Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/88140
Type: Artigo
Title: Integer programming approaches for minimum stabbing problems
Title Alternative: 
Author: Piva, Breno
Souza, Cid C. de
Frota, Yuri
Simonetti, Luidi
Abstract: The problem of finding structures with minimum stabbing number has received considerable attention from researchers. Particularly, [10] study the minimum stabbing number of perfect matchings (mspm), spanning trees (msst) and triangulations (mstr) associated to set of points in the plane. The complexity of the mstr remains open whilst the other two are known to be . This paper presents integer programming (ip) formulations for these three problems, that allowed us to solve them to optimality through ip branch-and-bound (b&b) or branch-and-cut (b&c) algorithms. Moreover, these models are the basis for the development of Lagrangian heuristics. Computational tests were conducted with instances taken from the literature where the performance of the Lagrangian heuristics were compared with that of the exact b&b and b&c algorithms. The results reveal that the Lagrangian heuristics yield solutions with minute, and often null, duality gaps for instances with several hundreds of points in small computation times. To our knowledge, this is the first computational study ever reported in which these three stabbing problems are considered and where provably optimal solutions are given. © 2014 EDP Sciences, ROADEF, SMAI.
The problem of finding structures with minimum stabbing number has received considerable attention from researchers. Particularly, [10] study the minimum stabbing number of perfect matchings (mspm), spanning trees (msst) and triangulations (mstr) associat
Subject: Programação inteira
Otimização combinatória
Geometria computacional
Complexidade computacional
Algoritmos branch and bound
Algoritmos branch-and-cut
Country: França
Editor: EDP Sciences
Citation: Rairo - Operations Research. , v. 48, n. 2, p. 211 - 233, 2014.
Rights: aberto
Aberto
Identifier DOI: 10.1051/ro/2014008
Address: https://www.rairo-ro.org/articles/ro/abs/2014/02/ro140008/ro140008.html
Date Issue: 2014
Appears in Collections:IC - Artigos e Outros Documentos

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