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

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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.

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