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Flying elephants: a general method for solving non-differentiable problems

Author

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  • Adilson Elias Xavier

    (Federal University of Rio de Janeiro)

  • Vinicius Layter Xavier

    (Federal University of Rio de Janeiro)

Abstract

Flying Elephants (FE) is a generalization and a new interpretation of the Hyperbolic Smoothing approach. The article introduces the fundamental smoothing procedures. It contains a general overview of successful applications of the approach for solving a select set of five important problems, namely: distance geometry, covering, clustering, Fermat–Weber and hub location. For each problem the original non-smooth formulation and the succedaneous completely differentiable one are presented. Computational experiments for all related problems obtained results that exhibited a high level of performance according to all criteria: consistency, robustness and efficiency. For each problem some results to illustrate the performance of FE are also presented.

Suggested Citation

  • Adilson Elias Xavier & Vinicius Layter Xavier, 2016. "Flying elephants: a general method for solving non-differentiable problems," Journal of Heuristics, Springer, vol. 22(4), pages 649-664, August.
    • Handle: RePEc:spr:joheur:v:22:y:2016:i:4:d:10.1007_s10732-014-9268-8
    DOI: 10.1007/s10732-014-9268-8
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    References listed on IDEAS

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    1. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2011. "Benders Decomposition for Large-Scale Uncapacitated Hub Location," Operations Research, INFORMS, vol. 59(6), pages 1477-1490, December.
    2. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
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    Cited by:

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    2. Mudassir Shams & Bruno Carpentieri, 2024. "A High-Order Numerical Scheme for Efficiently Solving Nonlinear Vectorial Problems in Engineering Applications," Mathematics, MDPI, vol. 12(15), pages 1-33, July.

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