Skip to main content
SpringerLink
Log in

A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem

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

Abstract

The generalized vertex cover problem, an extension of classic minimum vertex cover problem, is an important NP-hard combinatorial optimization problem with a wide range of applications. The aim of this paper is to design an efficient local search algorithm with tabu strategy and perturbation mechanism to solve this problem. Firstly, we use tabu strategy to prevent the local search from immediately returning to a previously visited candidate solution and avoiding the cycling problem. Secondly, we propose the flip gain for each vertex, and then the tabu strategy is combined with the flip gain for vertex selecting. Finally, we apply a simple perturbation mechanism to help the search to escape from deep local optima and to bring diversification into the search. The experiments are carried on random instances with up to 1000 vertexes and 450,000 edges. The experimental results show that our algorithm performs better than a state-of-art algorithm in terms of both solution quality and computational efficiency in most instances.

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

Similar content being viewed by others

References

  1. Richter S, Helmert M, Gretton C (2007) A stochastic local search approach to vertex cover. In: Proceedings of KI-07, pp 412–426

  2. Pullan W, Hoos HH (2006) Dynamic local search for the maximum clique problem. J Artif Intell Res (JAIR) 25:159–185

    MATH  Google Scholar 

  3. Evans I (1998) An evolutionary heuristic for the minimum vertex cover problem. In: Proceedings of EP-98, pp 377–386

  4. Cai S, Su K, Chen Q (2010) EWLS: a new local search for minimum vertex cover. In: Proceedings of AAAI-10, pp 45–50

  5. Cai S, Kaile S, Sattar A (2011) Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artif Intell 175(9–10):1672–1696

    Article  MathSciNet  MATH  Google Scholar 

  6. Cai S, Kaile S, Luo C, Sattar A (2013) NuMVC: an efficient local search algorithm for minimum vertex cover. J Artif Intell Res (JAIR) 46:687–716

    MathSciNet  MATH  Google Scholar 

  7. Cai S, Lin J, Su K (2015) Two weighting local search for minimum vertex cover. In: Proceedings of AAAI-15, pp 1107–1113

  8. Aggarwal C, Orlin J, Tai R (1997) Optimized crossover for the independent set problem. Oper Res 45:226–234

    Article  MathSciNet  MATH  Google Scholar 

  9. Andrade DV, Resende MGC, Werneck RFF (2008) Fast local search for the maximum independent set problem. In: Proceedings of WEA-08, pp 220–234

  10. Barbosa VC, Campos LCD (2004) A novel evolutionary formulation of the maximum independent set problem. J Comb Optim 8(4):419–437

    Article  MathSciNet  MATH  Google Scholar 

  11. Karp R, Miller RE, Theater JW (1972) Complexity of computer computations. Plenum Press, New York

    Google Scholar 

  12. Karp RM (1972) Reducibility among combinatorial problems. Plenum Press, New York, pp 85–103

    Google Scholar 

  13. Jovanovic R, Tuba M (2011) An ant colony optimization algorithm with improved pheromone correction strategy for the minimum weight vertex cover problem. Appl Soft Comput J 11(8):5360–5366

    Article  Google Scholar 

  14. Bouamama S, Blum C, Boukerram A (2012) A population-based iterated greedy algorithm for the minimum weight vertex cover problem[J]. Appl Soft Comput 12(6):1632–1639

    Article  Google Scholar 

  15. Zhou T, Lü Z, Wang Y, et al (2015) Multi-start iterated tabu search for the minimum weight vertex cover problem. J Comb Optim 1–17. doi:10.1007/s10878-015-9909-3

  16. Hassin R, Levin A (2006) The minimum generalized vertex cover problem. ACM Trans Algorithm 2:66–78

    Article  MathSciNet  MATH  Google Scholar 

  17. Voss S, Fink A (2012) A hybridized tabu search approach for the minimum weight vertex cover problem. JOH 18:869–876

    Google Scholar 

  18. Chandu DP (2014) A parallel genetic algorithm for generalized vertex cover problem. arXiv:1411.7612

  19. Kochenberger G, Lewis M, Glover F, et al. (2015) Exact solutions to generalized vertex covering problems: a comparison of two models. Optim Lett 9(7):1331–1339

    Article  MathSciNet  MATH  Google Scholar 

  20. Milanovic M (2010) Solving the generalized vertex cover problem by genetic algorithm. Comput Inf 29:1251–1265

    MATH  Google Scholar 

  21. Glover F (1989) Tabu search—Part I. ORSA J Comput 1(3):190–206

    Article  MATH  Google Scholar 

  22. Glover F (1990) Tabu search—Part II. ORSA J Comput 2(1):4–32

    Article  MATH  Google Scholar 

  23. Battiti R, Protasi M (2001) Reactive local search for the maximum clique problem. Algorithmica 29(4):610–637

    Article  MathSciNet  MATH  Google Scholar 

  24. Mazure B, Sais L, Grégoire É (1997) Tabu search for sat. In: Proceedings of AAAI-97, pp 281–285

  25. Smyth K, Hoos HH, Stützle T (2003) Iterated robust tabu search for max-SAT. In: Canadian conference on AI, pp 129–144

  26. Li X, Yin M (2014) Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput Appl 24(3–4):723–734

    Article  Google Scholar 

  27. Li X, Yin M (2014) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247

    Article  Google Scholar 

  28. Li X, Zhang J, Yin M (2014) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 24(7–8):1867–1877

    Article  Google Scholar 

  29. Wang Y, Ouyang D, Zhang L, Yin M (2015) A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity. SCIENCE CHINA Info Sci. doi:10.1007/s11432-015-5377-8

    Google Scholar 

  30. Li X, Yin M (2015) Modified cuckoo search algorithm with self adaptive parameter method. Info Sci 298:80–97

    Article  Google Scholar 

  31. Li X, Yin M (2013) Multiobjective binary biogeography based optimization for feature selection using gene expression data. IEEE Trans NanoBiosci 12(4):343–353

    Article  Google Scholar 

  32. Huang P, Yin M (2014) An upper (lower) bound for Max (Min) CSP. SCIENCE CHINA Info Sci 57(7):072109(9)

    MathSciNet  MATH  Google Scholar 

  33. Gent IP, Walsh T (1993) Towards an understanding of hill-climbing procedures for SAT. In: Proceedings of AAAI-93, pp 28–33

  34. McAllester D, Selman B, Kautz H (1997) Evidence for invariants in local search. In: Proceedings of AAAI-97, pp 321–326

  35. Li C, Huang W (2005) Diversification and determinism in local search for satisfiability. In: Proceedings of SAT-05, pp 158–172

Download references

Acknowledgments

The authors of this paper express sincere gratitude to all the anonymous reviewers for their hard work. This work was supported in part by NSFC under Grant Nos. (61370156, 61403076, 61403077) and Program for New Century Excellent Talents in University (NCET-13-0724).

Author information

Authors and Affiliations

  1. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130024, China

    Ruizhi Li, Shuli Hu & Minghao Yin

  2. Key Lab of Symbol Computation and Knowledge Engineer of Ministry of Education, Jilin University, Changchun, 130012, China

    Yiyuan Wang

Authors
  1. Ruizhi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuli Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yiyuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minghao Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghao Yin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, R., Hu, S., Wang, Y. et al. A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem. Neural Comput & Applic 28, 1775–1785 (2017). https://doi.org/10.1007/s00521-015-2172-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-2172-9

Keywords

Search

Navigation