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Heuristics to Reduce the Number of Simplices in Longest Edge Bisection Refinement of a Regular n-Simplex

  • Guillermo Aparicio
  • Leocadio G. Casado
  • Boglárka G-Tóth
  • Eligius M. T. Hendrix
  • Inmaculada García
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8580)

Abstract

In several areas like Global Optimization using branch-and-bound methods, the unit n-simplex is refined by bisecting the longest edge such that a binary search tree appears. The refinement usually selects the first longest edge and ends when the size of the sub-simplices generated in the refinement is smaller than a given accuracy. Irregular sub-simplices may have more than one longest edge only for n ≥ 3. The question is how to choose the longest edge to be bisected such that the number of sub-simplices in the generated binary tree is minimal. The difficulty of this Combinatorial Optimization problem increases with n. Therefore, heuristics are studied that aim to minimize the number of generated simplices.

Keywords

Regular Simplex Longest Edge Bisection Complete Binary Tree 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Guillermo Aparicio
    • 1
  • Leocadio G. Casado
    • 2
  • Boglárka G-Tóth
    • 3
  • Eligius M. T. Hendrix
    • 4
  • Inmaculada García
    • 4
  1. 1.TIC 146: Supercomputing-Algorithms Research GroupUniversidad de Almería, Agrifood Campus of International Excellence (ceiA3)Spain
  2. 2.Department of InformaticsUniversity of Almería, Agrifood Campus of International Excellence (ceiA3)Spain
  3. 3.Department of Differential EquationsBudapest University of Technology and EconomicsBudapestHungary
  4. 4.Department of Computer ArchitectureUniversidad de Málaga, Campus de TeatinosSpain

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