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On Simplicial Longest Edge Bisection in Lipschitz Global Optimization

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Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8580))

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Abstract

Simplicial subsets are popular in branch-and-bound methods for Global Optimization. Longest Edge Bisection is a convenient way to divide a simplex. When the number of dimensions is greater than two, irregular simplices (not all edges have the same length) may appear with more than one longest edge. In these cases, the first longest edge is usually selected. We study the impact of other selection rule of the longest edge to be bisected next on the development of a branch-and-bound algorithm to solve multidimensional Lipschitz Global Optimization instances. Experiments show a significant reduction in the number of evaluated simplices for most of the test problems.

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Authors and Affiliations

  1. Universidad de Almería (ceiA3), Almería, Spain

    Juan F. R. Herrera & Leocadio G. Casado

  2. Universidad de Málaga, Málaga, Spain

    Eligius M. T. Hendrix & Inmaculada García

Authors
  1. Juan F. R. Herrera
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  2. Leocadio G. Casado
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  3. Eligius M. T. Hendrix
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  4. Inmaculada García
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Editor information

Editors and Affiliations

  1. School of Engineering, University of Basilicata, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Computer and Information Sciences, Covenant University, Ota, Nigeria

    Sanjay Misra

  3. Department of Production and Systems, University of Minho, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha

  4. DICAR, Polytecnico di Bari, 70125, Bari, Italy

    Carmelo Torre

  5. University of Minho, Braga, Portugal

    Jorge Gustavo Rocha  & Maria Irene Falcão  & 

  6. Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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© 2014 Springer International Publishing Switzerland

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Herrera, J.F.R., Casado, L.G., Hendrix, E.M.T., García, I. (2014). On Simplicial Longest Edge Bisection in Lipschitz Global Optimization. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8580. Springer, Cham. https://doi.org/10.1007/978-3-319-09129-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-09129-7_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09128-0

  • Online ISBN: 978-3-319-09129-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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