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

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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.

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The authors would like to thank the two referees for their comments.

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Correspondence to Adilson Elias Xavier.

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Xavier, A.E., Xavier, V.L. Flying elephants: a general method for solving non-differentiable problems. J Heuristics 22, 649–664 (2016). https://doi.org/10.1007/s10732-014-9268-8

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  • DOI: https://doi.org/10.1007/s10732-014-9268-8

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