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Nonlinear biobjective optimization: improvements to interval branch & bound algorithms

Author

Listed:
  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

  • Jose Campusano

    (Pontificia Universidad Católica de Valparaíso)

  • Damir Aliquintui

    (Pontificia Universidad Católica de Valparaíso)

Abstract

Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository ( https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop ).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:1:d:10.1007_s10898-019-00768-z
    DOI: 10.1007/s10898-019-00768-z
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    References listed on IDEAS

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    1. 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.
    2. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    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. J. L. Redondo & J. Fernández & P. M. Ortigosa, 2017. "FEMOEA: a fast and efficient multi-objective evolutionary algorithm," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 113-135, February.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    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.

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