The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

Derek H. Smith, Roberto Montemanni, Stephanie Perkins

Research output: Contribution to journalArticlepeer-review

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Let G=(V,E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances.
Original languageEnglish
Article number253
Issue number10
Early online date4 Oct 2020
Publication statusE-pub ahead of print - 4 Oct 2020


  • combinatorial optimization
  • maximum clique
  • hybrid algorithm
  • tabu search
  • benchmarks


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