An adaptive multistart tabu search approach to solve the maximum clique problem

Given an undirected graph G = (V,E) with vertex set V = {1, ..., n} and edge set E ⊆ V × 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-theart algorithms. Computational results show that our proposed algorithm attains the largest known clique for 79 benchmarks.