Authors: Duarte, Abraham
Escudero, Laureano
Martí, Rafael
Mladenović, Nenad 
Pantrigo, Juan José
Sánchez-Oro, Jesús
Title: Variable neighborhood search for the vertex separation problem
Journal: Computers and Operations Research
Volume: 39
Issue: 12
First page: 3247
Last page: 3255
Issue Date: 1-Dec-2012
Rank: M21
ISSN: 0305-0548
DOI: 10.1016/j.cor.2012.04.017
Abstract: 
The Vertex Separation Problem belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. This optimization problem is strongly related to other well-known graph problems; such as the Path-Width, the Node Search Number or the Interval Thickness, among others. All of these optimization problems are NP-hard and have practical applications in VLSI (Very Large Scale Integration), computer language compiler design or graph drawing. Up to know, they have been generally tackled with exact approaches, presenting polynomial-time algorithms to obtain the optimal solution for specific types of graphs. However, in spite of their practical applications, these problems have been ignored from a heuristic perspective, as far as we know. In this paper we propose a pure 0-1 optimization model and a metaheuristic algorithm based on the variable neighborhood search methodology for the Vertex Separation Problem on general graphs. Computational results show that small instances can be optimally solved with this optimization model and the proposed metaheuristic is able to find high-quality solutions with a moderate computing time for large-scale instances.
Keywords: Combinatorial optimization | Layout problems | Metaheuristics | Variable neigborhood search
Publisher: Elsevier
Project: Spanish Ministry of Science and Innovation, Grants TIN2009-07516 and TIN2011-28151
Government of the Community of Madrid, grant S2009/TIC-1542

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