Skip to main content
Springer Nature Link
Log in

Solving the Set Covering Problem with a Binary Black Hole Inspired Algorithm

  • Conference paper
  • First Online:
Computational Science and Its Applications – ICCSA 2016 (ICCSA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9786))

Included in the following conference series:

  • 1275 Accesses

Abstract

There are multiple problems in several industries that can be solved with combinatorial optimization. In this sense, the Set Covering Problem is one of the most representative of them, being used in various branches of engineering and science, allowing find a set of solutions that meet the needs identified in the restrictions that have the lowest possible cost. This paper presents an algorithm inspired by binary black holes (BBH) to resolve known instances of SPC from the OR-Library. Also, it reproduces the behavior of black holes, using various operators to bring good solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Vasko, F., Wolf, F., Stott, K.: Optimal selection of ingot sizes via set covering. Oper. Res. 35(3), 346–353 (1987)

    Article  Google Scholar 

  2. Desrochers, M., Soumis, F.: A column generation approach to the urban transit crew scheduling problem. Transp. Sci. 23(1), 1–13 (1989)

    Article  MATH  Google Scholar 

  3. Bellmore, M., Ratliff, H.D.: Optimal defense of multi-commodity networks. Manage. Sci. 18(4–part–i), B-174 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  4. Garfinkel, R.S., Nemhauser, G.L.: Optimal political districting byimplicit enumeration techniques. Manage. Sci. 347, 267–276 (2015)

    Google Scholar 

  5. Amini, F., Ghaderi, P.: Hybridization of harmony search and ant colony optimization for optimal locating of structural dampers. Appl. Soft Comput. 13(5), 2272–2280 (2013)

    Article  Google Scholar 

  6. Karp, R.: Reducibility among combinatorial problems (1972). http://www.cs.berkeley.edu/~luca/cs172/karp.pdf

    Google Scholar 

  7. Hatamlou, A.: Black hole: a new heuristic optimization approach for data clustering. Inf. Sci. 222, 175–184 (2013)

    Article  MathSciNet  Google Scholar 

  8. Ataim, P.: Resolución del problema de set-covering usando un algoritmo genético (2005)

    Google Scholar 

  9. Wang, B.S.: Caro and Crawford, “Multi-objective robust optimization using a postoptimality sensitivity analysis technique: application to a wind turbine design”. J. Mech. Design 137(1), 11 (2015)

    Article  Google Scholar 

  10. Crawford, B., Soto, R., Johnson, F., Paredes, F.: A timetabling applied case solved with ant colony optimization. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Prokopova, Z., Silhavy, P. (eds.) Artificial Intelligence Perspectives and Applications. AISC, vol. 347, pp. 267–276. Springer, Heidelberg (2015)

    Google Scholar 

  11. Marianov, R.: The queuing probabilistic location set coveringproblem and some extensions. Department of Electrical Engineering, PontificiaUniversidad Católica de Chile (2002)

    Google Scholar 

  12. ReVelle, C., Toregas, C., Falkson, L.: Applications of the location set-covering problem. Geog. Anal. 8(1), 65–76 (1976)

    Article  Google Scholar 

  13. Walker, W.: Using the set-covering problem to assign fire companies to fire houses. The New York City-Rand Institute (1974)

    Google Scholar 

  14. Crawford, B., Soto, R., Johnson, F., Misra, S., Paredes, F.: The use of metaheuristics to software project scheduling problem. In: Murgante, B., Misra, S., Rocha, A.M.A.C., Torre, C., Rocha, J.G., Falcão, M.I., Taniar, D., Apduhan, B.O., Gervasi, O. (eds.) ICCSA 2014, Part V. LNCS, vol. 8583, pp. 215–226. Springer, Heidelberg (2014)

    Google Scholar 

  15. Soto, R., Crawford, B., Galleguillos, C., Barraza, J., Lizama, S., Muñoz, A., Vilches, J., Misra, S., Paredes, F.: Comparing cuckoo search, bee colony, firefly optimization, and electromagnetism-like algorithms for solving the set covering problem. In: Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2015. LNCS, vol. 9155, pp. 187–202. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  16. Crawford, B., Soto, R., Peña, C., Riquelme-Leiva, M., Torres-Rojas, C., Misra, S., Johnson, F., Paredes, F.: A comparison of three recent nature-inspired metaheuristics for the set covering problem. In: Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2015. LNCS, vol. 9158, pp. 431–443. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  17. Hawking, S.: Agujeros negros y pequeños universos. Planeta (1994)

