Skip to main content

The effect of spin-flip symmetry on the performance of the simple GA

  • Conference paper
  • First Online:
Parallel Problem Solving from Nature — PPSN V (PPSN 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1498))

Included in the following conference series:

  • 171 Accesses


We use the one-dimensional nearest neighbor interaction functions (NNIs) to show how the presence of symmetry in a fitness function greatly influences the convergence behavior of the simple genetic algorithm (SGA). The effect of symmetry on the SGA supports the statement that it is not the amount of interaction present in a fitness function, measured e.g. by Davidor's epistasis variance and the experimental design techniques introduced by Reeves and Wright, which is important, but the kind of interaction. The NNI functions exhibit a minimal amount of second order interaction, are trivial to optimize deterministically and yet show a wide range of SGA behavior. They have been extensively studied in statistical physics; results from this field explain the negative effect of symmetry on the convergence behavior of the SGA. This note intends to introduce them to the GA-community.

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

Access this chapter

Institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others


  1. L. Altenberg. Fitness distance correlation analysis: an instructive counterexample. In Th. Bäck, editor, Proceedings of the 7th International Conference on Genetic Algorithms, pages 57–64. Morgan Kaufmann Publishers, 1997.

    Google Scholar 

  2. Y. Davidor. Epistasis variance: a viewpoint on GA-hardness. In G. J. E. Rawlins, editor, Foundations of Genetic Algorithms, pages 23–35. Morgan Kaufmann Publishers. 1991.

    Google Scholar 

  3. E. Ising. Beitrag zur Theorie des Ferromagnetismus. Z. Physik, 31:235, 1924.

    Google Scholar 

  4. J. Jäckle, R. B. Stinchcombe, and S. Cornell. Freezing of nonequilibrium domain structures in a kinetic Ising model. J. Stat. Phys., 62:425–433, 1991.

    Article  Google Scholar 

  5. S. A. Kauffman. Adaptation on rugged fitness landscapes. In Lectures in the Sciences of Complexity, volume I of SFI studies, pages 619–712. Addison Wesley, 1989.

    Google Scholar 

  6. H. A. Kramers and G. H. Wannier. Statistics of the two-dimensional ferromagnet. Part I. Phys. Rev., 60:252–262, 1941.

    Article  MATH  MathSciNet  Google Scholar 

  7. T. M. Liggett. Interacting Particle Systems. Springer Verlag, 1985.

    Google Scholar 

  8. B. Naudts. Measuring GA-hardness. PhD thesis, University of Antwerp, RUCA, Belgium, 1998.

    Google Scholar 

  9. B. Naudts and A. Verschoren. SGA search dynamics on second order functions. In J.-K. Hao, E. Lutton, E. Ronald, M. Schoenauer, and D. Snyers, editors, Artificial Evolution 97. Springer Verlag, 1998.

    Google Scholar 

  10. Lars Onsager. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Physical Review, 65(3):117–149, feb 1944.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Prügel-Bennett and J. L. Shapiro. The dynamics of a genetic algorithm for simple Ising systems. Physica D, 104:75–114, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Reeves and C. Wright. An experimental design perspective on genetic algorithms. In L. D. Whitley and M. D. Vose, editors, Foundations of Genetic Algorithms 3, pages 7–22. Morgan Kaufmann Publishers, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Agoston E. Eiben Thomas Bäck Marc Schoenauer Hans-Paul Schwefel

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Naudts, B., Naudts, J. (1998). The effect of spin-flip symmetry on the performance of the simple GA. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN V. PPSN 1998. Lecture Notes in Computer Science, vol 1498. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65078-2

  • Online ISBN: 978-3-540-49672-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics