Skip to main content

Evolutionary Search of Binary Orthogonal Arrays

  • Conference paper
  • First Online:
Parallel Problem Solving from Nature – PPSN XV (PPSN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11101))

Included in the following conference series:

Abstract

Orthogonal Arrays (OA) represent an interesting breed of combinatorial designs that finds applications in several domains such as statistics, coding theory, and cryptography. In this work, we address the problem of constructing binary OA through evolutionary algorithms, an approach which received little attention in the combinatorial designs literature. We focus on the representation of a feasible solution, which we encode as a set of Boolean functions whose truth tables are used as the columns of a binary matrix, and on the design of an appropriate fitness function and variation operators for this problem. We finally present experimental results obtained with genetic algorithms (GA) and genetic programming (GP) on optimizing such fitness function, and compare the performances of these two metaheuristics with respect to the size of the considered problem instances. The experimental results show that GP outperforms GA at handling this type of problem, as it converges to an optimal solution in all considered problem instances but one.

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

Access this chapter

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. Carlet, C., Guilley, S.: Correlation-immune boolean functions for easing counter measures to side-channel attacks. Algebraic Curves Finite Fields: Cryptograph. Other Appl. 16, 41–70 (2014)

    MathSciNet  Google Scholar 

  2. Colbourn, C.J., Dinitz, J.H.: Handbook of Combinatorial Designs. CRC Press, Boca Raton (2006)

    Book  Google Scholar 

  3. Hedayat, A.S., Sloane, N.J.A., Stufken, J.: Orthogonal Arrays: Theory and Applications. Springer, Heidelberg (2012). https://doi.org/10.1007/978-1-4612-1478-6

    Book  MATH  Google Scholar 

  4. Mariot, L., Leporati, A.: Heuristic search by particle swarm optimization of boolean functions for cryptographic applications. In: Genetic and Evolutionary Computation Conference, Companion Material Proceedings , GECCO 2015, Madrid, Spain, 11–15 July 2015, pp. 1425–1426 (2015)

    Google Scholar 

  5. Mariot, L., Picek, S., Jakobovic, D., Leporati, A.: Evolutionary algorithms for the design of orthogonal latin squares based on cellular automata. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2017, Berlin, Germany, 15–19 July 2017, pp. 306–313 (2017)

    Google Scholar 

  6. Millan, W., Clark, A., Dawson, E.: Heuristic design of cryptographically strong balanced boolean functions. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 489–499. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054148

    Chapter  Google Scholar 

  7. Picek, S., Jakobovic, D., Miller, J.F., Batina, L., Cupic, M.: Cryptographic boolean functions: one output, many design criteria. Appl. Soft Comput. 40, 635–653 (2016)

    Article  Google Scholar 

  8. Poli, R., Langdon, W.B., McPhee, N.F.: A Field Guide to Genetic Programming (2008). http://lulu.com and freely available at http://www.gp-field-guide.org.uk. (With contributions by J.R. Koza)

  9. Safadi, R., Wang, R.: The use of genetic algorithms in the construction of mixed multilevel orthogonal arrays. Technical report, Olin Corp Cheshire CT Olin Research Center (1992)

    Google Scholar 

  10. Sloane, N.J.: A library of orthogonal arrays. Fixed-level arrays with more than three levels: OA 16(4.2) (2007)

    Google Scholar 

  11. Stinson, D.R.: Combinatorial Designs: Constructions and Analysis. Springer, Heidelberg (2007). https://doi.org/10.1007/b97564

    Book  MATH  Google Scholar 

  12. Wang, R., Safadi, R.: Generating mixed multilevel orthogonal arrays by simulated annealing. In: Page, C., LePage, R. (eds.) Computing Science and Statistics, pp. 557–560. Springer, New York (1992). https://doi.org/10.1007/978-1-4612-2856-1_100

    Chapter  Google Scholar 

Download references

Acknowledgments

This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-4882.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luca Mariot .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mariot, L., Picek, S., Jakobovic, D., Leporati, A. (2018). Evolutionary Search of Binary Orthogonal Arrays. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99253-2_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99252-5

  • Online ISBN: 978-3-319-99253-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics