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Cat Swarm Optimization with Different Binarization Methods for Solving Set Covering Problems

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

Abstract

In this paper, we present a Binary cat swarm optimization for solving the Set covering problem. The Set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behaviour of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. Moreover, eight different transfer functions and five discretization techniques are considered for solving the binary problem. We illustrate this approach with 65 instances of the problem and select the best transfer function and discretization technique to solve this problem.

Keywords

Binary Cat Swarm Optimization Set covering problem Metaheuristic 

Notes

Acknowledgments

The author Broderick Crawford is supported by grant CONICYT/FONDE-CYT/REGULAR/1140897 and Ricardo Soto is supported by grant CONICYT/FONDECYT/INICIACION/11130459.

References

  1. 1.
    Aickelin, U.: An indirect genetic algorithm for set covering problems. J. Oper. Res. Soc. 1118–1126 (2002)Google Scholar
  2. 2.
    Ali, A.I., Thiagarajan, H.: A network relaxation based enumeration algorithm for set partitioning. Eur. J. Oper. Res. 38(1), 76–85 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Amini, F., Ghaderi, P.: Hybridization of harmony search and ant colony optimization for optimal locating of structural dampers. Appl. Soft Comput. 2272–2280 (2013)Google Scholar
  4. 4.
    Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Oper. Res. 12(2), 300–304 (1964)CrossRefGoogle Scholar
  5. 5.
    Beasley, J.: A Lagrangian heuristic for set covering problems. Naval Res. Logist. 37, 151–164 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Beasley, J., Jornsten, K.: Enhancing an algorithm for set covering problems. Eur. J. Oper. Res. 58(2), 293–300 (1992)CrossRefzbMATHGoogle Scholar
  7. 7.
    Bellmore, M., Ratliff, H.D.: Optimal defense of multi-commodity networks. Manage. Sci. 18(4-Part-I), B174–B185 (1971)Google Scholar
  8. 8.
    Breuer, M.A.: Simplification of the covering problem with application to boolean expressions. J. Assoc. Comput. Mach. 17(1), 166–181 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Caprara, A., Fischetti, M., Toth, P.: Algorithms for the set covering problem. Ann. Oper. Res. 98, 353–371 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Christofides, N.: Zero-one programming using non-binary tree-search. Comput. J. 14(4), 418–421 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Chu, S., Tsai, P.: Computational intelligence based on the behavior of cats. Int. J. Innov. Comput. Inf. Control 163–173 (2007)Google Scholar
  12. 12.
    Chu, S., Tsai, P., Pan, J.: Cat swarm optimization. In: Trends in Artificial Intelligence, pp. 854–858. Springer, Berlin, Heidelberg (2006)Google Scholar
  13. 13.
    Crawford, B., Soto, R., Aballay, F., Misra, S., Johnson, F., Paredes, F.: A teaching-learning-based optimization algorithm for solving set covering problems. In: Computational Science and Its Applications, pp. 421–430 (2015)Google Scholar
  14. 14.
    Crawford, B., Soto, R., Berrios, N., Johnson, F., Paredes, F., Castro, C., Norero, E.: A binary cat swarm optimization algorithm for the non-unicost set covering problem. Math. Probl. Eng. 2015(Article ID 578541), 1–8 (2015)Google Scholar
  15. 15.
    Crawford, B., Soto, R., Cuesta, R., Paredes, F.: Application of the artificial bee colony algorithm for solving the set covering problem. Sci. World J. 2014(Article ID 189164), 1–8 (2014)Google Scholar
  16. 16.
    Crawford, B., Soto, R., Monfroy, E.: Cultural algorithms for the set covering problem. In: Tan, Y., Shi, Y., Mo, H. (eds.) Advances in Swarm Intelligence. 4th International Conference. Lecture Notes in Computer Science, vol. 7929, pp. 27–34. Springer, Harbin, China (2013)Google Scholar
  17. 17.
