IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v64y2016i2d10.1007_s10898-015-0375-3.html
   My bibliography  Save this article

Node selection strategies in interval Branch and Bound algorithms

Author

Listed:
  • Bertrand Neveu

    (Imagine LIGM Université Paris–Est)

  • Gilles Trombettoni

    (University of Montpellier)

  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

Abstract

We present in this article new strategies for selecting nodes in interval Branch and Bound algorithms for constrained global optimization. For a minimization problem the standard best-first strategy selects a node with the smallest lower bound of the objective function estimate. We first propose new node selection policies where an upper bound of each node/box is also taken into account. The good accuracy of this upper bound achieved by several contracting operators leads to a good performance of the node selection rule based on this criterion. We propose another strategy that also makes a tradeoff between diversification and intensification by greedily diving into potential feasible regions at each node of the best-first search. These new strategies obtain better experimental results than classical best-first search on difficult constrained global optimization instances.

Suggested Citation

  • Bertrand Neveu & Gilles Trombettoni & Ignacio Araya, 2016. "Node selection strategies in interval Branch and Bound algorithms," Journal of Global Optimization, Springer, vol. 64(2), pages 289-304, February.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:2:d:10.1007_s10898-015-0375-3
    DOI: 10.1007/s10898-015-0375-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-015-0375-3
    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/s10898-015-0375-3?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. Robert Bixby & Edward Rothberg, 2007. "Progress in computational mixed integer programming—A look back from the other side of the tipping point," Annals of Operations Research, Springer, vol. 149(1), pages 37-41, February.
    2. Jordan Ninin & Frédéric Messine, 2011. "A metaheuristic methodology based on the limitation of the memory of interval branch and bound algorithms," Journal of Global Optimization, Springer, vol. 50(4), pages 629-644, August.
    3. Ignacio Araya & Gilles Trombettoni & Bertrand Neveu & Gilles Chabert, 2014. "Upper bounding in inner regions for global optimization under inequality constraints," Journal of Global Optimization, Springer, vol. 60(2), pages 145-164, October.
    4. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    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. Bertrand Neveu & Martin Gorce & Pascal Monasse & Gilles Trombettoni, 2019. "A generic interval branch and bound algorithm for parameter estimation," Journal of Global Optimization, Springer, vol. 73(3), pages 515-535, March.
    2. Ignacio Araya & Jose Campusano & Damir Aliquintui, 2019. "Nonlinear biobjective optimization: improvements to interval branch & bound algorithms," Journal of Global Optimization, Springer, vol. 75(1), pages 91-110, September.
    3. Ignacio Araya & Bertrand Neveu, 2018. "lsmear: a variable selection strategy for interval branch and bound solvers," Journal of Global Optimization, Springer, vol. 71(3), pages 483-500, July.

    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. Ricardo M. Lima & Ignacio E. Grossmann, 2017. "On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study," Computational Optimization and Applications, Springer, vol. 66(1), pages 1-37, January.
    2. Yi Zhang & Nikolaos V. Sahinidis & Carlos Nohra & Gang Rong, 2020. "Optimality-based domain reduction for inequality-constrained NLP and MINLP problems," Journal of Global Optimization, Springer, vol. 77(3), pages 425-454, July.
    3. Bertrand Neveu & Martin Gorce & Pascal Monasse & Gilles Trombettoni, 2019. "A generic interval branch and bound algorithm for parameter estimation," Journal of Global Optimization, Springer, vol. 73(3), pages 515-535, March.
    4. Xiaoyi Gu & Santanu S. Dey & Jean-Philippe P. Richard, 2024. "Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 884-899, May.
    5. Jaromił Najman & Dominik Bongartz & Alexander Mitsos, 2021. "Linearization of McCormick relaxations and hybridization with the auxiliary variable method," Journal of Global Optimization, Springer, vol. 80(4), pages 731-756, August.
    6. Liang, Zheng & Liang, Yingzong & Luo, Xianglong & Chen, Jianyong & Yang, Zhi & Wang, Chao & Chen, Ying, 2022. "Superstructure-based mixed-integer nonlinear programming framework for hybrid heat sources driven organic Rankine cycle optimization," Applied Energy, Elsevier, vol. 307(C).
    7. Iosif Pappas & Nikolaos A. Diangelakis & Efstratios N. Pistikopoulos, 2021. "The exact solution of multiparametric quadratically constrained quadratic programming problems," Journal of Global Optimization, Springer, vol. 79(1), pages 59-85, January.
    8. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.
    9. W. Brian Lambert & Andrea Brickey & Alexandra M. Newman & Kelly Eurek, 2014. "Open-Pit Block-Sequencing Formulations: A Tutorial," Interfaces, INFORMS, vol. 44(2), pages 127-142, April.
    10. Luo, Xianglong & Huang, Xiaojian & El-Halwagi, Mahmoud M. & Ponce-Ortega, José María & Chen, Ying, 2016. "Simultaneous synthesis of utility system and heat exchanger network incorporating steam condensate and boiler feedwater," Energy, Elsevier, vol. 113(C), pages 875-893.
    11. Artur M. Schweidtmann & Alexander Mitsos, 2019. "Deterministic Global Optimization with Artificial Neural Networks Embedded," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 925-948, March.
    12. Cafieri, Sonia & Omheni, Riadh, 2017. "Mixed-integer nonlinear programming for aircraft conflict avoidance by sequentially applying velocity and heading angle changes," European Journal of Operational Research, Elsevier, vol. 260(1), pages 283-290.
    13. Shyam S. G. Perumal & Jesper Larsen & Richard M. Lusby & Morten Riis & Tue R. L. Christensen, 2022. "A column generation approach for the driver scheduling problem with staff cars," Public Transport, Springer, vol. 14(3), pages 705-738, October.
    14. Martin L. Smith & Stewart J. Wicks, 2014. "Medium-Term Production Scheduling of the Lumwana Mining Complex," Interfaces, INFORMS, vol. 44(2), pages 176-194, April.
    15. Pavlo Muts & Ivo Nowak & Eligius M. T. Hendrix, 2020. "The decomposition-based outer approximation algorithm for convex mixed-integer nonlinear programming," Journal of Global Optimization, Springer, vol. 77(1), pages 75-96, May.
    16. Alexandra M. Newman & Enrique Rubio & Rodrigo Caro & Andrés Weintraub & Kelly Eurek, 2010. "A Review of Operations Research in Mine Planning," Interfaces, INFORMS, vol. 40(3), pages 222-245, June.
    17. Timo Berthold & Jakob Witzig, 2021. "Conflict Analysis for MINLP," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 421-435, May.
    18. Amaro Sousa & Carlos Borges Lopes & Paulo Monteiro, 2016. "Compact ILP formulations for the routing and wavelength assignment problem in the design of optical transport networks with regenerators," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(2), pages 189-213, May.
    19. Huang, Xiaojian & Lu, Pei & Luo, Xianglong & Chen, Jianyong & Yang, Zhi & Liang, Yingzong & Wang, Chao & Chen, Ying, 2020. "Synthesis and simultaneous MINLP optimization of heat exchanger network, steam Rankine cycle, and organic Rankine cycle," Energy, Elsevier, vol. 195(C).
    20. Subramanian, Avinash S.R. & Gundersen, Truls & Barton, Paul I. & Adams, Thomas A., 2022. "Global optimization of a hybrid waste tire and natural gas feedstock polygeneration system," Energy, Elsevier, vol. 250(C).

    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:jglopt:v:64:y:2016:i:2:d:10.1007_s10898-015-0375-3. 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.