Finding a maximum clique in an arbitrary graph
SIAM Journal on Computing
An O(m + nlog n) algorithm for the maximum-clique problem in circular-arc graphs
Journal of Algorithms
On the effectiveness of genetic search in combinatorial optimization
SAC '95 Proceedings of the 1995 ACM symposium on Applied computing
Memetic algorithms: a short introduction
New ideas in optimization
A simple heuristic based genetic algorithm for the maximum clique problem
SAC '98 Proceedings of the 1998 ACM symposium on Applied Computing
Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Hybrid Genetic Algorithm for the Maximum Clique Problem
Proceedings of the 6th International Conference on Genetic Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Variable neighborhood search for the maximum clique
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
A hybrid heuristic for the maximum clique problem
Journal of Heuristics
A study of ACO capabilities for solving the maximum clique problem
Journal of Heuristics
A new trust region technique for the maximum weight clique problem
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
Dynamic local search for the maximum clique problem
Journal of Artificial Intelligence Research
Cooperating local search for the maximum clique problem
Journal of Heuristics
An exact algorithm for the maximum clique problem
Operations Research Letters
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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 of 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 by metaheuristics. We first design a memetic algorithm (MA) for this purpose. Computational experiments conducted on the DIMACS benchmark instances clearly show that our MA not only outperforms existing genetic approaches, but it also compares very well to state-of-the-art algorithms regarding the maximal clique size found after different runs. Furthermore, we show that a hybridization of MA with an iterated local search (ILS) improves the stability of the algorithm. This hybridization (MA-ILS) permits to find two distinct maximal cliques of size 79 and one of size 80 for the C2000.9 instance of the DIMACS benchmark.