    Crawford, B., Soto, R., Monfroy, E., Palma, W., Castro, C., Paredes, F.: Parameter tuning of a choice-a function based hyperheuristic using particle swarm optimization. Expert Syst. Appl. 1690–1695 (2013)Google Scholar
  18. 18.
    Crawford, B., Soto, R., Olivares-Suárez, M., Palma, W., Paredes, F., Olguin, E., Norero, E.: A binary coded firefly algorithm that solves the set covering problem. Rom. J. Inf. Sci. Technol. 17, 252–264 (2014)Google Scholar
  19. 19.
    Crawford, B., Soto, R., Olivares-Suárez, M., Paredes, F.: A binary firefly algorithm for the set covering problem. In: 3rd Computer Science On-line Conference 2014, Modern Trends and Techniques in Computer Science, vol. 285, pp. 65–73. Springer (2014)Google Scholar
  20. 20.
    Crawford, B., Soto, R., Peña, C., Palma, W., Johnson, F., Paredes, F.: Solving the set covering problem with a shuffled frog leaping algorithm. In: Nguyen, N.T., Trawinski, B., Kosala, R. (eds.) Intelligent Information and Database Systems—7th Asian Conference. LNCS, vol. 9012, pp. 41–50. Springer, Bali, Indonesia (2015)Google Scholar
  21. 21.
    Day, R.H.: Letter to the editor on optimal extracting from a multiple file data storage system: an application of integer programming. Oper. Res. 13(3), 482–494 (1965)CrossRefGoogle Scholar
  22. 22.
    Fisher, M.L., Rosenwein, M.B.: An interactive optimization system for bulk-cargo ship scheduling. Naval Res. Logist. 36(1), 27–42 (1989)CrossRefGoogle Scholar
  23. 23.
    Freeman, B.A., Jucker, J.V.: The line balancing problem. J. Ind. Eng. 18, 361–364 (1967)Google Scholar
  24. 24.
    Goldberg, D.: Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Syst. 139–167 (1990)Google Scholar
  25. 25.
    Gouwanda, D., Ponnambalam, S.: Evolutionary search techniques to solve set covering problems. World Acad. Sci. Eng. Technol. 39, 20–25 (2008)Google Scholar
  26. 26.
    Lessing, L., Dumitrescu, I., Stutzle, T.: A comparison between aco algorithms for the set covering problem. In: Ant Colony Optimization and Swarm Intelligence, pp. 1–12 (2004)Google Scholar
  27. 27.
    Mirjalili, S., Lewis, A.: S-shaped versus v-shaped transfer functions for binary particle swarm optimization. Swarm Evol. Comput. 9, 1–14 (2013)CrossRefGoogle Scholar
  28. 28.
    Panda, G., Pradhan, P., Majhi, B.: IIR system identification using cat swarm optimization. Expert Syst. Appl. 38, 12671–12683 (2011)CrossRefGoogle Scholar
  29. 29.
    Ren, Z., Feng, Z., Ke, L., Zhang, Z.: New ideas for applying ant colony optimization to the set covering problem. Comput. Ind. Eng. 774–784 (2010)Google Scholar
  30. 30.
    Ribeiro, C.C., Minoux, M., Penna, M.C.: An optimal column-generation-with-ranking algorithm for very large scale set partitioning problems in traffic assignment. Eur. J. Oper. Res. 41(2), 232–239 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Sharafi, Y., Khanesar, M., Teshnehlab, M.: Discrete binary cat swarm optimization algorithm. In: Computer, Control and Communication, pp. 1–6 (2013)Google Scholar
  32. 32.
    Tsai, P., Pan, J., Chen, S., Liao, B.: Enhanced parallel cat swarm optimization based on the Taguchi method. Expert Syst. Appl. 39, 6309–6319 (2012)CrossRefGoogle Scholar
  33. 33.
    Vasko, F.J., Wolf, F.E., Stott, K.L.: Optimal selection of ingot sizes via set covering. Oper. Res. 35(3), 346–353 (1987)CrossRefGoogle Scholar
  34. 34.
    Walker, W.: Using the set-covering problem to assign fire companies to fire houses. Oper. Res. 22, 275–277 (1974)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Broderick Crawford
    • 1
    • 2
    • 3
  • Ricardo Soto
    • 1
    • 4
    • 5
  • Natalia Berrios
    • 1
    Email author
  • Eduardo Olguín
    • 2
  1. 1.Pontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Universidad San SebastiánProvidenciaChile
  3. 3.Universidad Central de ChileSantiagoChile
  4. 4.Universidad Autónoma de ChileTemucoChile
  5. 5.Universidad Cientifica del SurLimaPeru

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