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The maximum clique problem involves finding the largest set of pairwise adjacent vertices in a graph. The problem is classic but still attracts much attention because of its hardness and its prominent applications. Our work is based on the existence of an order on all the vertices whereby those belonging to a maximum clique stay close enough to each other. Such an order can be identified via the extraction of a particular subgraph from the original graph. The problem can consequently be seen as a permutation problem that can be addressed efficiently with an evolutionary-like algorithm, here we use a memetic algorithm (MA). Computational experiments conducted on DIMACS benchmark instances clearly show our MA which not only outperforms existing genetic approaches, but also compares very well to state-of-the-art algorithms.

SUBGRAPH EXTRACTION AND MEMETIC ALGORITHM FOR THE MAXIMUM CLIQUE PROBLEM