    Google Scholar 

  18. S. Hawking and M. Jackson, A brief history of time. Dove Audio, 1993

    Google Scholar 

  19. Crawford, B., Soto, R., Riquelme-Leiva, M., Peña, C., Torres-Rojas, C., Johnson, F., Paredes, F.: Modified binary firefly algorithms with different transfer functions for solving set covering problems. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Prokopova, Z., Silhavy, P. (eds.) Software Engineering in Intelligent Systems. AISC, vol. 349, pp. 307–315. Springer, Heidelberg (2015)

    Google Scholar 

  20. Farahmandian, M., Hatamlou, A.: Solving optimization problems using black hole algorithm. J. Adv. Comput. Sci. Technol. 4(1), 68–74 (2015)

    Article  Google Scholar 

  21. Beasley, J.: Or-library (1990). http://people.brunel.ac.uk/~mastjjb/jeb/orlib/scpinfo.html

  22. Beasley, J.E.: An algorithm for set covering problem. Euro. J. Oper. Res. 31(1), 85–93 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  23. Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O. (eds.): ICCSA 2015. LNCS, vol. 9155. Springer, Heidelberg (2015)

    Google Scholar 

  24. Beasley, J.E.: A Lagrangian heuristic for set-covering problems. Naval Res. Logistics 1(37), 151–164 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  25. Nemati, M., Salimi, R., Bazrkar, N.: Black holes algorithm: a swarm algorithm inspired of black holes for optimization problems. IAES Int. J. Artif. Intell. (IJ-AI) 2(3), 143–150 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

Broderick Crawford is supported by Grant CONICYT / FONDECYT / REGULAR / 1140897. Ricardo Soto is supported by Grant CONICYT / FONDECYT / REGULAR / 1160455. Sebastiásn Mansilla, Álvaro Gómez and Juan Salas are supported by Postgraduate Grant Pontificia Universidad Católica de Valparaiso 2015 (INF-PUCV 2015).

Author information

Authors and Affiliations

  1. Pontificia Universidad Catóólica de Valparaíso, 2362807, Valparaíso, Chile

    Álvaro Gómez Rubio, Broderick Crawford, Ricardo Soto, Adrián Jaramillo, Sebastián Mansilla Villablanca & Juan Salas

  2. Universidad Central de Chile, 8370178, Santiago, Chile

    Broderick Crawford

  3. Universidad Autónoma de Chile, 7500138, Santiago, Chile

    Ricardo Soto

  4. Universidad Espíritu Santo, Guayaquil, Ecuador

    Ricardo Soto

  5. Facultad de Ingeniería y Tecnología, Universidad San Sebastián, Bellavista 7, 8420524, Santiago, Chile

    Broderick Crawford & Eduardo Olguín

  6. Covenant University, 110001, Ogun, Nigeria

    Sanjay Misra

Authors
  1. Álvaro Gómez Rubio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Broderick Crawford
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ricardo Soto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eduardo Olguín
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sanjay Misra
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Adrián Jaramillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sebastián Mansilla Villablanca
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Juan Salas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Álvaro Gómez Rubio or Broderick Crawford .

Editor information

Editors and Affiliations

  1. University of Perugia , Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata , Potenza, Italy

    Beniamino Murgante

  3. Covenant University , Ota, Nigeria

    Sanjay Misra

  4. University of Minho , Braga, Portugal

    Ana Maria A. C. Rocha

  5. Polytechnic University , Bari, Italy

    Carmelo M. Torre

  6. Monash University , Clayton, Victoria, Australia

    David Taniar

  7. Kyushu Sangyo University , Fukuoka, Japan

    Bernady O. Apduhan

  8. Saint Petersburg State University , Saint Petersburg, Russia

    Elena Stankova

  9. Beijing University of Posts & Telecommunication , Beijing, China

    Shangguang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Rubio, Á.G. et al. (2016). Solving the Set Covering Problem with a Binary Black Hole Inspired Algorithm. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42085-1_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42084-4

  • Online ISBN: 978-3-319-42085-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics