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A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity

基于超边配置检测和权值多样化策略的局部搜索改进算法求解集合覆盖问题

Abstract

The unicost version of well-known set covering problem (SCP) is central to a wide variety of practical applications for which finding an optimal solution quickly is crucial. In this paper, we propose a new local searchbased algorithm for the unicost SCP which follows the general framework of the popular stochastic local search with a particular focus on the hyperedge selection strategy and weight diversity strategy. Specifically, a strategy as called hyperedge configuration checking strategy is proposed here to avoid the search trajectory which leads to local optima. Additionally, a new weight diversity strategy is proposed for the diversification of search results, by changing the weight of both covered and uncovered vertices in the current solution. The experimental results show that our algorithm significantly outperforms the state-of-the-art heuristic algorithm by one to two orders of magnitudes on the 85 classical instances. Also, our algorithm improves the current optimal solutions of 11 instances.

创新点

本文提出了一个基于随机局部搜索求解集合覆盖的算法. 在本文中, 提出一种超边配置检测策略用来避免陷入局部最优. 更重要地, 通过改变未覆盖和覆盖顶点的权值,本文设计了一种权值多样化策略用来得到更多地不同的解. 在经典的85个测试用例上, 实验结果给出本文设计的局部搜索算法比目前最好的启发式算法,能够使用更短的时间找到更好的候选解.

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References

  1. 1

    Karp R M. Reducibility among combinatorial problems. In: Complexity of Computer Computations. New York: Plenum Press, 1972. 85–103

  2. 2

    Chakrabarty K. Test scheduling for core-based systems using mixed-integer linear programming. IEEE Trans Comput- Aided Des Integr Circuits Syst, 2000, 19: 1163–1174

  3. 3

    van Bevern R. Towards optimal and expressive kernelization for d-Hitting Set. Comput Comb, 2012, 7434: 121–132

  4. 4

    Ausiello G, D’Atri A, Protasi M. Structure preserving reductions among convex optimization problems. J Comput Syst Sci, 1980, 21: 136–153

  5. 5

    Cai S W, Su K L, Luo C, et al. NuMVC: An efficient local search algorithm for minimum vertex cover. J Artif Intell Res, 2014, 46: 687–716

  6. 6

    Dinur I, Safra S. On the hardness of approximating minimum vertex cover. Ann Math, 2005, 162: 439–485

  7. 7

    Caprara A, Fischetti M, Toth P. A heuristic method for the set covering problem. Oper Res, 1999, 47: 730–743

  8. 8

    Reiter R. A theory of diagnosis from first principles. Artif Intell, 1987, 32: 57–95

  9. 9

    Zhao X F, Ouyang D T. Improved algorithms for deriving all minimal conflict sets in model-based diagnosis. In: Proceedings of the Intelligent Computing 3rd International Conference on Advanced Intelligent Computing Theories and Applications. Berlin: Springer, 2007. 157–166

  10. 10

    Angel E, Bampis E, Gourvès L. On the minimum hitting set of bundles problem. Theor Comput Sci, 2009, 410: 4534–4542

  11. 11

    Sellis T K. Multiple-query optimization. ACM Trans Database Syst, 1988, 13: 23–52

  12. 12

    Avella P, Boccia M, Vasilyev I. Computational experience with general cutting planes for the Set Covering problem. Oper Res Lett, 2009, 37: 16–20

  13. 13

    Björklund P, Värbrand P, Yuan D. A column generation method for spatial TDMA scheduling in ad hoc networks. Ad Hoc Netw, 2004, 2: 405–418

  14. 14

    Hemazro T D, Jaumard B, Marcotte O. A column generation and branch-and-cut algorithm for the channel assignment problem. Comput Oper Res, 2008, 35: 1204–1226

  15. 15

    Caprara A, Toth P, Fischetti M. Algorithms for the set covering problem. Ann Oper Res, 2000, 98: 353–371

  16. 16

    Pereira J, Averbakh I. The robust set covering problem with interval data. Ann Oper Res, 2013, 207: 217–235

  17. 17

    Yelbay S B, Birbil I, Bülbül K. The set covering problem revisited: an empirical study of the value of dual information. J Ind Manag Optimiz, 2015, 11: 575–594

  18. 18

    Galinier P, Hertz A. Solution techniques for the large set covering problem. Discret Appl Mathematics, 2007, 155: 312–326

  19. 19

    Yagiura M, Kishida M, Ibaraki T. A 3-flip neighborhood local search for the set covering problem. Eur J Oper Res, 2006, 172: 472–499

  20. 20

    Kinney G W, Barnes J W, Colletti B W. A reactive tabu search algorithm with variable clustering for the unicost set covering problem. Int J Oper Res, 2007, 2: 156–172

  21. 21

    Caserta M. Tabu search-based metaheuristic algorithm for large-scale set covering problems. Metaheuristics Progress Complex Syst Opt, 2007, 39: 43–63

  22. 22

    Umetani S, Yagiura M. Relaxation heuristics for the set covering problem. J Oper Res Soc Jpn, 2007, 50: 350–375

  23. 23

    Lan G, De Puy G W, Whitehouse G E. An effective and simple heuristic for the set covering problem. Eur J Oper Res, 2007, 176: 1387–1403

  24. 24

    Bautista J, Pereira J. A GRASP algorithm to solve the unicost set covering problem. Comput Oper Res, 2007, 34: 3162–3173

