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Nonlinear biobjective optimization: improving the upper envelope using feasible line segments

Author

Listed:
  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

  • Damir Aliquintui

    (Pontificia Universidad Católica de Valparaíso)

  • Franco Ardiles

    (Pontificia Universidad Católica de Valparaíso)

  • Braulio Lobo

    (Pontificia Universidad Católica de Valparaíso)

Abstract

In this work, we propose a segment-based representation for the upper bound of the non-dominated set in interval branch & bound solvers for biobjective non linear optimization. We ensure that every point over the upper line segments is dominated by at least one point in the feasible objective region. Segments are generated by linear envelopes of the image of feasible line segments. Finally, we show that the segment-based representation together with methods for generating upper line segments allows us to converge more quickly to the desired precision of the whole strategy. The code of our solver can be found in our git repository ( https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop ).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:2:d:10.1007_s10898-021-00991-7
    DOI: 10.1007/s10898-021-00991-7
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    References listed on IDEAS

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    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 & 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.
    3. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Panos M. Pardalos & Antanas Žilinskas & Julius Žilinskas, 2017. "Non-Convex Multi-Objective Optimization," Springer Optimization and Its Applications, Springer, number 978-3-319-61007-8, June.
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