Variable neighborhood search for the maximum clique

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.