On Simplicial Longest Edge Bisection in Lipschitz Global Optimization

J.F.R. Herrera, L.G. Casado, E.M.T. Hendrix, I. Garcia

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

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
Original languageEnglish
Title of host publicationComputational Science ans Its Applications - ICCSA 2014, Part II
EditorsB. Murgante, S. Misra, A.M.A.C. Rocha, C. Torre, J.G. Rocha, M.I. Falcao, D. Taniar, B.O. Apduhan, O. Gervasi
Place of PublicationCham
Pages104-114
Number of pages827
DOIs
Publication statusPublished - 2014

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Number8580

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    Herrera, J. F. R., Casado, L. G., Hendrix, E. M. T., & Garcia, I. (2014). On Simplicial Longest Edge Bisection in Lipschitz Global Optimization. In B. Murgante, S. Misra, A. M. A. C. Rocha, C. Torre, J. G. Rocha, M. I. Falcao, D. Taniar, B. O. Apduhan, & O. Gervasi (Eds.), Computational Science ans Its Applications - ICCSA 2014, Part II (pp. 104-114). (Lecture Notes in Computer Science; No. 8580).. https://doi.org/10.1007/978-3-319-09129-7_8