithms are widely used to solve combinatorial maximization problems. At each step of such an algorithm a search strategy selects an active subset of feasible solutions for examination. In this paper we discuss the formal properties and the practical value of search strategies based on branching from the largest upper bound (BLUB strategies). We investigate conditions under which BLUB strategies are optimal in the sense that they minimize the number of subsets generated. Counterexamples show that the conditions given in the literature are not strong enough and a correct optimality condition is formulated. Finally, we argue that the practical objections raised against BLUB strategies are not necessarily convincing.

Suggested Citation

  • Fox, B. L. & Lenstra, J. K. & Rinnooy Kan, A. H. G. & Schrage, L. E., 1977. "Branching From The Largest Upper Bound: Folklore And Facts," Econometric Institute Archives 272158, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272158
    DOI: 10.22004/ag.econ.272158
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/272158/files/erasmus095.pdf
    Download Restriction: no
    File URL: https://ageconsearch.umn.edu/record/272158/files/erasmus095.pdf?subformat=pdfa
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.272158?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. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    2. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    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. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    2. Coşar Gözükırmızı & Metin Demiralp, 2019. "Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic," Mathematics, MDPI, vol. 7(4), pages 1-23, April.
    3. Ekart, Aniko & Nemeth, S. Z., 2005. "Stability analysis of tree structured decision functions," European Journal of Operational Research, Elsevier, vol. 160(3), pages 676-695, February.
    4. Hanif D. Sherali & J. Cole Smith & Antonio A. Trani, 2002. "An Airspace Planning Model for Selecting Flight-plans Under Workload, Safety, and Equity Considerations," Transportation Science, INFORMS, vol. 36(4), pages 378-397, November.
    5. Rosato, Paolo & Stellin, Giuseppe, 1995. "MULTI CRITERIA ANALYSIS IN FARM MANAGEMENT FOLLOWING THE COMMON AGRICULTURAL POLICY REFORM: AN APPLICATION OF MULTI-OBJECTIVE INTEGER LINEAR PROGRAMMING; Proceedings of the 4th Minnesota Padova Conference on Food, Agriculture, and the Environment, 19," Working Papers 14414, University of Minnesota, Center for International Food and Agricultural Policy.
    6. Kezong Tang & Xiong-Fei Wei & Yuan-Hao Jiang & Zi-Wei Chen & Lihua Yang, 2023. "An Adaptive Ant Colony Optimization for Solving Large-Scale Traveling Salesman Problem," Mathematics, MDPI, vol. 11(21), pages 1-26, October.
    7. Jiancheng Long & Wai Yuen Szeto, 2019. "Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks," Operations Research, INFORMS, vol. 67(1), pages 167-182, January.
    8. Amine Lamine & Mahdi Khemakhem & Brahim Hnich & Habib Chabchoub, 2016. "Solving constrained optimization problems by solution-based decomposition search," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 672-695, October.
    9. Hasan Pirkul, 1987. "A heuristic solution procedure for the multiconstraint zero‐one knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 161-172, April.
    10. Shuangyan Li & Yijing Liang & Zhenjie Wang & Dezhi Zhang, 2021. "An Optimization Model of a Sustainable City Logistics Network Design Based on Goal Programming," Sustainability, MDPI, vol. 13(13), pages 1-20, July.
    11. Syam Menon & Linus Schrage, 2002. "Order Allocation for Stock Cutting in the Paper Industry," Operations Research, INFORMS, vol. 50(2), pages 324-332, April.
    12. Weiqiang Pan & Zhilong Shan & Ting Chen & Fangjiong Chen & Jing Feng, 2016. "Optimal pilot design for OFDM systems with non-contiguous subcarriers based on semi-definite programming," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(2), pages 297-305, October.
    13. Joseph, Anito & Gass, Saul I. & Bryson, Noel, 1998. "An objective hyperplane search procedure for solving the general all-integer linear programming (ILP) problem," European Journal of Operational Research, Elsevier, vol. 104(3), pages 601-614, February.
    14. Wang, Lizhi & Nikouei Mehr, Maryam, 2019. "An optimization approach to epistasis detection," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1069-1076.
    15. Kyoungmi Hwang & Dohyun Kim & Kyungsik Lee & Chungmok Lee & Sungsoo Park, 2017. "Embedded variable selection method using signomial classification," Annals of Operations Research, Springer, vol. 254(1), pages 89-109, July.
    16. Balev, Stefan & Yanev, Nicola & Freville, Arnaud & Andonov, Rumen, 2008. "A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 63-76, April.
    17. Drexl, Andreas, 1990. "Scheduling of project networks by job assignment," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 247, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    18. Yi-Feng Hung & Wei-Chih Chen, 2011. "A heterogeneous cooperative parallel search of branch-and-bound method and tabu search algorithm," Journal of Global Optimization, Springer, vol. 51(1), pages 133-148, September.
    19. Mahmoudi, Reza & Saidi, Saeid & Emrouznejad, Ali, 2025. "Mathematical programming in public bus transit design and operations: Emerging technologies and sustainability – A review," Socio-Economic Planning Sciences, Elsevier, vol. 98(C).
    20. Cameron MacKenzie & Hiba Baroud & Kash Barker, 2016. "Static and dynamic resource allocation models for recovery of interdependent systems: application to the Deepwater Horizon oil spill," Annals of Operations Research, Springer, vol. 236(1), pages 103-129, January.

    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:ags:eureia:272158. 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: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.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.