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Exploiting Tree Decomposition for Guiding Neighborhoods Exploration for VNS

Published online by Cambridge University Press:  18 April 2013

Mathieu Fontaine ,
Samir Loudni  and
Patrice Boizumault
Mathieu Fontaine
Affiliation:
Universitéde Caen Basse-Normandie, CNRS, UMR 6072 GREYC, 14032 Caen, France. [email protected]
Samir Loudni
Affiliation:
Universitéde Caen Basse-Normandie, CNRS, UMR 6072 GREYC, 14032 Caen, France. [email protected]
Patrice Boizumault
Affiliation:
Universitéde Caen Basse-Normandie, CNRS, UMR 6072 GREYC, 14032 Caen, France. [email protected]
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Abstract

Tree decomposition introduced by Robertson and Seymour aims to decompose a problem into clusters constituting an acyclic graph. There are works exploiting tree decomposition for complete search methods. In this paper, we show how tree decomposition can be used to efficiently guide local search methods that use large neighborhoods like VNS. We propose DGVNS (Decomposition Guided VNS) which uses the graph of clusters in order to build neighborhood structures enabling better diversification and intensification. Second, we introduce tightness dependent tree decomposition which allows to take advantage of both the structure of the problem and the constraints tightness. Third, experiments performed on random instances (GRAPH) and real life instances (CELAR, SPOT5 and tagSNP) show the appropriateness and the efficiency of our approach. Moreover, we study and discuss the influence of the width of the tree decomposition on our approach and the relevance of removing clusters with very few proper variables from the tree decomposition.

Keywords

Variable neighborhood searchtree decompositionmaximum cardinality searchcost functions netwokconstraint propagation
Type
Research Article
Information
RAIRO - Operations Research , Volume 47 , Issue 2: ConstraintProgramming , April 2013 , pp. 91 - 123
Copyright
© EDP Sciences, ROADEF, SMAI, 2013

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