ESAGP – A Semantic GP Framework Based on Alignment in the Error Space

  • Stefano Ruberto
  • Leonardo Vanneschi
  • Mauro Castelli
  • Sara Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8599)

Abstract

This paper introduces the concepts of error vector and error space, directly bound to semantics, one of the hottest topics in genetic programming. Based on these concepts, we introduce the notions of optimally aligned individuals and optimally coplanar individuals. We show that, given optimally aligned, or optimally coplanar, individuals, it is possible to construct a globally optimal solution analytically. Thus, we introduce a genetic programming framework for symbolic regression called Error Space Alignment GP (ESAGP) and two of its instances: ESAGP-1, whose objective is to find optimally aligned individuals, and ESAGP-2, whose objective is to find optimally coplanar individuals. We also discuss how to generalize the approach to any number of dimensions. Using two complex real-life applications, we provide experimental evidence that ESAGP-2 outperforms ESAGP-1, which in turn outperforms both standard GP and geometric semantic GP. This suggests that “adding dimensions” is beneficial and encourages us to pursue the study in many different directions, that we summarize in the final part of the manuscript.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)MATHGoogle Scholar
  2. 2.
    Nguyen, Q.U.: Examining Semantic Diversity and Semantic Locality of Operators in Genetic Programming. PhD thesis, University College Dublin, Ireland (July 18, 2011)Google Scholar
  3. 3.
    Beadle, L., Johnson, C.G.: Semantic analysis of program initialisation in genetic programming. Genetic Programming and Evolvable Machines 10(3), 307–337 (2009)CrossRefGoogle Scholar
  4. 4.
    McPhee, N.F., Ohs, B., Hutchison, T.: Semantic building blocks in genetic programming. In: O’Neill, M., Vanneschi, L., Gustafson, S., Esparcia Alcázar, A.I., De Falco, I., Della Cioppa, A., Tarantino, E. (eds.) EuroGP 2008. LNCS, vol. 4971, pp. 134–145. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Nguyen, Q.U., Nguyen, X.H., O’Neill, M., McKay, R.I., Galvan-Lopez, E.: Semantically-based crossover in genetic programming: application to real-valued symbolic regression. Genetic Programming and Evolvable Machines 12(2), 91–119 (2011)CrossRefGoogle Scholar
  6. 6.
    Nguyen, Q.U., Nguyen, X.H., O’Neill, M.: Semantics based mutation in genetic programming: The case for real-valued symbolic regression. In: Matousek, R., Nolle, L. (eds.) 15th International Conference on Soft Computing, Mendel 2009, pp. 73–91 (2009)Google Scholar
  7. 7.
    Moraglio, A., Krawiec, K., Johnson, C.G.: Geometric semantic genetic programming. In: Coello Coello, C.A., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 21–31. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Vanneschi, L., Castelli, M., Manzoni, L., Silva, S.: A new implementation of geometric semantic GP and its application to problems in pharmacokinetics. In: Krawiec, K., Moraglio, A., Hu, T., Şima Etaner-Uyar, A., Hu, B. (eds.) EuroGP 2013. LNCS, vol. 7831, pp. 205–216. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Vanneschi, L., Silva, S., Castelli, M., Manzoni, L.: Geometric semantic genetic programming for real life applications. In: GP Theory and Practice. Springer (2013)Google Scholar
  10. 10.
    Martinez, Y., Naredo, E., Trujillo, L., Galvan-Lopez, E.: Searching for novel regression functions. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 16–23 (2013)Google Scholar
  11. 11.
    Mitchell, T.M.: Machine Learning. McGraw-Hill (1997)Google Scholar
  12. 12.
    MATLAB: version 7.10.0 (R2010a). The MathWorks Inc., Natick, Massachusetts (2010)Google Scholar
  13. 13.
    Wedin, P.: On angles between subspaces of a finite dimensional inner product space. In: Kagstrom, B., Ruhe, A., (eds.): Matrix Pencils. Lecture Notes in Mathematics, 263–285. Springer (1983)Google Scholar
  14. 14.
    Archetti, F., Lanzeni, S., Messina, E., Vanneschi, L.: Genetic programming for computational pharmacokinetics in drug discovery and development. Genetic Programming and Evolvable Machines 8, 413–432 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Stefano Ruberto
    • 1
    • 2
  • Leonardo Vanneschi
    • 3
  • Mauro Castelli
    • 3
  • Sara Silva
    • 2
    • 4
    • 5
  1. 1.GSSI, Gran Sasso Science Institute, INFNL’AquilaItaly
  2. 2.INESC-ID, ISTUniversity of LisbonLisbonPortugal
  3. 3.ISEGIUniversidade Nova de LisboaLisbonPortugal
  4. 4.LabMAg, FCULUniversity of LisbonLisbonPortugal
  5. 5.CISUCUniversidade de CoimbraCoimbraPortugal

Personalised recommendations