IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v68y2017i4d10.1007_s10898-017-0503-3.html
   My bibliography  Save this article

Guided dive for the spatial branch-and-bound

Author

Listed:
  • D. Gerard

    (University of Liège)

  • M. Köppe

    (University of California)

  • Q. Louveaux

    (University of Liège)

Abstract

We study the spatial Brand-and-Bound algorithm for the global optimization of nonlinear problems. In particular we are interested in a method to find quickly good feasible solutions. Most spatial Branch-and-Bound-based solvers use a non-global solver at a few nodes to try to find better incumbents. We show that it is possible to improve the branching rules and the node priority by exploiting the solutions from the non-global solver. We also propose several smart adaptive strategies to choose when to run the non-global solver. We show that despite the time spent in solving more NLP problems in the nodes, the new strategies enable the algorithm to find the first good incumbents faster and to prove the global optimality faster. Numerous easy, medium size as well as hard NLP instances from the Coconut library are benchmarked. All experiments are run using the open source solver Couenne.

Suggested Citation

  • D. Gerard & M. Köppe & Q. Louveaux, 2017. "Guided dive for the spatial branch-and-bound," Journal of Global Optimization, Springer, vol. 68(4), pages 685-711, August.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:4:d:10.1007_s10898-017-0503-3
    DOI: 10.1007/s10898-017-0503-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0503-3
    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/s10898-017-0503-3?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. Eligius M. T. Hendrix & Boglárka G.-Tóth, 2010. "Nonlinear Programming algorithms," Springer Optimization and Its Applications, in: Introduction to Nonlinear and Global Optimization, chapter 5, pages 91-136, Springer.
    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. Fengqiao Luo & Sanjay Mehrotra, 2021. "A geometric branch and bound method for robust maximization of convex functions," Journal of Global Optimization, Springer, vol. 81(4), pages 835-859, December.
    2. R. Cambini & R. Riccardi & D. Scopelliti, 2023. "Solving linear multiplicative programs via branch-and-bound: a computational experience," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.

    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. M. Soledad Aronna & J. Frédéric Bonnans & Pierre Martinon, 2013. "A Shooting Algorithm for Optimal Control Problems with Singular Arcs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 419-459, August.
    2. Brage Rugstad Knudsen & Hanne Kauko & Trond Andresen, 2019. "An Optimal-Control Scheme for Coordinated Surplus-Heat Exchange in Industry Clusters," Energies, MDPI, vol. 12(10), pages 1-22, May.
    3. Aydogmus, Ozgur & TOR, Ali Hakan, 2021. "A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Zebian, Hussam & Gazzino, Marco & Mitsos, Alexander, 2012. "Multi-variable optimization of pressurized oxy-coal combustion," Energy, Elsevier, vol. 38(1), pages 37-57.
    5. Daniel Word & Jia Kang & Johan Akesson & Carl Laird, 2014. "Efficient parallel solution of large-scale nonlinear dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 59(3), pages 667-688, December.
    6. Paul Armand & Joël Benoist & Riadh Omheni & Vincent Pateloup, 2014. "Study of a primal-dual algorithm for equality constrained minimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 405-433, December.
    7. Sebastian Sager & Mathieu Claeys & Frédéric Messine, 2015. "Efficient upper and lower bounds for global mixed-integer optimal control," Journal of Global Optimization, Springer, vol. 61(4), pages 721-743, April.
    8. Sadrani, Mohammad & Tirachini, Alejandro & Antoniou, Constantinos, 2022. "Vehicle dispatching plan for minimizing passenger waiting time in a corridor with buses of different sizes: Model formulation and solution approaches," European Journal of Operational Research, Elsevier, vol. 299(1), pages 263-282.
    9. Dominik Bongartz & Alexander Mitsos, 2017. "Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations," Journal of Global Optimization, Springer, vol. 69(4), pages 761-796, December.
    10. Alexander Mitsos & Jaromił Najman & Ioannis G. Kevrekidis, 2018. "Optimal deterministic algorithm generation," Journal of Global Optimization, Springer, vol. 71(4), pages 891-913, August.
    11. Cao, Yankai & Zavala, Victor M. & D’Amato, Fernando, 2018. "Using stochastic programming and statistical extrapolation to mitigate long-term extreme loads in wind turbines," Applied Energy, Elsevier, vol. 230(C), pages 1230-1241.
    12. Bethany L. Nicholson & Wei Wan & Shivakumar Kameswaran & Lorenz T. Biegler, 2018. "Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 70(2), pages 321-350, June.
    13. Huster, Wolfgang R. & Vaupel, Yannic & Mhamdi, Adel & Mitsos, Alexander, 2018. "Validated dynamic model of an organic Rankine cycle (ORC) for waste heat recovery in a diesel truck," Energy, Elsevier, vol. 151(C), pages 647-661.
    14. Zebian, Hussam & Mitsos, Alexander, 2012. "A double-pinch criterion for regenerative Rankine cycles," Energy, Elsevier, vol. 40(1), pages 258-270.
    15. Seung-Jun Shin & Duck Bong Kim & Guodong Shao & Alexander Brodsky & David Lechevalier, 2017. "Developing a decision support system for improving sustainability performance of manufacturing processes," Journal of Intelligent Manufacturing, Springer, vol. 28(6), pages 1421-1440, August.
    16. Lizarraga-Garcia, Enrique & Ghobeity, Amin & Totten, Mark & Mitsos, Alexander, 2013. "Optimal operation of a solar-thermal power plant with energy storage and electricity buy-back from grid," Energy, Elsevier, vol. 51(C), pages 61-70.
    17. Dizqah, Arash M. & Maheri, Alireza & Busawon, Krishna, 2014. "An accurate method for the PV model identification based on a genetic algorithm and the interior-point method," Renewable Energy, Elsevier, vol. 72(C), pages 212-222.
    18. Máša, Vítězslav & Stehlík, Petr & Touš, Michal & Vondra, Marek, 2018. "Key pillars of successful energy saving projects in small and medium industrial enterprises," Energy, Elsevier, vol. 158(C), pages 293-304.
    19. Gabriel Haeser, 2018. "A second-order optimality condition with first- and second-order complementarity associated with global convergence of algorithms," Computational Optimization and Applications, Springer, vol. 70(2), pages 615-639, June.
    20. Paweł Tomtas & Amadeusz Skwiot & Elżbieta Sobiecka & Andrzej Obraniak & Katarzyna Ławińska & Tomasz P. Olejnik, 2021. "Bench Tests and CFD Simulations of Liquid–Gas Phase Separation Modeling with Simultaneous Liquid Transport and Mechanical Foam Destruction," Energies, MDPI, vol. 14(6), pages 1-14, 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:spr:jglopt:v:68:y:2017:i:4:d:10.1007_s10898-017-0503-3. 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.