A Binary Grasshopper Optimisation Algorithm Applied to the Set Covering Problem

  • Broderick Crawford
  • Ricardo Soto
  • Alvaro Peña
  • Gino Astorga
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 765)

Abstract

Many of the problems addressed at the industrial level are of a combinatorial type and a sub-assembly not less than these are of the NP-hard type. The design of algorithms that solve combinatorial problems based on the continuous metaheuristic of swarm intelligence is an area of interest at an industrial level. In this article, we explore a general binarization mechanism of continuous metaheuristics based on the percentile concept. In particular, we apply the percentile concept to the Grasshopper optimization algorithm in order to solve the set covering problem (SCP). The experiments are designed with the aim of demonstrating the usefulness of the percentile concept in binarization. Additionally, we verify the effectiveness of our algorithm through reference instances. The results indicate the binary grasshopper optimization algorithm (BGOA) obtains adequate results when evaluated with a combinatorial problem such as the SCP.

References

  1. 1.
    Khatibinia, M., Yazdani, H.: Accelerated multi-gravitational search algorithm for size optimization of truss structures. Swarm Evol. Comput. (2017)Google Scholar
  2. 2.
    Barman, S., Kwon, Y.-K.: A novel mutual information-based boolean network inference method from time-series gene expression data. PloS one 12(2), e0171097 (2017)CrossRefGoogle Scholar
  3. 3.
    Crawford, B., Soto, R., Monfroy, E., Astorga, G.. García, J., Cortes, E.: A meta-optimization approach for covering problems in facility location. In: Workshop on Engineering Applications, pp. 565–578. Springer (2017)Google Scholar
  4. 4.
    García, J., Crawford, B., Soto, R., Astorga, G.: A percentile transition ranking algorithm applied to knapsack problem. In: Proceedings of the Computational Methods in Systems and Software, pp. 126–138. Springer (2017)Google Scholar
  5. 5.
    García, J., Crawford, B., Soto, R., García, P.: A multi dynamic binary black hole algorithm applied to set covering problem. In: International Conference on Harmony Search Algorithm, pp. 42–51. Springer (2017)Google Scholar
  6. 6.
    García, J., Crawford, B., Soto, R., Astorga, G.: A percentile transition ranking algorithm applied to binarization of continuous swarm intelligence metaheuristics. In: International Conference on Soft Computing and Data Mining, pp. 3–13. Springer (2018)Google Scholar
  7. 7.
    Franceschetti, A., Demir, E., Honhon, D., Van Woensel, T., Laporte, G., Stobbe, M.: A metaheuristic for the time-dependent pollution-routing problem. Eur. J. Oper. Res. 259(3), 972–991 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Crawford, B., Soto, R., Astorga, G., García, J., Castro, C., Paredes, F.: Putting continuous metaheuristics to work in binary search spaces. Complexity 2017 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yang, X.-S., Deb, S.: Cuckoo search via lévy flights. In: 2009 World Congress on Nature and Biologically Inspired Computing, NaBIC 2009, pp. 210–214. IEEE (2009)Google Scholar
  10. 10.
    Hatamlou, A.: Black hole: a new heuristic optimization approach for data clustering. Inf. Sci. 222, 175–184 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yang, X.-S.: A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 65–74 (2010)CrossRefGoogle Scholar
  12. 12.
    Saremi, S., Mirjalili, S., Lewis, A.: Grasshopper optimisation algorithm: theory and application. Adv. Eng. Softw. 105, 30–47 (2017)CrossRefGoogle Scholar
  13. 13.
    Balaji, S., Revathi, N.: A new approach for solving set covering problem using jumping particle swarm optimization method. Nat. Comput. 15(3), 503–517 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Gary, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness (1979)Google Scholar
  15. 15.
    Lu, Y., Vasko, F.J.: An or practitioner’s solution approach for the set covering problem. Int. J. Appl. Metaheuristic Comput. (IJAMC) 6(4), 1–13 (2015)CrossRefGoogle Scholar
  16. 16.
    Li, Y., Cai, Z.: Gravity-based heuristic for set covering problems and its application in fault diagnosis. J. Syst. Eng. Electron. 23(3), 391–398 (2012)CrossRefGoogle Scholar
  17. 17.
    Kasirzadeh, A., Saddoune, M., Soumis, F.: Airline crew scheduling: models, algorithms, and data sets. EURO J. Transp. Logist. 6(2), 111–137 (2017)CrossRefGoogle Scholar
  18. 18.
    Horváth, M., Kis, T.: Computing strong lower and upper bounds for the integrated multiple-depot vehicle and crew scheduling problem with branch-and-price. Cent. Eur. J. Oper. Res. 1–29 (2017)Google Scholar
  19. 19.
    Stojković, M.: The operational flight and multi-crew scheduling problem. Yugoslav J. Oper. Res. 15(1) (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    García, J., Crawford, B., Soto, R., Carlos, C., Paredes, F.: A k-means binarization framework applied to multidimensional knapsack problem. Appl. Intell. 1–24 (2017)Google Scholar
  21. 21.
    García, J., Pope, C., Altimiras, F.: A distributed k-means segmentation algorithm applied to lobesia botrana recognition. Complexity 2017 (2017)Google Scholar
  22. 22.
    Graells-Garrido, E., García, J.: Visual exploration of urban dynamics using mobile data. In: International Conference on Ubiquitous Computing and Ambient Intelligence, pp. 480–491. Springer (2015)Google Scholar
  23. 23.
    Graells-Garrido, E., Peredo, O., García, J.: Sensing urban patterns with antenna mappings: the case of Santiago, Chile. Sensors 16(7), 1098 (2016)CrossRefGoogle Scholar
  24. 24.
    Peredo, O.F., García, J.A., Stuven, R., Ortiz, J.M.: Urban dynamic estimation using mobile phone logs and locally varying anisotropy. In: Geostatistics Valencia 2016, pp. 949–964. Springer (2017)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Broderick Crawford
    • 1
  • Ricardo Soto
    • 1
  • Alvaro Peña
    • 1
  • Gino Astorga
    • 1
  1. 1.School of EngineeringPontificia Universidad Católica de ValparaísoValparaísoChile

Personalised recommendations