### 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 language | English |
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Title of host publication | Computational Science ans Its Applications - ICCSA 2014, Part II |

Editors | B. 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 Publication | Cham |

Pages | 104-114 |

Number of pages | 827 |

DOIs | |

Publication status | Published - 2014 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Number | 8580 |

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## Cite this

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