An Iterated Local Search ILS-CHC for the Maximum Vertex-Weighted Clique Problem

In this paper, we tackle the Maximum Vertex-Weighted Clique Problem MVWCP. This problem consists to find in any weighted and non-oriented graph a clique with the maximum weight, i.e. a complete subgraph which has a maximum weight. MVWCP is an NP-hard combinatorial optimization problem with many practical applications. The objective of this work is to provide good quality solutions in reasonable computational times. Thus, we propose an iterated local search method ILS-CHC which explores the search space using a combined local search method and two levels of perturbation. Experimental studies conducted on the DIMACS benchmark instances show that the proposed approach compares favorably with the state-of-the-art methods and that it is even able to find better cliques than those found in the literature in many instances.