Neural Computing and Applications

, Volume 29, Issue 10, pp 755–765 | Cite as

A restart local search algorithm for solving maximum set k-covering problem

  • Yiyuan Wang
  • Dantong Ouyang
  • Minghao Yin
  • Liming Zhang
  • Yonggang Zhang
Original Article


The maximum set k-covering problem (MKCP) is a famous combinatorial optimization problem with widely many practical applications. In our work, we design a restart local search algorithm for solving MKCP, which is called RNKC. This algorithm effectively makes use of several advanced ideas deriving from the random restart mechanism and the neighborhood search method. RNKC designs a new random restart method to deal with the serious cycling problem of local search algorithms. Thanks to the novel neighborhood search method that allows a neighborhood exploration of as many feasible search areas as possible, the RNKC can obtain some greatly solution qualities. Comprehensive results on the classical instances show that the RNKC algorithm competes very favorably with a famous commercial solver CPLEX. In particular, it discovers some improved and great results and matches the same solution quality for some instances.


Random restart Neighborhood search Maximum set k-covering problem 



We would like to thank the anonymous referees for their helpful comments. This work was supported in part by NSFC under Grant Nos. (61402196, 61272208, 61672261, 61133011, 61170092, 61003101) and the China Postdoctoral Science Foundation under Grant No. 2013M541302.

Compliance with ethical standards

Conflict of interest

The authors declare 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.


