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ISRN Computational Mathematics
Volume 2012 (2012), Article ID 671423, 12 pages
http://dx.doi.org/10.5402/2012/671423
Research Article

Consistent Neighborhood Search for Combinatorial Optimization

1École des Mines d'Alès, LGI2P Research Center, Parc Scientifique Georges Besse, 30035 Nimes Cedex 01, France
2Faculty of Economics and Social Sciences, HEC–University of Geneva, Uni-Mail, 1211 Geneva 4, Switzerland

Received 11 May 2012; Accepted 28 June 2012

Academic Editors: D. S. Corti, R. K. Upadhyay, and E. Weber

Copyright © 2012 Michel Vasquez and Nicolas Zufferey. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Many optimization problems (from academia or industry) require the use of a local search to find a satisfying solution in a reasonable amount of time, even if the optimality is not guaranteed. Usually, local search algorithms operate in a search space which contains complete solutions (feasible or not) to the problem. In contrast, in Consistent Neighborhood Search (CNS), after each variable assignment, the conflicting variables are deleted to keep the partial solution feasible, and the search can stop when all the variables have a value. In this paper, we formally propose a new heuristic solution method, CNS, which has a search behavior between exhaustive tree search and local search working with complete solutions. We then discuss, with a unified view, the great success of some existing heuristics, which can however be considered within the CNS framework, in various fields: graph coloring, frequency assignment in telecommunication networks, vehicle fleet management with maintenance constraints, and satellite range scheduling. Moreover, some lessons are given in order to have guidelines for the adaptation of CNS to other problems.