Skip to main content
SpringerLink
Log in

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

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Alipour MM, Razavi SN, Derakhshi MRF, Balafar MA (2018) A hybrid algorithm using a genetic algorithm and multiagent reinforcement learning heuristic to solve the traveling salesman problem. Neural Comput Appl 30(9):2935–2951

    Article  Google Scholar 

  2. Brimberg J, Mladenović N, Urošević D (2015) Solving the maximally diverse grouping problem by skewed general variable neighborhood search. Inf Sci 295:650–675

    Article  Google Scholar 

  3. Brimberg J, Janićijević S, Mladenović N, Urošević D (2017) Solving the clique partitioning problem as a maximally diverse grouping problem. Optim Lett 11(6):1123–1135

    Article  MathSciNet  Google Scholar 

  4. Brusco MJ, Köhn HF (2009) Clustering qualitative data based on binary equivalence relations: neighborhood search heuristics for the clique partitioning problem. Psychometrika 74(4):685

    Article  MathSciNet  Google Scholar 

  5. Charon I, Hudry O (2006) Noising methods for a clique partitioning problem. Discret Appl Math 154(5):754–769

    Article  MathSciNet  Google Scholar 

  6. Charon I, Hudry O (2007) Application of the“ descent with mutations” metaheuristic to a clique partitioning problem. In: 2007 IEEE international conference on research. Innovation and vision for the future, IEEE, pp 29–35

  7. De Amorim SG, Barthélemy JP, Ribeiro CC (1992) Clustering and clique partitioning: simulated annealing and Tabu search approaches. J Classif 9(1):17–41

    Article  MathSciNet  Google Scholar 

  8. Dorndorf U, Pesch E (1994) Fast clustering algorithms. ORSA J Comput. 6(2):141–153

    Article  Google Scholar 

  9. Dorndorf U, Jaehn F, Pesch E (2008) Modelling robust flight-gate scheduling as a clique partitioning problem. Transp Sci 42(3):292–301

    Article  Google Scholar 

  10. Dorndorf U, Jaehn F, Pesch E (2012) Flight gate scheduling with respect to a reference schedule. Ann Oper Res 194(1):177–187

    Article  MathSciNet  Google Scholar 

  11. Glover F, Laguna M (1998) Tabu search. In: Handbook of combinatorial optimization. Springer, New York, pp 2093–2229

    Chapter  Google Scholar 

  12. Grötschel M, Wakabayashi Y (1989) A cutting plane algorithm for a clustering problem. Math Program 45(1–3):59–96

    Article  MathSciNet  Google Scholar 

  13. Grötschel M, Wakabayashi Y (1990) Facets of the clique partitioning polytope. Math Program 47(1–3):367–387

    Article  MathSciNet  Google Scholar 

  14. Guénoche A (2011) Consensus of partitions: a constructive approach. Adv Data Anal Classif 5(3):215–229

    Article  MathSciNet  Google Scholar 

  15. Hudry O (2019) Application of the “descent with mutations” metaheuristic to a clique partitioning problem. RAIRO Oper Res 53(3):1083–1095

    Article  MathSciNet  Google Scholar 

  16. Jaehn F, Pesch E (2013) New bounds and constraint propagation techniques for the clique partitioning problem. Discret Appl Math 161(13–14):2025–2037

    Article  MathSciNet  Google Scholar 

  17. Ji X, Mitchell JE (2007) Branch-and-price-and-cut on the clique partitioning problem with minimum clique size requirement. Discret Optim 4(1):87–102

    Article  MathSciNet  Google Scholar 

  18. Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591

    Google Scholar 

  19. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  MathSciNet  Google Scholar 

  20. Li R, Hu S, Wang J (2015) The community structure of the constraint satisfaction problem instances of model RB. J Comput Theoret Nanosci 12(12):6088–6093

    Article  Google Scholar 

  21. Li R, Hu S, Zhang H, Yin M (2016) An efficient local search framework for the minimum weighted vertex cover problem. Inf Sci 372:428–445

    Article  Google Scholar 

  22. Li R, Wu X, Liu H, Wu J, Yin M (2018) An efficient local search for the maximum edge weighted clique problem. IEEE Access 6:10743–10753

    Article  Google Scholar 

  23. Marcotorchino J, Michaud P (1981) Heuristic approach of the similarity aggregation problem. Method Oper Res 43:395–404

    MATH  Google Scholar 

  24. Mehrotra A, Trick MA (1998) Cliques and clustering: a combinatorial approach. Oper Res Lett 22(1):1–12

    Article  MathSciNet  Google Scholar 

  25. Oosten M, Rutten JH, Spieksma FC (2001) The clique partitioning problem: facets and patching facets. Netw Int J 38(4):209–226

    MathSciNet  MATH  Google Scholar 

  26. Palubeckis G, Ostreika A (2014) Tomkevičius A (2014) An iterated Tabu search approach for the clique partitioning problem. Sci World J 2014:1–10

    Article  Google Scholar 

  27. Régnier S (1983) Sur quelques aspects mathématiques des problèmes de classification automatique. Mathématiques et Sciences Humaines 82(20)

  28. Wakabayashi Y (1986) Aggregation of binary relations: algorithmic and polyhedral investigations. PhD thesis, Universität Ausburg

  29. Wang H, Alidaee B, Glover F, Kochenberger G (2006) Solving group technology problems via clique partitioning. Int J Flex Manuf Syst 18(2):77–97

    Article  Google Scholar 

  30. Wang Y, Cai S, Yin M (2016) Two efficient local search algorithms for maximum weight clique problem. In: AAAI, pp 805–811

  31. Zhang X, Li X, Wang J (2017) Local search algorithm with path relinking for single batch-processing machine scheduling problem. Neural Comput Appl 28(1):313–326

    Article  Google Scholar 

  32. Zhou Y, Hao JK, Goëffon A (2016) A three-phased local search approach for the clique partitioning problem. J Combin Optim 32(2):469–491

    Article  MathSciNet  Google Scholar 

  33. Zhou Y, Wang Y, Gao J, Luo N, Wang J (2018) An efficient local search for partial vertex cover problem. Neural Comput Appl 30(7):2245–2256

    Article  Google Scholar 

  34. Zhou Y, Wang R, Zhao C, Luo Q, Metwally MA (2019) Discrete greedy flower pollination algorithm for spherical traveling salesman problem. Neural Comput Appl 31(7):2155–2170

    Article  Google Scholar 

Download references

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.

Author information

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

Authors
  1. Shuli Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoli Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ruizhi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Minghao Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghao Yin.

Ethics declarations

Conflicts of interest

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.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-020-05289-5

Keywords

Search

Navigation