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Discrete Applied Mathematics
Volume 145, Issue 1, 30 December 2004, Pages 117-125
Graph Optimization IV
 
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doi:10.1016/j.dam.2003.09.012    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2004 Published by Elsevier B.V.

Variable neighborhood search for the maximum clique

Pierre HansenE-mail The Corresponding Author, a, Nenad MladenoviImage a, b and Dragan UroImage eviImage b

a GERAD and HEC Montréal 3000 ch. de la Côte-Sainte-Catherine, Montréal, Canada H3T 1V6 b Mathematical Institute, Serbian Academy of Science, Kneza Mihajla 35, Belgrade 11000, Serbia, Montenegro, Yugoslavia

Received 27 February 2001; 
Revised 17 June 2003; 
accepted 19 September 2003. 
Available online 13 August 2004.

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Abstract

Maximum clique is one of the most studied NP-hard optimization problem on graphs because of its simplicity and its numerous applications. A basic variable neighborhood search heuristic for maximum clique that combines greedy with the simplicial vertex test in its descent step is proposed and tested on standard test problems from the literature. Despite its simplicity, the proposed heuristic outperforms most of the well-known approximate solution methods. Moreover, it gives solution of equal quality to those of the state-of-the-art heuristic of Battiti and Protasi in half the time.

Author Keywords: Combinatorial optimization; Graphs; Maximum clique; Heuristics; Variable neighborhood search

Article Outline

1. Introduction
2. Basic principles of VNS
3. VNS for the MCP
3.1. Preliminaries
3.2. VND for the MCP
3.3. Shaking
4. Computational results
References




Discrete Applied Mathematics
Volume 145, Issue 1, 30 December 2004, Pages 117-125
Graph Optimization IV
 
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