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lsmear: a variable selection strategy for interval branch and bound solvers

Author

Listed:
  • Ignacio Araya

    (Escuela de Ing. Informática)

  • Bertrand Neveu

    (Imagine LIGM Université Paris–Est)

Abstract

Smear-based variable selection strategies are well-known and commonly used by branch-and-prune interval-based solvers. They estimate the impact of the variables on each constraint of the system by using the partial derivatives and the sizes of the variable domains. Then they aggregate these values, in some way, to estimate the impact of each variable on the whole system. The variable with the greatest impact is then selected. A problem of these strategies is that they, generally, consider all constraints equally important. In this work, we propose a new variable selection strategy which first weights the constraints by using the optimal Lagrangian multipliers of a linearization of the original problem. Then, the impact of the variables is computed with a typical smear-based function but taking into account the weights of the constraints. The strategy isg tested on a set of well-known benchmark instances outperforming significantly the classical variable selection strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:3:d:10.1007_s10898-017-0569-y
    DOI: 10.1007/s10898-017-0569-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Citations

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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.

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