Journal of Combinatorial Optimization

, Volume 32, Issue 2, pp 531–549 | Cite as

Solving the maximum vertex weight clique problem via binary quadratic programming

  • Yang Wang
  • Jin-Kao Hao
  • Fred Glover
  • Zhipeng Lü
  • Qinghua Wu


In recent years, the general binary quadratic programming (BQP) model has been widely applied to solve a number of combinatorial optimization problems. In this paper, we recast the maximum vertex weight clique problem (MVWCP) into this model which is then solved by a probabilistic tabu search algorithm designed for the BQP. Experimental results on 80 challenging DIMACS-W and 40 BHOSLIB-W benchmark instances demonstrate that this general approach is viable for solving the MVWCP problem.


Maximum vertex weight clique Binary quadratic programming Probabilistic tabu search 



We are grateful to the reviewers and the editors for their comments which help us to improve the paper. This work was supported by National Natural Science Foundation of China (Grant Nos. 71501157, 71172124), China Postdoctoral Science Foundation (Grant No. 2015M580873) and Northwestern Polytechnical University (Grant No. 3102015RW007).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Yang Wang
    • 1
  • Jin-Kao Hao
    • 2
    • 3
  • Fred Glover
    • 4
  • Zhipeng Lü
    • 5
  • Qinghua Wu
    • 6
  1. 1.School of ManagementNorthwestern Polytechnical UniversityXi’anChina
  2. 2.LERIAUniversité d’AngersAngersFrance
  3. 3.Institut Universitaire de FranceParisFrance
  4. 4.OptTek Systems, IncBoulderUSA
  5. 5.School of Computer Science and TechnologyHuazhong University of Science and TechnologyWuhanChina
  6. 6.School of ManagementHuazhong University of Science and TechnologyWuhanChina

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