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Node selection strategies in interval Branch and Bound algorithms

Author

Listed:
  • Bertrand Neveu

    (Imagine LIGM Université Paris–Est)

  • Gilles Trombettoni

    (University of Montpellier)

  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

Abstract

We present in this article new strategies for selecting nodes in interval Branch and Bound algorithms for constrained global optimization. For a minimization problem the standard best-first strategy selects a node with the smallest lower bound of the objective function estimate. We first propose new node selection policies where an upper bound of each node/box is also taken into account. The good accuracy of this upper bound achieved by several contracting operators leads to a good performance of the node selection rule based on this criterion. We propose another strategy that also makes a tradeoff between diversification and intensification by greedily diving into potential feasible regions at each node of the best-first search. These new strategies obtain better experimental results than classical best-first search on difficult constrained global optimization instances.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:2:d:10.1007_s10898-015-0375-3
    DOI: 10.1007/s10898-015-0375-3
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    References listed on IDEAS

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    1. Robert Bixby & Edward Rothberg, 2007. "Progress in computational mixed integer programming—A look back from the other side of the tipping point," Annals of Operations Research, Springer, vol. 149(1), pages 37-41, February.
    2. Jordan Ninin & Frédéric Messine, 2011. "A metaheuristic methodology based on the limitation of the memory of interval branch and bound algorithms," Journal of Global Optimization, Springer, vol. 50(4), pages 629-644, August.
    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. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
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    Cited by:

    1. Victor Reyes & Ignacio Araya, 2025. "Node selection through upper bounding local search methods in branch & bound solvers for NCOPs," Journal of Global Optimization, Springer, vol. 91(2), pages 355-369, February.
    2. Sourour Elloumi & Amélie Lambert & Bertrand Neveu & Gilles Trombettoni, 2025. "Global solution of quadratic problems using interval methods and convex relaxations," Journal of Global Optimization, Springer, vol. 91(2), pages 331-353, February.
    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. 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.
    5. Bertrand Neveu & Martin Gorce & Pascal Monasse & Gilles Trombettoni, 2019. "A generic interval branch and bound algorithm for parameter estimation," Journal of Global Optimization, Springer, vol. 73(3), pages 515-535, March.

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