IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v260y2017i3p934-948.html
   My bibliography  Save this article

Constraint propagation using dominance in interval Branch & Bound for nonlinear biobjective optimization

Author

Listed:
  • Martin, Benjamin
  • Goldsztejn, Alexandre
  • Granvilliers, Laurent
  • Jermann, Christophe

Abstract

Constraint propagation has been widely used in nonlinear single-objective optimization inside interval Branch & Bound algorithms as an efficient way to discard infeasible and non-optimal regions of the search space. On the other hand, when considering two objective functions, constraint propagation is uncommon. It has mostly been applied in combinatorial problems inside particular methods. The difficulty is in the exploitation of dominance relations in order to discard the so-called non-Pareto optimal solutions inside a decision domain, which complicates the design of complete and efficient constraint propagation methods exploiting dominance relations.

Suggested Citation

  • Martin, Benjamin & Goldsztejn, Alexandre & Granvilliers, Laurent & Jermann, Christophe, 2017. "Constraint propagation using dominance in interval Branch & Bound for nonlinear biobjective optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 934-948.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:934-948
    DOI: 10.1016/j.ejor.2016.05.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716303824
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.05.045?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. Benjamin Martin & Alexandre Goldsztejn & Laurent Granvilliers & Christophe Jermann, 2016. "On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach," Journal of Global Optimization, Springer, vol. 64(1), pages 3-16, January.
    2. Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2015. "On the representation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 245(3), pages 767-778.
    3. Alexandre Goldsztejn & Ferenc Domes & Brice Chevalier, 2014. "First order rejection tests for multiple-objective optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 653-672, April.
    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. Ignacio Araya & Damir Aliquintui & Franco Ardiles & Braulio Lobo, 2021. "Nonlinear biobjective optimization: improving the upper envelope using feasible line segments," Journal of Global Optimization, Springer, vol. 79(2), pages 503-520, February.
    2. Charles Audet & Frédéric Messine & Jordan Ninin, 2022. "Numerical certification of Pareto optimality for biobjective nonlinear problems," Journal of Global Optimization, Springer, vol. 83(4), pages 891-908, August.
    3. 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.
    4. Marendet, Antoine & Goldsztejn, Alexandre & Chabert, Gilles & Jermann, Christophe, 2020. "A standard branch-and-bound approach for nonlinear semi-infinite problems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 438-452.

    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. Ignacio Araya & Damir Aliquintui & Franco Ardiles & Braulio Lobo, 2021. "Nonlinear biobjective optimization: improving the upper envelope using feasible line segments," Journal of Global Optimization, Springer, vol. 79(2), pages 503-520, February.
    2. Charles Audet & Frédéric Messine & Jordan Ninin, 2022. "Numerical certification of Pareto optimality for biobjective nonlinear problems," Journal of Global Optimization, Springer, vol. 83(4), pages 891-908, August.
    3. 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.
    4. Satya Tamby & Daniel Vanderpooten, 2021. "Enumeration of the Nondominated Set of Multiobjective Discrete Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 72-85, January.
    5. Kerstin Dächert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jörg Wenzel, 2022. "Multicriteria asset allocation in practice," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 349-373, June.
    6. Dukkanci, Okan & Karsu, Özlem & Kara, Bahar Y., 2022. "Planning sustainable routes: Economic, environmental and welfare concerns," European Journal of Operational Research, Elsevier, vol. 301(1), pages 110-123.
    7. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.
    8. Burdett, Robert & Kozan, Erhan, 2016. "A multi-criteria approach for hospital capacity analysis," European Journal of Operational Research, Elsevier, vol. 255(2), pages 505-521.
    9. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    10. Holzmann, Tim & Smith, J.C., 2018. "Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations," European Journal of Operational Research, Elsevier, vol. 271(2), pages 436-449.
    11. Diego Pecin & Ian Herszterg & Tyler Perini & Natashia Boland & Martin Savelsbergh, 2024. "A fast and robust algorithm for solving biobjective mixed integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 221-262, August.
    12. Gabriele Eichfelder & Oliver Stein & Leo Warnow, 2024. "A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1736-1766, November.
    13. Ozgu Turgut & Evrim Dalkiran & Alper E. Murat, 2019. "An exact parallel objective space decomposition algorithm for solving multi-objective integer programming problems," Journal of Global Optimization, Springer, vol. 75(1), pages 35-62, September.
    14. Eichfelder, Gabriele & Warnow, Leo, 2023. "Advancements in the computation of enclosures for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 310(1), pages 315-327.
    15. Kerstin Dachert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jorg Wenzel, 2021. "Multicriteria asset allocation in practice," Papers 2103.10958, arXiv.org.
    16. Kerstin Dächert & Sauleh Siddiqui & Javier Saez-Gallego & Steven A. Gabriel & Juan Miguel Morales, 2019. "A Bicriteria Perspective on L-Penalty Approaches – a Corrigendum to Siddiqui and Gabriel’s L-Penalty Approach for Solving MPECs," Networks and Spatial Economics, Springer, vol. 19(4), pages 1199-1214, December.
    17. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    18. Doğan, Ilgın & Lokman, Banu & Köksalan, Murat, 2022. "Representing the nondominated set in multi-objective mixed-integer programs," European Journal of Operational Research, Elsevier, vol. 296(3), pages 804-818.
    19. Lourdes Uribe & Johan M Bogoya & Andrés Vargas & Adriana Lara & Günter Rudolph & Oliver Schütze, 2020. "A Set Based Newton Method for the Averaged Hausdorff Distance for Multi-Objective Reference Set Problems," Mathematics, MDPI, vol. 8(10), pages 1-29, October.
    20. Mesquita-Cunha, Mariana & Figueira, José Rui & Barbosa-Póvoa, Ana Paula, 2023. "New ϵ−constraint methods for multi-objective integer linear programming: A Pareto front representation approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 286-307.

    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:eee:ejores:v:260:y:2017:i:3:p:934-948. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.