Skip to main content
Springer Nature Link
Log in

Fireworks Explosion Can Solve the Set Covering Problem

  • Conference paper
  • First Online:
Artificial Intelligence Perspectives in Intelligent Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 464))

  • 1175 Accesses

Abstract

The Set Covering Problem is a formal model for many practical optimization problems. It consists in finding a subset of columns in a zero/one matrix such that they cover all the rows of the matrix at a minimum cost. To solve the Set Covering Problem we will use a metaheuristic called Fireworks Algorithm (FWA) inspired by the fireworks explosion. Through the observation of the way that fireworks explode is much similar to the way that an individual searches the optimal solution in swarm. Fireworks algorithm consists of four parts, i.e., the explosion operator, the mutation operator, the mapping rule and selection strategy.

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. 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 

  2. Goldberg, D.: Real-Coded Genetic Algorithms, Virtual Alphabets, and Blocking. Complex Syst. 5, 139–167 (1990)

    Google Scholar 

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

    Google Scholar 

  4. 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. 40, 1690–1695 (2013)

    Google Scholar 

  5. 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, vol. 17, pp. 252–264 (2014)

    Google Scholar 

  6. 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, Switzerland (2014)

    Google Scholar 

  7. 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 

  8. Tan, Y.: Fireworks Algorithm. Springer, Berlin (2015)

    Google Scholar 

  9. Caprara, A., Fischetti, M., Toth, P.: Algorithms for the set covering problem. Ann. Oper. Res. 98, 353–371 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ali, A.I., Thiagarajan, H.: A network relaxation based enumeration algorithm for set partitioning. Eur. J. Oper. Res. 38(1), 76–85 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Walker, W.: Using the set-covering problem to assign fire companies to fire houses. Oper. Res. 22, 275–277 (1974)

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Oper. Res. 12(2), 300–304 (1964)

    Article  Google Scholar 

  14. Fisher, M.L., Rosenwein, M.B.: An interactive optimization system for bulk-cargo ship scheduling. Naval Res. Logist. 36(1), 27–42 (1989)

    Article  Google Scholar 

  15. Freeman, B.A., Jucker, J.V.: The line balancing problem. J. Ind. Eng. 18, 361–364 (1967)

    Google Scholar 

  16. 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)

    Article  MathSciNet  MATH  Google Scholar 

  17. Breuer, M.A.: Simplification of the covering problem with application to boolean expressions. J. Assoc. Comput. Mach. 17, 166–181 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  18. Christofides, N.: Zero-one programming using non-binary tree-search. Comput. J. 14(4), 418–421 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  19. Garfinkel, R.S., Nemhauser, G.L.: Optimal political districting by implicit enumeration techniques. Manag. Sci. 16(8), B495–B508 (1970)

    Article  MATH  Google Scholar 

  20. Housos, E., Elmroth, T.: Automatic optimization of subproblems in scheduling airline crews. Interfaces 27(5), 68–77 (1997)

    Article  Google Scholar 

  21. Mirjalili, S., Lewis, A.: S-shaped versus v-shaped transfer functions for binary particle swarm optimization. Swarm Evol. Comput. 9, 1–14 (2013)

    Article  Google Scholar 

  22. Beasley, J.: A lagrangian heuristic for set covering problems. Naval Res. Logist. 37, 151–164 (1990)

    Article  MathSciNet  MATH  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Broderick Crawford, Ricardo Soto & Gonzalo Astudillo

  2. Universidad Central de Chile, Santiago, Chile

    Broderick Crawford

  3. Universidad San Sebastián, Santiago, Chile

    Broderick Crawford & Eduardo Olguín

  4. Universidad Autónoma de Chile, Santiago, Chile

    Ricardo Soto

  5. Universidad Científica del Sur, Lima, Peru

    Ricardo Soto

Authors
  1. Broderick Crawford
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Soto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gonzalo Astudillo
    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

Corresponding author

Correspondence to Gonzalo Astudillo .

Editor information

Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Roman Senkerik

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zuzana Kominkova Oplatkova

  4. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  5. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Crawford, B., Soto, R., Astudillo, G., Olguín, E. (2016). Fireworks Explosion Can Solve the Set Covering Problem. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Silhavy, P., Prokopova, Z. (eds) Artificial Intelligence Perspectives in Intelligent Systems. Advances in Intelligent Systems and Computing, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-319-33625-1_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-33625-1_43

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33623-7

  • Online ISBN: 978-3-319-33625-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics