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A symmetry-based splitting strategy for discretizable distance geometry problems

Author

Listed:
  • Felipe Fidalgo

    (Federal University of Santa Catarina)

  • Douglas S. Gonçalves

    (Federal University of Santa Catarina)

  • Carlile Lavor

    (University of Campinas)

  • Leo Liberti

    (École Polytechnique)

  • Antonio Mucherino

    (Université de Rennes 1)

Abstract

Discretizable distance geometry problems consist in a subclass of distance geometry problems where the search space can be discretized and reduced to a tree. Such problems can be tackled by applying a branch-and-prune algorithm, which is able to perform an exhaustive enumeration of the solution set. In this work, we exploit the concept of symmetry in the search tree for isolating subtrees that are explored only one time for improving the algorithm performances. The proposed strategy is based on the idea of dividing an original instance of the problem into sub-instances that can thereafter be solved (almost) independently. We present some computational experiments on a set of artificially generated instances, with exact distances, to validate the theoretical results.

Suggested Citation

  • Felipe Fidalgo & Douglas S. Gonçalves & Carlile Lavor & Leo Liberti & Antonio Mucherino, 2018. "A symmetry-based splitting strategy for discretizable distance geometry problems," Journal of Global Optimization, Springer, vol. 71(4), pages 717-733, August.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:4:d:10.1007_s10898-018-0610-9
    DOI: 10.1007/s10898-018-0610-9
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    References listed on IDEAS

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    1. Antonio Mucherino & Carlile Lavor & Leo Liberti & Nelson Maculan, 2012. "The Discretizable Molecular Distance Geometry Problem," Post-Print hal-00756940, HAL.
    2. Carlile Lavor & Leo Liberti & Antonio Mucherino, 2013. "The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances," Journal of Global Optimization, Springer, vol. 56(3), pages 855-871, July.
    3. Antonio Mucherino & Carlile Lavor & Leo Liberti, 2012. "The Discretizable Distance Geometry Problem," Post-Print hal-00756943, HAL.
    4. Carlile Lavor & Leo Liberti & Nelson Maculan & Antonio Mucherino, 2012. "The discretizable molecular distance geometry problem," Computational Optimization and Applications, Springer, vol. 52(1), pages 115-146, May.
    5. Lavor, Carlile & Liberti, Leo & Maculan, Nelson & Mucherino, Antonio, 2012. "Recent advances on the Discretizable Molecular Distance Geometry Problem," European Journal of Operational Research, Elsevier, vol. 219(3), pages 698-706.
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    Citations

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    Cited by:

    1. Simon J. L. Billinge & Phillip M. Duxbury & Douglas S. Gonçalves & Carlile Lavor & Antonio Mucherino, 2018. "Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures," Annals of Operations Research, Springer, vol. 271(1), pages 161-203, December.

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