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International Conference on Computational Science and Its Applications

ICCSA 2016: Computational Science and Its Applications – ICCSA 2016 pp 273–283Cite as

Solving Set Covering Problem with Fireworks Explosion

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

Abstract

To solve the Set Covering Problem we will use a metaheuristic Fireworks Algorithm 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 (FWA) consists of four parts, i.e., the explosion operator, the mutation operator, the mapping rule and selection strategy. 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.

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References

  1. Crawford, B., Soto, R., Monfroy, E.: Cultural algorithms for the set covering problem. In: Tan, Y., Shi, Y., Mo, H. (eds.) ICSI 2013, Part II. LNCS, vol. 7929, pp. 27–34. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  2. Goldberg, D.: Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Syst. 5, 139–167 (1990)

    MathSciNet  MATH  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(5), 2272–2280 (2013)

    Article  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(5), 1690–1695 (2013)

    Article  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. Rom. J. Inf. Sci. Technol. 17, 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: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds.) Modern Trends and Techniques in Computer Science. Advances in Intelligent Systems and Computing, vol. 285, pp. 65–73. Springer, Heidelberg (2014)

    Chapter  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., Trawiński, B., Kosala, R. (eds.) ACIIDS 2015. LNCS, vol. 9012, pp. 41–50. Springer, Heidelberg (2015)

    Google Scholar 

  8. Tan, Y.: Fireworks Algorithm: A Novel Swarm Intelligence Optimization Method. Springer, Heidelberg (2015)

    Book  MATH  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 

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Acknowledgements

The author Broderick Crawford is supported by grant CONICYT/FONDECYT/REGULAR/1140897 and Ricardo Soto is supported by grant CONICYT/FONDECYT/INICIACION/1160455.

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

    Broderick Crawford & Eduardo Olguín

  4. Universidad Autónoma de Chile, Santiago, Chile

    Ricardo Soto

  5. Universidad Cientifica del Sur, Lima, Peru

    Ricardo Soto

  6. Covenant University, Ota, Nigeria

    Sanjay Misra

Authors
  1. Broderick Crawford
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  2. Ricardo Soto
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  3. Gonzalo Astudillo
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  4. Eduardo Olguín
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  5. Sanjay Misra
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Corresponding author

Correspondence to Gonzalo Astudillo .

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

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© 2016 Springer International Publishing Switzerland

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Crawford, B., Soto, R., Astudillo, G., Olguín, E., Misra, S. (2016). Solving Set Covering Problem with Fireworks Explosion. 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_21

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  • DOI: https://doi.org/10.1007/978-3-319-42085-1_21

  • 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)

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