Local search metaheuristics for the critical node problem

Local search metaheuristics for the critical node problem

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Article ID: iaor20161391
Volume: 67
Issue: 3
Start Page Number: 209
End Page Number: 221
Publication Date: May 2016
Journal: Networks
Authors: , , ,
Keywords: graphs, heuristics: local search
Abstract:

We present two metaheuristics for the Critical Node Problem, that is, the maximal fragmentation of a graph through the deletion of k nodes. The two metaheuristics are based on the Iterated Local Search and Variable Neighborhood Search frameworks. Their main characteristic is to exploit two smart and computationally efficient neighborhoods which we show can be implemented far more efficiently than the classical neighborhood based on the exchange of any two nodes in the graph, and which we prove is equivalent to the classical neighborhood in the sense that it yields the same set of neighbors. Solutions to improve the overall running time without deteriorating the quality of the solution computed are also illustrated. The results of the proposed metaheuristics outperform those currently available in literature.

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