  1. 1.
    Saha B, Getoor L (2009) On maximum coverage in the streaming model & application to multi-topic blog-watch. SDM 9:697–708Google Scholar
  2. 2.
    Bautista J, Pereira J (2006) Modeling the problem of locating collection areas for urban waste management. An application to the metropolitan area of Barcelona. Omega 34(6):617–629CrossRefGoogle Scholar
  3. 3.
    Chierichetti F, Kumar R, Tomkins A (2010) Max-cover in map-reduce. In: Proceedings of the 19th international conference on World wide web. ACM, 2010: 231–240Google Scholar
  4. 4.
    Yu H, Yuan D (2013) Set coverage problems in a one-pass data stream. In: Proceedings of the 2013 SIAM international conference on data mining, pp 758-766Google Scholar
  5. 5.
    Stergiou S, Tsioutsiouliklis K (2015) Set cover at web scale. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, 2015: 1125–1133Google Scholar
  6. 6.
    Dasgupta A, Ghosh A, Kumar R et al (2007) The discoverability of the web. In: Proceedings of the 16th international conference on World Wide Web. ACM, 2007: 421–430Google Scholar
  7. 7.
    Yiyuan W, Jianan W (2016) An effective local search algorithm for a special hitting set problem. Transylv Rev 24(80):1–12Google Scholar
  8. 8.
    Michael RG, David SJ (1979) Computers and intractability: a guide to the theory of NP-completeness. WH Free. Co., San FrzbMATHGoogle Scholar
  9. 9.
    Li X, Yin M (2016) A particle swarm inspired cuckoo search algorithm for real parameter optimization. Soft Comput 20(4):1389–1413CrossRefGoogle Scholar
  10. 10.
    Li X, Li M (2015) Multiobjective local search algorithm-based decomposition for multiobjective permutation flow shop scheduling problem. IEEE Trans Eng Manage 62(4):544–557CrossRefGoogle Scholar
  11. 11.
    Zhang X, Li X, Wang J (2016) Local search algorithm with path relinking for single batch-processing machine scheduling problem. Neural Comput Appl. doi: 10.1007/s00521-016-2339-z Google Scholar
  12. 12.
    Li X, Yin M (2014) Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput Appl 24(3–4):723–734CrossRefGoogle Scholar
  13. 13.
    Li X, Wang J, Yin M (2014) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247CrossRefGoogle Scholar
  14. 14.
    Li X, Zhang J, Yin M (2014) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 24(7–8):1867–1877CrossRefGoogle Scholar
  15. 15.
    Gao J, Wang JN, Yin MH (2015) Experimental analyses on phase transitions in compiling satisfiability problems. Sci China Inf Sci 58(3):1–11CrossRefGoogle Scholar
  16. 16.
    Li X, Yin M (2016) Modified differential evolution with self-adaptive parameters method. J Comb Optim 31(2):546–576MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Li R, Hu S, Gao J et al (2016) GRASP for connected dominating set problems. Neural Comput Appl. doi: 10.1007/s00521-016-2429-y Google Scholar
  18. 18.
    Zhou Y, Zhang H, Li R et al (2016) Two local search algorithms for partition vertex cover problem. J Comput Theor Nanosci 13(1):743–751CrossRefGoogle Scholar
  19. 19.
    Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Marques-Silva JP, Sakallah KA (1999) GRASP: a search algorithm for propositional satisfiability. IEEE Trans Comput 48(5):506–521MathSciNetCrossRefGoogle Scholar
  21. 21.
    Laguna M, Marti R (1999) GRASP and path relinking for 2-layer straight line crossing minimization. Inf J Comput 11(1):44–52CrossRefzbMATHGoogle Scholar
  22. 22.
    Houck CR, Joines JA, Kay MG (1996) Comparison of genetic algorithms, random restart and two-opt switching for solving large location-allocation problems. Comput Oper Res 23(6):587–596CrossRefzbMATHGoogle Scholar
  23. 23.
    Shin K, Jung J, Lee S et al (2015) BEAR: block elimination approach for random walk with restart on large graphs. In: Proceedings of the 2015 ACM SIGMOD international conference on management of data. ACM, 2015: 1571–1585Google Scholar
  24. 24.
    Datta T, Srinidhi N, Chockalingam A et al (2010) Random-restart reactive tabu search algorithm for detection in large-MIMO systems. Commun Lett IEEE 14(12):1107–1109CrossRefGoogle Scholar
  25. 25.
    Wang Y, Li R, Zhou Y et al (2016) A path cost-based GRASP for minimum independent dominating set problem. Neural Comput Appl. doi: 10.1007/s00521-016-2324-6 Google Scholar
  26. 26.
    Glover F (1989) Tabu search-part I. ORSA J Comput 1(3):190–206CrossRefzbMATHGoogle Scholar
  27. 27.
    Glover F (1990) Tabu search—part II. ORSA J Comput 2(1):4–32CrossRefzbMATHGoogle Scholar
  28. 28.
    Ruizhi L, Shuli H, Yiyuan W, Minghao Y, A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem. Neural Comput Appl. doi: 10.1007/s00521-015-2172-9
  29. 29.
    Cai S, Su K (2013) Local search for Boolean Satisfiability with configuration checking and subscore. Artif Intell 204:75–98CrossRefzbMATHGoogle Scholar
  30. 30.
    Wang Y, Cai S, Yin M (2016) Two efficient local search algorithms for maximum weight clique problem. Thirtieth AAAI Conf Artif Intell, pp 805–811Google Scholar
  31. 31.
    Wang Y, Yin M, Ouyang D et al (2016) A novel local search algorithm with configuration checking and scoring mechanism for the set k-covering problem. Int Trans Oper Res. doi: 10.1111/itor.12280 zbMATHGoogle Scholar
  32. 32.
    Beasley JE (1990) OR-Library: distributing test problems by electronic mail. J Oper Res Soc 41(11):1069–1072CrossRefGoogle Scholar
  33. 33.
    Balas E, Ho A (1980) Set covering algorithms using cutting planes, heuristics, and subgradient optimization: a computational study. Springer, Berlin HeidelbergzbMATHGoogle Scholar
  34. 34.
    Beasley JE (1987) An algorithm for set covering problem. Eur J Oper Res 31(1):85–93MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Beasley JE (1990) A lagrangian heuristic for set-covering problems. Naval Research Logistics (NRL) 37(1):151–164MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Gao C, Yao X, Weise T et al (2015) An efficient local search heuristic with row weighting for the unicost set covering problem. Eur J Oper Res 246(3):750–761MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Wang Y, Ouyang DT, Zhang L et al (1007) A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity. Sci China Inf Sci 2015:10Google Scholar
  38. 38.
    Xia Z, Wang X, Sun X et al (2016) A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parallel Distrib Syst 27(2):340–352CrossRefGoogle Scholar
  39. 39.
    Fu Z, Ren K, Shu J et al (2015) Enabling personalized search over encrypted outsourced data with efficiency improvement. IEEE Trans Parallel Distrib Syst. doi: 10.1109/TPDS.2015.2506573 Google Scholar
  40. 40.
    Zhangjie F, Xingming S, Qi L et al (2015) Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing. IEICE Trans Commun 98(1):190–200Google Scholar
  41. 41.
    Ren YJ, Shen J, Wang J et al (2015) Mutual verifiable provable data auditing in public cloud storage. J Internet Technol 16(2):317–323Google Scholar
  42. 42.
    Tinghuai MA, Jinjuan Z, Meili T et al (2015) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans Inf Syst 98(4):902–910Google Scholar
  43. 43.
    Wen X, Shao L, Xue Y et al (2015) A rapid learning algorithm for vehicle classification. Inf Sci 295:395–406CrossRefGoogle Scholar
  44. 44.
    Chen B, Shu H, Coatrieux G et al (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51(1):124–144MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Xia Z, Wang X, Sun X et al (2014) Steganalysis of least significant bit matching using multi-order differences. Secur Commun Networks 7(8):1283–1291CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Yiyuan Wang
    • 1
    • 2
  • Dantong Ouyang
    • 1
    • 2
  • Minghao Yin
    • 2
    • 3
  • Liming Zhang
    • 1
    • 2
  • Yonggang Zhang
    • 1
    • 2
  1. 1.College of Computer Science and TechnologyJilin UniversityChangchunChina
  2. 2.Key Laboratory of Symbol Computation and Knowledge Engineering of Ministry of EducationJilin UniversityChangchunChina
  3. 3.School of Computer Science and Information TechnologyNortheast Normal UniversityChangchunChina

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