  25. 25

    Ablanedo-Rosas J H, Rego C. Surrogate constraint normalization for the set covering problem. Eur J Oper Res, 2010, 205: 540–551

  26. 26

    Sundar S, Singh A. A hybrid heuristic for the set covering problem. Oper Res, 2012, 12: 345–365

  27. 27

    Crawford B, Soto R, Cuesta R, et al. Application of the artificial bee colony algorithm for solving the set covering problem. Sci World J, 2014, 2014: 189164

  28. 28

    Mulati M H, Constantino A A. Ant-Line: a line-oriented ACO algorithm for the set covering problem. In: Proceedings of the IEEE International Conference of the Chilean Computer Science Society, Curico, 2011. 265–274

  29. 29

    Ren Z G, Feng Z R, Ke L J, et al. New ideas for applying ant colony optimization to the set covering problem. Comput Ind Eng, 2010, 58: 774–784

  30. 30

    Beasley J E, Chu P C. A genetic algorithm for the set covering problem. Eur J Oper Res, 1996, 94: 392–404

  31. 31

    Naji-Azimi Z, Toth P, Galli L. An electromagnetism metaheuristic for the unicost set covering problem. Eur J Oper Res, 2010, 205: 290–300

  32. 32

    Glover F. Tabu search-part I. ORSA J Comput, 1989, 1: 190–206

  33. 33

    Selman B, Kautz H A, Cohen B. Noise strategies for improving local search. In: Proceedings of National Conference on Artificial Intelligence, Seattle, 1994. 337–343

  34. 34

    Cai S W, Su K L. Comprehensive score: towards efficient local search for sat with long clauses. In: Proceedings of the International Joint Conference on Artificial Intelligence, Beijing, 2013. 489–495

  35. 35

    Cai S W, Su K L. Local search with configuration checking for SAT. In: Proceedings of the IEEE International Conference on Tools with Artificial Intelligence, Boca Raton, 2011. 59–66

  36. 36

    Luo C, Cai SW, Wu W, et al. Double configuration checking in stochastic local search for satisfiability. In: Proceedings of National Conference on Artificial Intelligence, Québec, 2014. 2703–2709

  37. 37

    Cai S W, Su K L. Local search for boolean satisfiability with configuration checking and subscore. Artif Intell, 2013, 204: 75–98

  38. 38

    Luo C, Cai S W, Su K L, et al. Clause states based configuration checking in local search for satisfiability. IEEE Trans cybern, 2014, 45: 1014–1027

  39. 39

    Luo C, Cai S W, Wu W, et al. CCLS: an efficient local search algorithm for weighted maximum satisfiability. IEEE Trans Comput, 2015, 64: 1830–1843

  40. 40

    Beasley J E. OR-Library: distributing test problems by electronic mail. J Oper Res Soc, 1990, 41: 1069–1072

  41. 41

    Xu K, Boussemart F, Hemery F, et al. A simple model to generate hard satisfiable instances. In: Proceedings of the International Joint Conference on Artificial Intelligence, Edinburgh, 2005. 337–342

  42. 42

    Selman B, Levesque H J, Mitchell D G. A new method for solving hard satisfiability problems. In: Proceedings of National Conference on Artificial Intelligence, San Jose, 1992. 440–446

  43. 43

    Li C M, Huang W Q. Diversification and determinism in local search for satisfiability. Lect Notes Comput Sci, 2005, 3569: 158–172

  44. 44

    Gent I P, Walsh T. Towards an understanding of hill-climbing procedures for SAT. In: Proceedings of National Conference on Artificial Intelligence, Washington, 1993. 28–33

  45. 45

    Cai S W, Su K L, Sattar A. Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artif Intell, 2011, 175: 1672–1696

  46. 46

    Xu K, Li W. Many hard examples in exact phase transitions. Theor Comput Sci, 2006, 355: 291–302

  47. 47

    Xu K, Li W. Exact phase transitions in random constraint satisfaction problems. J Artif Intell Res, 2000, 12: 93–103

  48. 48

    Xu K, Boussemart F, Hemery F, et al. Random constraint satisfaction: easy generation of hard (satisfiable) instances. Artif Intell, 2007, 171: 514–534

  49. 49

    Gao J, Wang J N, Yin M H. Experimental analyses on phase transitions in compiling satisfiability problems. Sci China Inf Sci, 2015, 58: 032104

  50. 50

    Huang P, Yin M H. An upper (lower) bound for Max (Min) CSP. Sci China Inf Sci, 2014, 57: 072109

  51. 51

    Grossman T, Wool A. Computational experience with approximation algorithms for the set covering problem. Eur J Oper Res, 1997, 101: 81–92

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Acknowledgments

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61272208, 61370156, 61402196, 61503074, 61672261), Natural Science Foundation of Zhejiang Province (LY16F020004), and Program for New Century Excellent Talents in University (Grant No. NCET-13-0724). The authors of this paper express sincere gratitude to all the anonymous reviewers for their hard work.

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Correspondence to Minghao Yin.

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Wang, Y., Ouyang, D., Zhang, L. et al. A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity. Sci. China Inf. Sci. 60, 062103 (2017). https://doi.org/10.1007/s11432-015-5377-8

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Keywords

  • unicost set covering problem
  • hyperedge configuration checking
  • local search
  • weight diversity strategy
  • hyperedge selection strategy

关键词

  • 集合覆盖问题
  • 超边配置检测
  • 局部搜索
  • 权值多样化策略
  • 超边选择策略