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An adaptive multistart tabu search approach to solve the maximum clique problem. (English) Zbl 1275.90084

Summary: Given an undirected graph \(G=(V,E)\) with vertex set \(V={1,\dots,n}\) and an edge set \(E\subseteq V\times V\). The maximum clique problem is to determine in \(G\) a clique (i.e. a complete subgraph) of maximum cardinality. This paper presents an effective algorithm for the maximum clique problem. The proposed multistart tabu search algorithm integrates a constrained neighborhood, a dynamic tabu tenure mechanism and a long term memory based restart strategy. Our proposed algorithm is evaluated on the whole set of 80 DIMACS challenge benchmarks and compared with five state-of-the-art algorithms. Computational results show that our proposed algorithm attains the largest known clique for 79 benchmarks.

MSC:

90C27 Combinatorial optimization
90C35 Programming involving graphs or networks
90C59 Approximation methods and heuristics in mathematical programming
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