IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v60y2014i2p373-389.html
   My bibliography  Save this article

Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming

Author

Listed:
  • Wendel Melo
  • Marcia Fampa
  • Fernanda Raupp

Abstract

In this paper, we present a new hybrid algorithm for convex Mixed Integer Nonlinear Programming (MINLP). The proposed hybrid algorithm is an improved version of the classical nonlinear branch-and-bound (BB) procedure, where the enhancements are obtained with the application of the outer approximation algorithm on some nodes of the enumeration tree. The two methods are combined in such a way that each one collaborates to the convergence of the other. Computational experiments with benchmark instances of the MINLP problem show the good performance of the proposed algorithm, which is compared to the outer approximation algorithm, the nonlinear BB algorithm and the hybrid algorithm implemented in the solver Bonmin. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Wendel Melo & Marcia Fampa & Fernanda Raupp, 2014. "Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming," Journal of Global Optimization, Springer, vol. 60(2), pages 373-389, October.
  • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:373-389
    DOI: 10.1007/s10898-014-0217-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-014-0217-8
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10898-014-0217-8?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. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    2. Still, Claus & Westerlund, Tapio, 2006. "A sequential cutting plane algorithm for solving convex NLP problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 444-464, September.
    3. Walter Murray & Kien-Ming Ng, 2010. "An algorithm for nonlinear optimization problems with binary variables," Computational Optimization and Applications, Springer, vol. 47(2), pages 257-288, October.
    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. Marcia Fampa & Jon Lee & Wendel Melo, 2016. "A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space," Computational Optimization and Applications, Springer, vol. 65(1), pages 47-71, September.
    2. Arash Kaviani & Russell G. Thompson & Abbas Rajabifard & Majid Sarvi, 2020. "A model for multi-class road network recovery scheduling of regional road networks," Transportation, Springer, vol. 47(1), pages 109-143, February.
    3. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2020. "An overview of MINLP algorithms and their implementation in Muriqui Optimizer," Annals of Operations Research, Springer, vol. 286(1), pages 217-241, March.
    4. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2018. "Integrality gap minimization heuristics for binary mixed integer nonlinear programming," Journal of Global Optimization, Springer, vol. 71(3), pages 593-612, July.
    5. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2022. "Two linear approximation algorithms for convex mixed integer nonlinear programming," Annals of Operations Research, Springer, vol. 316(2), pages 1471-1491, September.

    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. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2020. "An overview of MINLP algorithms and their implementation in Muriqui Optimizer," Annals of Operations Research, Springer, vol. 286(1), pages 217-241, March.
    2. Wang, Zhuolin & You, Keyou & Song, Shiji & Zhang, Yuli, 2020. "Wasserstein distributionally robust shortest path problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 31-43.
    3. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2011. "A new class of functions for measuring solution integrality in the Feasibility Pump approach," DIS Technical Reports 2011-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. Marcia Fampa & Jon Lee & Wendel Melo, 2016. "A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space," Computational Optimization and Applications, Springer, vol. 65(1), pages 47-71, September.
    5. Ahmad Almuhtady & Seungchul Lee & Edwin Romeijn & Michael Wynblatt & Jun Ni, 2014. "A Degradation-Informed Battery-Swapping Policy for Fleets of Electric or Hybrid-Electric Vehicles," Transportation Science, INFORMS, vol. 48(4), pages 609-618, November.
    6. Sönke Behrends & Ruth Hübner & Anita Schöbel, 2018. "Norm bounds and underestimators for unconstrained polynomial integer minimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 73-107, February.
    7. M. A. Raayatpanah & H. Salehi Fathabadi & H. Bahramgiri & P. M. Pardalos, 2015. "Optimal-constrained multicast sub-graph over coded packet networks," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 723-738, May.
    8. Francisco Trespalacios & Ignacio E. Grossmann, 2015. "Algorithmic Approach for Improved Mixed-Integer Reformulations of Convex Generalized Disjunctive Programs," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 59-74, February.
    9. Zhou Wei & M. Montaz Ali & Liang Xu & Bo Zeng & Jen-Chih Yao, 2019. "On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 840-863, June.
    10. Tommy Andersson & Christer Andersson, 2009. "Solving House Allocation Problems with Risk-Averse Agents," Computational Economics, Springer;Society for Computational Economics, vol. 33(4), pages 389-401, May.
    11. Javier Cano & Javier M. Moguerza & Francisco J. Prieto, 2017. "Using Improved Directions of Negative Curvature for the Solution of Bound-Constrained Nonconvex Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 474-499, August.
    12. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    13. Duan Li & Xiaoling Sun & Ken McKinnon, 2005. "An Exact Solution Method for Reliability Optimization in Complex Systems," Annals of Operations Research, Springer, vol. 133(1), pages 129-148, January.
    14. Xiaoling Sun & Duan Li, 2000. "Asymptotic Strong Duality for Bounded Integer Programming: A Logarithmic-Exponential Dual Formulation," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 625-644, November.
    15. Terzi, Mourad & Ouazene, Yassine & Yalaoui, Alice & Yalaoui, Farouk, 2023. "Lot-sizing and pricing decisions under attraction demand models and multi-channel environment: New efficient formulations," Operations Research Perspectives, Elsevier, vol. 10(C).
    16. Xiaoguang Chen & Hayri Önal, 2014. "An Economic Analysis of the Future U.S. Biofuel Industry, Facility Location, and Supply Chain Network," Transportation Science, INFORMS, vol. 48(4), pages 575-591, November.
    17. David E. Bernal & Zedong Peng & Jan Kronqvist & Ignacio E. Grossmann, 2022. "Alternative regularizations for Outer-Approximation algorithms for convex MINLP," Journal of Global Optimization, Springer, vol. 84(4), pages 807-842, December.
    18. Andreas Lundell & Jan Kronqvist & Tapio Westerlund, 2022. "The supporting hyperplane optimization toolkit for convex MINLP," Journal of Global Optimization, Springer, vol. 84(1), pages 1-41, September.
    19. Peng, Cheng & Kouri, Drew P. & Uryasev, Stan, 2024. "Efficient and robust optimal design for quantile regression based on linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    20. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2018. "Integrality gap minimization heuristics for binary mixed integer nonlinear programming," Journal of Global Optimization, Springer, vol. 71(3), pages 593-612, July.

    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:60:y:2014:i:2:p:373-389. 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.