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Node selection through upper bounding local search methods in branch & bound solvers for NCOPs

Author

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  • Victor Reyes

    (Universidad Diego Portales)

  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

Abstract

Interval-based branch & bound solvers are commonly used for solving Nonlinear Continuous global Optimization Problems (NCOPs). In each iteration, the solver strategically chooses and processes a node within the search tree. The node is bisected and the two generated offspring nodes are processed by filtering methods. For each of these nodes, the solver also searches for new feasible solutions in order to update the best candidate solution. The cost of this solution is used for pruning non-optimal branches of the search tree. Thus, node selection and finding new solutions, stands as pivotal aspects in the functionality of these kind of solvers. The ability to find close-to-optimal solutions early in the search process may discard extensive non-optimal search space regions, thereby effectively reducing the overall size of the search tree. In this work, we propose three novel node selection algorithms that use the feasible solutions obtained through a cost-effective iterative method. Upon updating the best candidate solution, these algorithms strategically choose the node containing this solution for subsequent processing. The newly introduced strategies have been incorporated as node selection methods in a state-of-the-art branch & bound solver, showing promising results in a set of 57 benchmark instances.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jglopt:v:91:y:2025:i:2:d:10.1007_s10898-024-01403-2
    DOI: 10.1007/s10898-024-01403-2
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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. Arne Stolbjerg Drud, 1994. "CONOPT—A Large-Scale GRG Code," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 207-216, May.
    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. Victor Reyes & Ignacio Araya, 2021. "AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems," Journal of Global Optimization, Springer, vol. 79(2), pages 413-429, February.
    5. 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.
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