Skip to main content

A Study of Recombination Operators for the Cyclic Bandwidth Problem

  • Conference paper
  • First Online:
Artificial Evolution (EA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12052))

Abstract

This work is dedicated to a study of the NP-hard Cyclic Bandwidth Problem with the paradigm of memetic algorithms. To find out how to choose or design a suitable recombination operator for the problem, we study five classical permutation crossovers within a basic memetic algorithm integrating a simple descent local search procedure. We investigate the correlation between algorithmic performances and population diversity measured by the average population distance and entropy. This work invites more research to improve the two key components of the memetic algorithm: reinforcement of the local search and design of a meaningful recombination operator suitable for the problem.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Bansal, R., Srivastava, K.: A memetic algorithm for the cyclic antibandwidth maximization problem. Soft Comput. 15(2), 397–412 (2011)

    Article  Google Scholar 

  2. Benlic, U., Hao, J.K.: Memetic search for the quadratic assignment problem. Expert Syst. Appl. 42(1), 584–595 (2015)

    Article  Google Scholar 

  3. Bhatt, S.N., Leighton, F.T.: A framework for solving VLSI graph layout problems. J. Comput. Syst. Sci. 28(2), 300–343 (1984)

    Article  MathSciNet  Google Scholar 

  4. Boese, K.D.: Cost versus distance in the traveling salesman problem. UCLA Computer Science Department Los Angeles (1995)

    Google Scholar 

  5. Chen, Y., Hao, J.K.: Memetic search for the generalized quadratic multiple knapsack problem. IEEE Trans. Evol. Comput. 20(6), 908–923 (2016)

    Article  Google Scholar 

  6. Davis, L.: Applying adaptive algorithms to epistatic domains. In: International Joint Conference on Artificial Intelligence, vol. 85, pp. 162–164 (1985)

    Google Scholar 

  7. Fleurent, C., Ferland, J.: Object-oriented implementation of heuristic search methods for graph coloring. Cliques, Coloring, and Satisfiability. DIMACS Ser. Discrete Math. Theor. Comput. Sci. 6, 619–652 (1996)

    Article  Google Scholar 

  8. Freisleben, B., Merz, P.: A genetic local search algorithm for solving symmetric and asymmetric traveling salesman problems. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp. 616–621. IEEE (1996)

    Google Scholar 

  9. Goldberg, D.E., Lingle, R., et al.: Alleles, loci, and the traveling salesman problem. In: Proceedings of International Conference on Genetic Algorithms and Their Applications, vol. 154, pp. 154–159. Lawrence Erlbaum, Hillsdale (1985)

    Google Scholar 

  10. Hao, J.K.: Memetic algorithms in discrete optimization. In: Neri, F., Cotta, C., Moscato, P. (eds.) Handbook of Memetic Algorithms. Studies in Computational Intelligence, vol. 379, pp. 73–94. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-23247-3_6

    Chapter  Google Scholar 

  11. Jin, Y., Hao, J.K., Hamiez, J.P.: A memetic algorithm for the minimum sum coloring problem. Comput. Oper. Res. 43, 318–327 (2014)

    Article  MathSciNet  Google Scholar 

  12. Krasnogor, N., Smith, J.: A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Trans. Evol. Comput. 9(5), 474–488 (2005)

    Article  Google Scholar 

  13. Lai, X., Hao, J.K.: A tabu search based memetic algorithm for the max-mean dispersion problem. Comput. Oper. Res. 72, 118–127 (2016)

    Article  Google Scholar 

  14. Leung, J.Y., Vornberger, O., Witthoff, J.D.: On some variants of the bandwidth minimization problem. SIAM J. Comput. 13(3), 650–667 (1984)

    Article  MathSciNet  Google Scholar 

  15. Lin, Y.: The cyclic bandwidth problem. In: Chinese Science Abstracts Series A, vol. 14(2 Part A), p. 14 (1995)

    Google Scholar 

  16. Merz, P., Freisleben, B.: Memetic algorithms for the traveling salesman problem. Complex Syst. 13, 297–345 (1997)

    MathSciNet  MATH  Google Scholar 

  17. Moscato, P., Cotta, C.: A gentle introduction to memetic algorithms. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 105–144. Springer, Boston (2003). https://doi.org/10.1007/0-306-48056-5_5

