Skip to main content
SpringerLink
Log in

An Binary Black Hole Algorithm to Solve Set Covering Problem

  • Conference paper
  • First Online:
Trends in Applied Knowledge-Based Systems and Data Science (IEA/AIE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9799))

Abstract

The set covering problem (SCP) is one of the most representative combinatorial optimization problems and it has multiple applications in different situations of engineering, sciences and some other disciplines. It aims to find a set of solutions that meet the needs defined in the constraints having lowest possible cost. In this paper we used an existing binary algorithm inspired by Binary Black Holes (BBH), to solve multiple instances of the problem with known benchmarks obtained from the OR-library. The presented method emulates the behavior of these celestial bodies using a rotation operator to bring good solutions. After tray this algorithm, we implemented some improvements in certain operators, as well as added others also inspired by black holes physical behavior, to optimize the search and exploration to improving the results.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

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 by implicit enumeration techniques. Manage. Sci. 16(8), B–495 (1970)

    Article  MATH  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. Hawking, S.: Agujeros negros y pequeños universos. Planeta, Buenos Aires (1994)

    Google Scholar 

  9. Hawking, S., Jackson, M.: A Brief History of Time. Dove Audio, Beverly Hills (1993)

    Google Scholar 

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

    Google Scholar 

  11. Crawford, B., Soto, R., Olivares-Suarez, M., Palma, W., Paredes, F., Olguín, E., Norero, E.: A binary coded firefly algorithm that solves the set covering problem. Sci. Technol. 17(3), 252–264 (2014)

    Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O.: Computational Science and Its Applications-ICCSA 2015, vol. 9157. Springer, Cham (2015)

    Google Scholar 

  16. 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

Álvaro Gómez is supported by Postgraduate Grant Pontificia Universidad Católica de Valparaíso 2015 (INF-PUCV 2015). Broderick Crawford is supported by Grant CONICYT/FONDECYT/REGULAR/1140897. Ricardo Soto is supported by Grant CONICYT/FONDECYT/INICIACION/11130459. Adrián Jaramillo is supported by Postgraduate Grant Pontificia Universidad Católica de Valparaíso 2015 (INF-PUCV 2015). Sebastián Mansilla is supported by Postgraduate Grant Pontificia Universidad Católica de Valparaíso 2015 (INF-PUCV 2015). Juan Salas is supported by Postgraduate Grant Pontificia Universidad Católica de Valparaíso 2015 (INF-PUCV 2015).

Author information

Authors and Affiliations

  1. Pontificia Universidad Católica de Valparaíso, Santiago de Chile, Chile

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

  2. Universidad Autónoma de Chile, Santiago de Chile, Chile

    Ricardo Soto

  3. Universidad Científica del Sur, Lima, Peru

    Ricardo Soto

  4. Universidad San Sebastián, Santiago de Chile, Chile

    Broderick Crawford & Eduardo Olguín

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. Adrián Jaramillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sebastián Mansilla Villablanca
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Juan Salas
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Eduardo Olguín
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Álvaro Gómez Rubio , Broderick Crawford , Ricardo Soto , Adrián Jaramillo , Sebastián Mansilla Villablanca , Juan Salas or Eduardo Olguín .

Editor information

Editors and Affiliations

  1. Iwate Prefectural University , Iwate, Japan

    Hamido Fujita

  2. Department Computer Science, Texas State University, San Marcos, Texas, USA

    Moonis Ali

  3. Universiti Teknologi Malaysis (UTM), Bahru, Malaysia

    Ali Selamat

  4. Iwate Prefectural University , Iwate, Japan

    Jun Sasaki

  5. Iwate Prefectural University , Iwate, Japan

    Masaki Kurematsu

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). An Binary Black Hole Algorithm to Solve Set Covering Problem. In: Fujita, H., Ali, M., Selamat, A., Sasaki, J., Kurematsu, M. (eds) Trends in Applied Knowledge-Based Systems and Data Science. IEA/AIE 2016. Lecture Notes in Computer Science(), vol 9799. Springer, Cham. https://doi.org/10.1007/978-3-319-42007-3_74

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42007-3_74

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42006-6

  • Online ISBN: 978-3-319-42007-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation