Advertisement

A Beam-Search Approach to the Set Covering Problem

  • Victor ReyesEmail author
  • Ignacio Araya
  • Broderick Crawford
  • Ricardo Soto
  • Eduardo Olguín
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 464)

Abstract

In this work we present a beam-search approach applied to the Set Covering Problem. The goal of this problem is to choose a subset of columns of minimal cost covering every row. Beam Search constructs a search tree by using a breadth-first search strategy, however only a fixed number of nodes are kept and the rest are discarded. Even though original beam search has a deterministic nature, our proposal has some elements that makes it stochastic. This approach has been tested with a well-known set of 45 SCP benchmark instances from OR-Library showing promising results.

Keywords

SCP Beam search Branch-and-Bound Greedy 

Notes

Acknowledgments

Victor Reyes is supported by grant INF-PUCV 2015, Ricardo Soto is supported by grant CONICYT/FONDECYT/INICIACION/11130459, Broderick Crawford is supported by grant CONICYT/FONDECYT/REGULAR/1140897, and Ignacio Araya is supported by grant CONICYT/FONDECYT/INICIACION/11121366.

References

  1. 1.
    Balas, E., et al.: A class of location, distribution and scheduling problems: modeling and solution methods (1982)Google Scholar
  2. 2.
    Beasley, J.E.: An algorithm for set covering problem. Eur. J. Oper. Res. 31(1), 85–93 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Beasley, J.E., Chu, P.C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2), 392–404 (1996)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bennell, J.A., Song, X.: A beam search implementation for the irregular shape packing problem. J. Heuristics 16(2), 167–188 (2010)CrossRefzbMATHGoogle Scholar
  5. 5.
    Blum, C.: Beam-acohybridizing ant colony optimization with beam search: an application to open shop scheduling. Comput. Oper. Res. 32(6), 1565–1591 (2005)CrossRefzbMATHGoogle Scholar
  6. 6.
    Caprara, A., Toth, P., Fischetti, M.: Algorithms for the set covering problem. Ann. Oper. Res. 98(1–4), 353–371 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ceria, S., Nobili, P., Sassano, A.: A lagrangian-based heuristic for large-scale set covering problems. Math. Program. 81(2), 215–228 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chvatal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4(3), 233–235 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Michael, R.G., David, S.J.: Computers and intractability: a guide to the theory of np-completeness. San Francisco, p. 1979. Freeman, LA (1979)Google Scholar
  10. 10.
    Haouari, M, Chaouachi, J.S.: A probabilistic greedy search algorithm for combinatorial optimisation with application to the set covering problem. J. Oper. Res. Soc. 792–799 (2002)Google Scholar
  11. 11.
    Jacobs, L.W., Brusco, M.J.: Note: a local-search heuristic for large set-covering problems. Nav. Res. Logist. (NRL) 42(7), 1129–1140 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kim, K.H., Kang, J.S., Ryu, K.R.: A beam search algorithm for the load sequencing of outbound containers in port container terminals. OR Spectr. 26(1), 93–116 (2004)CrossRefzbMATHGoogle Scholar
  13. 13.
    Lan, G., DePuy, G.W., Whitehouse, G.E.: An effective and simple heuristic for the set covering problem. Eur. J. Oper. Res. 176(3), 1387–1403 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lessing, L., Dumitrescu, I., Stützle, T.: A comparison between aco algorithms for the set covering problem. Ant Colony Optimization and Swarm Intelligence, pp. 1–12. Springer, Berlin (2004)CrossRefGoogle Scholar
  15. 15.
    Norvig, P.: Paradigms of Artificial Intelligence Programming: Case Studies in Common LISP. Morgan Kaufmann (1992)Google Scholar
  16. 16.
    Ohlsson, M., Peterson, C., Söderberg, B.: An efficient mean field approach to the set covering problem. Eur. J. Oper. Res. 133(3), 583–595 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Ren, Z.-G., Feng, Z.-R., Ke, L.-J., Zhang, Z.-J.: New ideas for applying ant colony optimization to the set covering problem. Comput. Ind. Eng. 58(4), 774–784 (2010)CrossRefGoogle Scholar
  18. 18.
    Solar, M., Parada, V., Urrutia, R.: A parallel genetic algorithm to solve the set-covering problem. Comput. Oper. Res. 29(9), 1221–1235 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Wang, F., Lim, A.: A stochastic beam search for the berth allocation problem. Decis. Support Syst. 42(4), 2186–2196 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Victor Reyes
    • 1
    Email author
  • Ignacio Araya
    • 1
  • Broderick Crawford
    • 1
    • 2
    • 3
  • Ricardo Soto
    • 1
    • 4
    • 5
  • Eduardo Olguín
    • 2
  1. 1.Pontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Universidad San SebastiánSantiago Metropolitan RegionChile
  3. 3.Universidad Central de ChileSantiago Metropolitan RegionChile
  4. 4.Universidad Autónoma de ChileTemucoChile
  5. 5.Universidad Cientifica Del SurLimaPeru

Personalised recommendations