Solving the Maximum Clique Problem with Multi-Strategy Local Search

Maximum clique problem (MCP) is one of the most popular NP-hard optimization problems on graphs of its simplicity and its numerous applications. Since the combinatorial complexity of the MCP does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using various heuristic methods. In this paper, to solve the MCP, we propose a multi-strategy local search algorithm, which is based on single-step search, two-step search and space partition search techniques. The main body of the proposed algorithm is based on greedy search that is used to speed up its convergence rate. Single-step search, two-step search and space partition search techniques are used to avoid becoming trapped in local minima at the very start. Computational results on DIMACS benchmark graphs indicate that the proposed multi-strategy local search algorithm provides equal compromise between CPU time and accuracy among some recent effective algorithms for the MCP.