    Chapter  Google Scholar 

  18. Oliver, I., Smith, D., Holland, J.: A study of permutation crossover operators on the travelling salesman problem. In: Proceedings of the Second International Conference on Genetic Algorithms and their Application, pp. 224–230 (1987)

    Google Scholar 

  19. Ren, J., Hao, J.K., Rodriguez-Tello, E.: An iterated three-phase search approach for solving the cyclic bandwidth problem. IEEE Access 7, 98436–98452 (2019)

    Article  Google Scholar 

  20. Rodriguez-Tello, E., Betancourt, L.C.: An improved memetic algorithm for the antibandwidth problem. In: Hao, J.-K., Legrand, P., Collet, P., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) EA 2011. LNCS, vol. 7401, pp. 121–132. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35533-2_11

    Chapter  Google Scholar 

  21. Rodriguez-Tello, E., Hao, J.K., Torres-Jimenez, J.: An improved simulated annealing algorithm for bandwidth minimization. Eur. J. Oper. Res. 185(3), 1319–1335 (2008)

    Article  Google Scholar 

  22. Rodriguez-Tello, E., Narvaez-Teran, V., Lardeux, F.: Comparative study of different memetic algorithm configurations for the cyclic bandwidth sum problem. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018, Part I. LNCS, vol. 11101, pp. 82–94. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99253-2_7

    Chapter  Google Scholar 

  23. Rodriguez-Tello, E., Romero-Monsivais, H., Ramirez-Torres, G., Lardeux, F.: Tabu search for the cyclic bandwidth problem. Comput. Oper. Res. 57, 17–32 (2015)

    Article  MathSciNet  Google Scholar 

  24. Romero-Monsivais, H., Rodriguez-Tello, E., Ramírez, G.: A new branch and bound algorithm for the cyclic bandwidth problem. In: Batyrshin, I., Mendoza, M.G. (eds.) MICAI 2012, Part II. LNCS (LNAI), vol. 7630, pp. 139–150. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37798-3_13

    Chapter  Google Scholar 

  25. Rosenberg, A.L., Snyder, L.: Bounds on the costs of data encodings. Math. Syst. Theory 12(1), 9–39 (1978)

    Article  MathSciNet  Google Scholar 

  26. Syswerda, G.: Scheduling optimization using genetic algorithms. In: Handbook of Genetic Algorithms, pp. 322–349 (1991)

    Google Scholar 

  27. Wang, Y., Lü, Z., Hao, J.-K.: A study of multi-parent crossover operators in a memetic algorithm. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010, Part I. LNCS, vol. 6238, pp. 556–565. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_56

    Chapter  Google Scholar 

  28. Wu, Q., Hao, J.K.: Memetic search for the max-bisection problem. Comput. Oper. Res. 40(1), 166–179 (2013)

    Article  MathSciNet  Google Scholar 

  29. Zhou, Y., Hao, J., Glover, F.: Memetic search for identifying critical nodes in sparse graphs. IEEE Trans. Cybern. 49(10), 3699–3712 (2019)

    Article  Google Scholar 

Download references

Acknowledgments

We are grateful to the referees for their valuable suggestions and comments which helped us to improve the paper. Support from the China Scholarship Council (CSC, Grant 201608070103) for the first author and support from the Mexican Secretariat of Public Education through SEP-Cinvestav (2019–2020, Grant 00114) for the third author are also acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jin-Kao Hao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ren, J., Hao, JK., Rodriguez-Tello, E. (2020). A Study of Recombination Operators for the Cyclic Bandwidth Problem. In: Idoumghar, L., Legrand, P., Liefooghe, A., Lutton, E., Monmarché, N., Schoenauer, M. (eds) Artificial Evolution. EA 2019. Lecture Notes in Computer Science(), vol 12052. Springer, Cham. https://doi.org/10.1007/978-3-030-45715-0_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-45715-0_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45714-3

  • Online ISBN: 978-3-030-45715-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics