A Meta-Optimization Approach for Covering Problems in Facility Location

  • Broderick CrawfordEmail author
  • Ricardo Soto
  • Eric Monfroy
  • Gino Astorga
  • José García
  • Enrique Cortes
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 742)


In this paper, we solve the Set Covering Problem with a meta-optimization approach. One of the most popular models among facility location models is the Set Covering Problem. The meta-level metaheuristic operates on solutions representing the parameters of other metaheuristic. This approach is applied to an Artificial Bee Colony metaheuristic that solves the non-unicost set covering. The Artificial Bee Colony algorithm is a recent swarm metaheuristic technique based on the intelligent foraging behavior of honey bees. This metaheuristic owns a parameter set with a great influence on the effectiveness of the search. These parameters are fine-tuned by a Genetic Algorithm, which trains the Artificial Bee Colony metaheuristic by using a portfolio of set covering problems. The experimental results show the effectiveness of our approach which produces very near optimal scores when solving set covering instances from the OR-Library.


Covering problems Facility location Artificial bee colony algorithm Swarm intelligence 



Broderick Crawford is supported by grant CONICYT/FONDECYT/REGULAR 1171243 and Ricardo Soto is supported by Grant CONICYT/FONDECYT/REGULAR/1160455, Gino Astorga is supported by Postgraduate Grant, Pontificia Universidad Catolica de Valparaíso, 2015 and José García is supported by INF-PUCV 2016. This research was partially funded by CORFO Program Ingeniería 2030 PUCV - Consortium of Chilean Engineering Faculties.


  1. 1.
    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
  2. 2.
    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(189164), 1–8 (2014)CrossRefGoogle Scholar
  3. 3.
    Crawford, B., Soto, R., Surez, M.O., Paredes, F., Johnson, F.: Binary firefly algorithm for the set covering problem. In: 2014 9th Iberian Conference on Information Systems and Technologies (CISTI), pp. 1–5, June 2014Google Scholar
  4. 4.
    Crawford, B., Soto, R., Astorga, G., García, J., Castro, C., Paredes, F.: Putting continuous metaheuristics to work in binary search spaces. Complexity 2017 (2017). Pages 19Google Scholar
  5. 5.
    Crawford, B., Soto, R., Berríos, 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 (2015)Google Scholar
  6. 6.
    Crawford, B., Soto, R., Olivares-Suárez, M., Paredes, F.: A binary firefly algorithm for the set covering problem. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds.) Modern Trends and Techniques in Computer Science. AISC, vol. 285, pp. 65–73. Springer, Cham (2014). doi: 10.1007/978-3-319-06740-7_6 CrossRefGoogle Scholar
  7. 7.
    Crawford, B., Soto, R., Palma, W., Johnson, F., Paredes, F., Olguín, E.: A 2-level approach for the set covering problem: parameter tuning of artificial bee colony algorithm by using genetic algorithm. In: Tan, Y., Shi, Y., Coello, C. (eds.) Advances in Swarm Intelligence, vol. 8794, pp. 189–196. Springer, Cham (2014)Google Scholar
  8. 8.
    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., Trawiński, B., Kosala, R. (eds.) ACIIDS 2015. LNCS (LNAI), vol. 9012, pp. 41–50. Springer, Cham (2015). doi: 10.1007/978-3-319-15705-4_5 Google Scholar
  9. 9.
    Crawford, B., Valenzuela, C., Soto, R., Monfroy, E., Paredes, F.: Parameter tuning of metaheuristics using metaheuristics. Adv. Sci. Lett. 19(12), 3556–3559 (2013)CrossRefGoogle Scholar
  10. 10.
    Cuesta, R., Crawford, B., Soto, R., Paredes, F.: An artificial bee colony algorithm for the set covering problem. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds.) Modern Trends and Techniques in Computer Science. AISC, vol. 285, pp. 53–63. Springer, Cham (2014). doi: 10.1007/978-3-319-06740-7_5 CrossRefGoogle Scholar
  11. 11.
    Drezner, T., Drezner, Z., Goldstein, Z.: A stochastic gradual cover location problem. Nav. Res. Logist. (NRL) 57(4), 367–372 (2010). doi: 10.1002/nav.20410 MathSciNetzbMATHGoogle Scholar
  12. 12.
    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
  13. 13.
    García, J., Crawford, B., Soto, R., García, P.: A multi dynamic binary black hole algorithm applied to set covering problem. In: Del Ser, J. (ed.) Harmony Search Algorithm, pp. 42–51. Springer, Singapore (2017)CrossRefGoogle Scholar
  14. 14.
    Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes University, Engineering faculty, Computer Engineering Department (2005)Google Scholar
  15. 15.
    Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 459–471 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Karaboga, D., Gorkemli, B., Ozturk, C., Karaboga, N.: A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif. Intell. Rev. 42(3), 21–57 (2014)CrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    Schilling, D.A., Jayaraman, V., Barkhi, R.: A review of covering problem in facility location. Locat. Sci. 1(1), 25–55 (1993)zbMATHGoogle Scholar
  19. 19.
    Singh, A.: An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem. Appl. Soft Comput. 9(2), 625–631 (2009). doi: 10.1016/j.asoc.2008.09.001 CrossRefGoogle Scholar
  20. 20.
    Soto, R., Crawford, B., Muñoz, A., Johnson, F., Paredes, F.: Pre-processing, repairing and transfer functions can help binary electromagnetism-like algorithms. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds.) Artificial Intelligence Perspectives and Applications. Advances in Intelligent Systems and Computing, vol. 347, pp. 89–97. Springer, Cham (2015). doi: 10.1007/978-3-319-18476-0_10 Google Scholar
  21. 21.
    Soto, R., Crawford, B., Olivares, R., Barraza, J., Figueroa, I., Johnson, F., Paredes, F., Olguín, E.: Solving the non-unicost set covering problem by using cuckoo search and black hole optimization. Nat. Comput. 16, 1–17 (2017)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Toregas, C., Swain, R., ReVelle, C., Bergman, L.: The location of emergency service facilities. Oper. Res. 19(6), 1363–1373 (1971). doi: 10.1287/opre.19.6.1363 CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Broderick Crawford
    • 1
    Email author
  • Ricardo Soto
    • 1
  • Eric Monfroy
    • 2
  • Gino Astorga
    • 1
    • 3
  • José García
    • 1
    • 4
  • Enrique Cortes
    • 1
    • 5
  1. 1.Pontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.LINA, Universite de NantesNantesFrance
  3. 3.Universidad de ValparaísoValparaísoChile
  4. 4.Centro de Investigación y Desarrollo TelefónicaSantiagoChile
  5. 5.Universidad de Playa AnchaValparaísoChile

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