Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 496925
Title Generating a smallest binary tree by proper selection of the longest edges to bisect in a unit simplex refinement
Author(s) Salmerón, J.M.G.; Aparicio, G.; Casado, L.G.; García, I.; Hendrix, E.M.T.; Tóth, B.G.
Source Journal of Combinatorial Optimization 33 (2017)2. - ISSN 1382-6905 - p. 389 - 402.
DOI https://doi.org/10.1007/s10878-015-9970-y
Department(s) Operations Research and Logistics
WASS
Publication type Refereed Article in a scientific journal
Publication year 2017
Keyword(s) Bisection sequence - Branch-and-bound - Combinatorial optimization - Longest edge bisection - Regular simplex
Abstract

In several areas like global optimization using branch-and-bound methods for mixture design, the unit n-simplex is refined by longest edge bisection (LEB). This process provides a binary search tree. For (Formula presented.), simplices appearing during the refinement process can have more than one longest edge (LE). The size of the resulting binary tree depends on the specific sequence of bisected longest edges. The questions are how to calculate the size of one of the smallest binary trees generated by LEB and how to find the corresponding sequence of LEs to bisect, which can be represented by a set of LE indices. Algorithms answering these questions are presented here. We focus on sets of LE indices that are repeated at a level of the binary tree. A set of LEs was presented in Aparicio et al. (Informatica 26(1):17–32, 2015), for (Formula presented.). An additional question is whether this set is the best one under the so-called (Formula presented.)-valid condition.

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