Skip to main content
SpringerLink
Log in

Complexity reduction using expansive coding

  • Conference paper
  • First Online:
Evolutionary Computing (AISB EC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 865))

Included in the following conference series:

Abstract

This paper describes a new technique for reducing the complexity of algorithms, such as those used in digital signal processing, using a genetic algorithm (GA). The method, referred to as expansive coding, is a representation methodology which makes complicated combinatorial optimisation tasks easier to solve for a GA. Using this technique, the representation, operators and fitness function used by the GA become more complicated, but the search space becomes less epistatic, and therefore easier for the GA to tackle. This reduction in epistasis (interaction between parameters) is essential if the difficult task of complexity reduction is to be successfully achieved. Expansive coding spreads the task's complexity more evenly among the operators, fitness function and search space. We demonstrate how this technique can be applied to two cases of reduction of complexity of algorithms: a multiplier for quaternion numbers, and a Walsh transform computation. We suggest why the technique is more successful on the former task than the latter.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Barrett, A. Ramsay, and A. Sloman. POP-11: a Practical Language for Artificial Intelligence. Ellis Horwood, Chicester, 1985.

    Google Scholar 

  2. D. Beasley, D.R. Bull, and R.R. Martin. Reducing epistasis in combinatorial problems by expansive coding. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, pages 400–407. Morgan Kaufmann, 1993.

    Google Scholar 

  3. D. Beasley, D.R. Bull, and R.R. Martin. A sequential niche technique for multimodal function optimization. Evolutionary Computation, 1(2):101–125, 1993.

    Google Scholar 

  4. C-H.H. Chu. A genetic algorithm approach to the configuration of stack filters. In J.D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 219–224. Morgan Kaufmann, 1989.

    Google Scholar 

  5. Y. Davidor. Epistasis variance: Suitability of a representation to genetic algorithms. Complex Systems, 4:369–383, 1990.

    Google Scholar 

  6. L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, 1991.

    Google Scholar 

  7. H.F. de Groote. On the complexity of quaternion multiplication. Information Processing Letters, 3(6):177–179, 1975.

    Google Scholar 

  8. D.M. Etter, M.J. Hicks, and K.H. Cho. Recursive adaptive filter design using an adaptive genetic algorithm. In IEEE Int Conf Acou Speech Sig Proc, pages 635–638, 1982.

    Google Scholar 

  9. D.E. Goldberg. Genetic Algorithms in search, optimization and machine learning. Addison-Wesley, 1989.

    Google Scholar 

  10. J.J. Grefenstette. Optimization of control parameters for genetic algorithms, IEEE Trans SMC, 16:122–128, 1986.

    Google Scholar 

  11. W.R. Hamilton. Elements of Quaternions. Cambridge University Press, 1899.

    Google Scholar 

  12. D.H. Horrocks and D.R. Bull. The synthesis of complex signal multipliers. In V. Cappellini and A.G. Constantinides, editors, Proc. Int. Conf. Digital Signal Processing, pages 207–210. North-Holland, 1987.

    Google Scholar 

  13. S.J. Louis and G.J.E. Rawlins. Designer genetic algorithms: Genetic algorithms in structure design. In R.K. Belew and L.B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 53–60. Morgan Kaufmann, 1991.

    Google Scholar 

  14. R.R. Martin. Rotation by quaternions. Mathematical Spectrum, 17(2):42–48, 1983.

    Google Scholar 

  15. D. Suckley. Genetic algorithm in the design of FIR filters. IEE Proc-G, 138:234–238, 1991.

    Google Scholar 

  16. G. Syswerda. Schedule optimization using genetic algorithms. In L. Davis, editor, Handbook of Genetic Algorithms, chapter 21, pages 332–349. Van Nostrand Reinhold, 1991.

    Google Scholar 

  17. M. Vose and G. Liepins. Schema disruption. In R.K. Belew and L.B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 237–242. Morgan Kaufmann, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing Mathematics, University of Wales College of Cardiff, CF2 4YN, Cardiff, UK

    David Beasley & Ralph R. Martin

  2. Department of Electrical and Electronic Engineering, University of Bristol, BS8 1TR, Bristol, UK

    David R. Bull

Authors
  1. David Beasley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David R. Bull
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ralph R. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Terence C. Fogarty

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beasley, D., Bull, D.R., Martin, R.R. (1994). Complexity reduction using expansive coding. In: Fogarty, T.C. (eds) Evolutionary Computing. AISB EC 1994. Lecture Notes in Computer Science, vol 865. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58483-8_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-58483-8_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58483-4

  • Online ISBN: 978-3-540-48999-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation