Heuristics to Reduce the Number of Simplices in Longest Edge Bisection Refinement of a Regular n-Simplex
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.
KeywordsRegular Simplex Longest Edge Bisection Complete Binary Tree
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