A three-phased local search approach for the clique partitioning problem

This paper presents a three-phased local search heuristic CPP-P $$^{3}$$ 3 for solving the Clique Partitioning Problem (CPP). CPP-P $$^{3}$$ 3 iterates a descent search, an exploration search and a directed perturbation. We also define the Top Move of a vertex, in order to build a restricted and focused neighborhood. The exploration search is ensured by a tabu procedure, while the directed perturbation uses a GRASP-like method. To assess the performance of the proposed approach, we carry out extensive experiments on benchmark instances of the literature as well as newly generated instances. We demonstrate the effectiveness of our approach with respect to the current best performing algorithms both in terms of solution quality and computation efficiency. We present improved best solutions for a number of benchmark instances. Additional analyses are shown to highlight the critical role of the Top Move-based neighborhood for the performance of our algorithm and the relation between instance hardness and algorithm behavior.