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Evolution of Affine Transformations and Iterated Function Systems Using Hierarchical Evolution Strategy

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Genetic Programming (EuroGP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2038))

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Abstract

Often optimization problems involve the discovery of many scalar coefficients. Although genetic programming (GP) has been applied to the optimization and discovery of functions with an arbitrary number of scalar coefficients, recent results indicate that a method for fine-tuning GP scalar terminals can assist the discovery of solutions. In this paper we demonstrate an approach where genetic programming and evolution strategies (ES) are seamlessly combined. We apply our GP/ES hybrid, which we name Hierarchical Evolution Strategy, to the problem of evolving affine transformations and iterated function systems (IFS). We compare the results of our approach with GP and notice an improvement in performance in terms of discovering bsetter solutions and speed.

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References

  1. Back, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press 1996

    Google Scholar 

  2. Barnsley, M.F.: Fractals Everywhere. Academic Press, (1993)

    Google Scholar 

  3. Barnsley, M.F., and Hurd, L.P.: Fractal Image Compression. AK Peters, (1993)

    Google Scholar 

  4. Collet, P., Lutton, E., Raynal, F., and Schoenauer, M.: Individual GP: an alternative viewpoint for the resolution of complex problems. Proceedings of the Genetic and Evolutionary Computation Conference, volume 2, Morgan Kaufmann, (1999) 974–981

    Google Scholar 

  5. Cretin, G., Lutton, E., Levy-Vehel, J., Glevarec, P. and Roll, C.: Mixed IFS: Resolution of the inverse problem using genetic programming. Artificial Evolution, volume 1063 of LNCS Springer Verlag, (1996) 247–258

    Google Scholar 

  6. Foley, J.D., van Dam, A., Feiner, S.K., Huges, J.F.: Computer Graphics Principle and Practice. Addison-Wesley, (1990)

    Google Scholar 

  7. Hutchinson, J.E.: Fractals and Self Similarity. Indiana University Journal, Vol. 35,No.5, (1981)

    Google Scholar 

  8. Keller, R.E., Banzhaf, W., Mehnen, J., and Weinert, K.: CAD surface reconstruction from digitized 3D point data with a genetic programming/evolution strategy hybrid. Advances in Genetic Programming 3, MIT Press, (1999) 41–65

    Google Scholar 

  9. Sharman, K.C., Esparcia Alcazar, A.I., and Li, Y.: Evolving signal processing algorithms by genetic programming. First International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA, IEE, volume 414, (1995) 473–480

    Article  Google Scholar 

  10. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press (1992)

    Google Scholar 

  11. Langdon, W.B.: Genetic Programming and Data Structures, Kluwer Academic Publishers, (1998)

    Google Scholar 

  12. Lu, N.: Fractal Imaging. Academic Press, (1997)

    Google Scholar 

  13. Montana, J.D.: Strongly Typed Genetic Programming, Evolutionary Computation, 3(2), (1995) 199–230

    Article  Google Scholar 

  14. Nettleton, D.J. and Garigliano, R.: Evolutionary algorithms and the construction of fractals: solution of the inverse problem. Biosystems (33), Elsevier Science (1994) 221–231

    Google Scholar 

  15. Racine, A., Hamida, S.B., and Schoenauer, M.: Parametric coding vs genetic programming: A case study. In W.B. Langdon, Riccardo Poli, Peter Nordin, and Terry Fogarty, editors,Late-Breaking Papers of EuroGP-99, Goteborg, Sweeden, (1999) 13–22

    Google Scholar 

  16. Sarafopoulos, A.: Automatic generation of affine IFS and strongly typed genetic programming. Springer-Verlag, Genetic Programming, Proceedings of EuroGP’99, volume 1598 of LNCS, (1999) 149–160

    Chapter  Google Scholar 

  17. Schoenauer, M., Lamy, B., and Jouve F.:Identification of mechanical behaviour by genetic programming part II: Energy formulation. Technical report, Ecole Polytechnique, 91128 Palaiseau, France, (1995)

    Google Scholar 

  18. Schoenauer, M., Sebag, M., Jouve, F., Lamy, B., and Maitournam, H.: Evolutionary identification of macro-mechanical models. Advances in Genetic Programming 2, MIT Press, (1996) 467–488

    Google Scholar 

  19. Schwefel, P.H.: Evolution and Optimum Seeking. John Wiley & Sons, (1995)

    Google Scholar 

  20. Watt, A., and Watt, M.: Advanced Animation and Rendering Techniques Theory and Practice. Addison-Wesley, (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Media School National Centre for Computer Animation, Bournemouth University, Talbot Campus Fern Barrow, Poole, Dorset, BH12 5BB, UK

    Anargyros Sarafopoulos

Authors
  1. Anargyros Sarafopoulos
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Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham

    Julian Miller

  2. Computer Science Institute, University of Lausanne, Lausanne

    Marco Tomassini

  3. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy

    Pier Luca Lanzi

  4. Computer Science and Information Systems, University of Limerick, Limerick

    Conor Ryan

  5. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, Italy

    Andrea G. B. Tettamanzi

  6. Department of Computer Science, University College London, London

    William B. Langdon

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© 2001 Springer-Verlag Berlin Heidelberg

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Sarafopoulos, A. (2001). Evolution of Affine Transformations and Iterated Function Systems Using Hierarchical Evolution Strategy. In: Miller, J., Tomassini, M., Lanzi, P.L., Ryan, C., Tettamanzi, A.G.B., Langdon, W.B. (eds) Genetic Programming. EuroGP 2001. Lecture Notes in Computer Science, vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45355-5_14

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  • DOI: https://doi.org/10.1007/3-540-45355-5_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41899-3

  • Online ISBN: 978-3-540-45355-0

  • eBook Packages: Springer Book Archive

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