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A novel two-model local search algorithm with a self-adaptive parameter for clique partitioning problem

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Abstract

Given a complete edge-weighted undirected graph G(V, E, W), clique partitioning problem (CPP) aims to cluster all vertices into an unknown number of disjoint groups and the objective is to maximize the sum of the edge weights of the induced subgraphs. CPP is an NP-hard combinatorial optimization problem with many real-world applications. In this paper, we propose a novel two-model local search algorithm with a self-adaptive parameter (TMLS\(\_\)SA) to solve CPP. First, a simple solution is presented, that is, one vertex per group is used. Then, we present a two-model local search that is used to improve the solution which comprises a move operator model and an exchange operator model. In the local search phase, a gain function is used to guide the search toward a possible best solution, and a lock mechanism is also applied to prevent the local search from immediately returning to visited solutions. Finally, we execute a perturbation procedure to increase the diversity. The perturbation strength is updated self-adaptively according to the solutions obtained. Our algorithm TMLS\(\_\)SA is compared with several representative algorithms, and the experimental results show that TMLS\(\_\)SA is superior to competitors on almost all test instances with respect to the solution quality.

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Acknowledgements

This work was supported the project of Jilin Provincial Science and Technology Department under Grant No. 20190302109GX, National Natural Science Foundation of China (NSFC) under Grant No. 61806082, 61976050, the Fundamental Research Funds for the Central Universities No. 2412020QD008, Certificate of China Postdoctoral Science Foundation Grant No. 2019M651208.

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Authors and Affiliations

  1. School of Information Science and Technology, Northeast Normal University, Changchun, 130117, China

    Shuli Hu, Xiaoli Wu, Huan Liu & Minghao Yin

  2. School of Management Science and Information Engineering, Jilin University of Finance and Economics, Changchun, 130117, China

    Ruizhi Li

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  1. Shuli Hu
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  2. Xiaoli Wu
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  3. Huan Liu
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  4. Ruizhi Li
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  5. Minghao Yin
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Correspondence to Minghao Yin.

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The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Hu, S., Wu, X., Liu, H. et al. A novel two-model local search algorithm with a self-adaptive parameter for clique partitioning problem. Neural Comput & Applic 33, 4929–4944 (2021). https://doi.org/10.1007/s00521-020-05289-5

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