Skip to main content

Mutative Self-adaptation on the Sharp and Parabolic Ridge

  • Conference paper
Foundations of Genetic Algorithms (FOGA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4436))

Included in the following conference series:

Abstract

In this paper, the behavior of intermediate (μ/μ I ,λ)-ES with self-adaptation is considered for two classes of ridge functions: the sharp and the parabolic ridge. Using a step-by-step approach to describe the system’s dynamics, we will investigate the underlying causes for the different behaviors of the ES on these function types and the effects of intermediate recombination.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog Verlag, Stuttgart (1973)

    Google Scholar 

  2. Ostermeier, A., Gawelczyk, A., Hansen, N.: A derandomized approach to self-adaptation of evolution strategies. Evolutionary Computation 2(4), 369–380 (1995)

    Article  Google Scholar 

  3. Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)

    Article  Google Scholar 

  4. Schwefel, H.-P.: Adaptive Mechanismen in der biologischen Evolution und ihr Einfluß auf die Evolutionsgeschwindigkeit. Technical report, Technical University of Berlin. Abschlußbericht zum DFG-Vorhaben Re 215/2 (1974)

    Google Scholar 

  5. Bienvenüe, A., François, O.: Global convergence for evolution strategies in spherical problems: Some simple proofs and difficulties. Theoretical Computer Science 308, 269–289 (2003)

    Article  Google Scholar 

  6. Auger, A.: Convergence results for the (1,λ)-SA-ES using the theory of φ-irreducible Markov chains. Theoretical Computer Science 334, 35–69 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hart, W., DeLaurentis, J., Ferguson, L.: On the convergence of an implicitly self-adaptive evolutionary algorithm on one-dimensional unimodal problems. IEEE Transactions on Evolutionary Computation (2003) (to appear)

    Google Scholar 

  8. Hart, W.E.: Convergence of a discretized self-adaptive evolutionary algorithm on multi-dimensional problems 2003 (submitted)

    Google Scholar 

  9. Semenov, M.: Convergence velocity of evolutionary algorithms with self-adaptation. In: GECCO 2002, pp. 210–213 (2002)

    Google Scholar 

  10. Semenov, M., Terkel, D.: Analysis of convergence of an evolutionary algorithm with self-adaptation using a stochastic Lyapunov function. Evolutionary Computation 11(4), 363–379 (2003)

    Article  Google Scholar 

  11. Beyer, H.-G.: Toward a theory of evolution strategies: Self-adaptation. Evolutionary Computation 3(3), 311–347 (1996)

    Article  Google Scholar 

  12. Beyer, H.-G.: On the performance of (1,λ)-evolution strategies for the ridge function class. IEEE Transactions on Evolutionary Computation 5(3), 218–235 (2001)

    Article  Google Scholar 

  13. Oyman, A.I., Beyer, H.-G., Schwefel, H.-P.: Analysis of a simple ES on the parabolic ridge. Evolutionary Computation 8(3), 249–265 (2000)

    Article  Google Scholar 

  14. Beyer, H.-G.: Estimating the steady-state of CSA-ES on ridge functions. The Theory of Evolutionary Algorithms, Dagstuhl Seminar, Wadern, Germany (February 2004)

    Google Scholar 

  15. Arnold, D.V., Beyer, H.-G.: Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge. Technical Report CS-2006-02, Dalhousie University, Faculty of Computer Science (2006)

    Google Scholar 

  16. Beyer, H.-G., Schwefel, H.-P.: Evolution strategies: A comprehensive introduction. Natural Computing 1(1), 3–52 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Bäck, T.: Self-adaptation. In: Bäck, T., Fogel, D., Michalewicz, Z. (eds.) Handbook of Evolutionary Computation, pp. C7.1:1–C7.1:15 Oxford University Press, New York (1997)

    Google Scholar 

  18. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A First Course in Order Statistics. Wiley, New York (1992)

    MATH  Google Scholar 

  19. Arnold, D.V.: Noisy Optimization with Evolution Strategies. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  20. Beyer, H.-G.: The Theory of Evolution Strategies. In: Natural Computing Series, Springer, Heidelberg (2001)

    Google Scholar 

  21. Herdy, M.: Reproductive isolation as strategy parameter in hierarchically organized evolution strategies. In: Männer, R., Manderick, B. (eds.) Parallel Problem Solving from Nature, vol. 2, pp. 207–217. Elsevier, Amsterdam (1992)

    Google Scholar 

  22. Meyer-Nieberg, S., Beyer, H.-G.: On the analysis of self-adaptive recombination strategies: First results. In: McKay, B., et al. (eds.) Proc. 2005 Congress on Evolutionary Computation (CEC’05), Edinburgh, UK, Piscataway, NJ, pp. 2341–2348. IEEE Press, NJ, New York (2005)

    Chapter  Google Scholar 

  23. Braun, M.: Differential Equations and their Applications. Springer, Heidelberg (1998)

    Google Scholar 

  24. Beyer, H.G., Arnold, D.V.: The steady state behavior of (μ/μ I , λ)-ES on ellipsoidal fitness models disturbed by noise. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 525–536. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  25. Beyer, H.-G., Meyer-Nieberg, S.: Self-adaptation of evolution strategies under noisy fitness evaluations. Genetic Programming and Evolvable Machines (accepted, 2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Christopher R. Stephens Marc Toussaint Darrell Whitley Peter F. Stadler

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Meyer-Nieberg, S., Beyer, HG. (2007). Mutative Self-adaptation on the Sharp and Parabolic Ridge. In: Stephens, C.R., Toussaint, M., Whitley, D., Stadler, P.F. (eds) Foundations of Genetic Algorithms. FOGA 2007. Lecture Notes in Computer Science, vol 4436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73482-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73482-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73479-6

  • Online ISBN: 978-3-540-73482-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics