Abstract
This paper presents a three-phased local search heuristic CPP-P\(^{3}\) for solving the Clique Partitioning Problem (CPP). CPP-P\(^{3}\) 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.
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Notes
If some groups contain exactly one vertex, then several moves lead to equivalent solutions. Thus, |N(s)| can be slightly inferior to \(k \times |V|\).
The source code will be available upon publication of the paper at: http://www.info.univ-angers.fr/pub/hao/cpp.html.
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Acknowledgments
The work is partially supported by the PGMO project (2014–2016) from the FMJH Mathematical Foundation. Support for Yi Zhou from the China Scholarship Council is acknowledged. We would like to thank Dr. Dragan Urosević and the co-authors of Brimberg et al. (2015) for providing us with the binary code of their SGVNS algorithm. Thanks also go to the authors of Palubeckis et al. (2014) for publishing their source code. We are grateful to our reviewers for their insightful comments which helped us to improve the paper. We would like to express our gratitude to the editors of the Special Issue (Prof. Weidong Chen and Zhixiang Chen) for their valuable helps and suggestions.
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In memory of Professor Wenqi Huang who has dedicated his life to research on heuristic methods for optimization.
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Zhou, Y., Hao, JK. & Goëffon, A. A three-phased local search approach for the clique partitioning problem. J Comb Optim 32, 469–491 (2016). https://doi.org/10.1007/s10878-015-9964-9
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DOI: https://doi.org/10.1007/s10878-015-9964-9