Skip to main content
SpringerLink
Log in

Design of a Surrogate Model Assisted (1 + 1)-ES

  • Conference paper
  • First Online:
Parallel Problem Solving from Nature – PPSN XV (PPSN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11101))

Included in the following conference series:

Abstract

Surrogate models are employed in evolutionary algorithms to replace expensive objective function evaluations with cheaper though usually inaccurate estimates based on information gained in past iterations. Implications of the trade-off between computational savings on the one hand and potentially poor steps due to the inaccurate assessment of candidate solutions on the other are generally not well understood. We study the trade-off in the context of a surrogate model assisted \((1+1)\)-ES by considering a simple model for single steps. Based on the insights gained, we propose a step size adaptation mechanism for the strategy and experimentally evaluate it using several test functions.

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

Access this chapter

Log in via an institution
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 EPUB and 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

Notes

  1. 1.

    See Hansen et al. [6] for evolution strategy terminology.

  2. 2.

    Detailed derivations of Eqs. (3), (4), (5), and (6) can be found in a separate document at web.cs.dal.ca/~dirk/PPSN2018addendum.pdf.

References

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

    Book  Google Scholar 

  2. Arnold, D.V., Beyer, H.-G.: A general noise model and its effects on evolution strategy performance. IEEE Trans. Evol. Comput. 10(4), 380–391 (2006)

    Article  Google Scholar 

  3. Auger, A., Hansen, N., Perez Zerpa, J.M., Ros, R., Schoenauer, M.: Experimental comparisons of derivative free optimization algorithms. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 3–15. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02011-7_3

    Chapter  Google Scholar 

  4. Büche, D., Schraudolph, N.N., Koumoutsakos, P.: Accelerating evolutionary algorithms with Gaussian process fitness function models. IEEE Trans. Syst. Man Cybern. B Cybern. Part C 35(2), 183–194 (2005)

    Article  Google Scholar 

  5. Chen, Y., Zou, X.: Performance analysis of a (1+1) surrogate-assisted evolutionary algorithm. In: Huang, D.-S., Bevilacqua, V., Premaratne, P. (eds.) ICIC 2014. LNCS, vol. 8588, pp. 32–40. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09333-8_4

    Chapter  Google Scholar 

  6. Hansen, N., Arnold, D.V., Auger, A.: Evolution strategies. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 871–898. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-43505-2_44

    Chapter  Google Scholar 

  7. Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)

    Article  Google Scholar 

  8. Jin, Y.: Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol. Comput. 1(2), 61–70 (2011)

    Article  Google Scholar 

  9. Kern, S., Hansen, N., Koumoutsakos, P.: Local meta-models for optimization using evolution strategies. In: Runarsson, T.P., Beyer, H.-G., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 939–948. Springer, Heidelberg (2006). https://doi.org/10.1007/11844297_95

    Chapter  Google Scholar 

  10. Kern, S., Müller, S.D., Hansen, N., Büche, D., Ocenasek, J., Koumoutsakos, P.: Learning probability distributions in continuous evolutionary algorithms – a comparative review. Nat. Comput. 3(1), 77–112 (2004)

    Article  MathSciNet  Google Scholar 

  11. Loshchilov, I.: Surrogate-Assisted Evolutionary Algorithms. PhD thesis, Université Paris Sud - Paris XI (2013)

    Google Scholar 

  12. Loshchilov, I., Schoenauer, M., Sebag, M.: Comparison-based optimizers need comparison-based surrogates. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 364–373. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_37

    Chapter  Google Scholar 

  13. Loshchilov, I., Schoenauer, M., Sebag, M.: Intensive surrogate model exploitation in self-adaptive surrogate-assisted CMA-ES. In: Genetic and Evolutionary Computation Conference – GECCO 2013, pp. 439–446. ACM Press (2013)

    Google Scholar 

  14. Pitra, Z., Bajer, L., Repický, J., Holena, M.: Overview of surrogate-model versions of covariance matrix adaptation evolution strategy. In: Genetic and Evolutionary Computation Conference Companion, pp. 1622–1629. ACM Press (2017)

    Google Scholar 

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

    Google Scholar 

  16. Schwefel, H.-P.: Numerical Optimization of Computer Models. Wiley, Hoboken (1981)

    MATH  Google Scholar 

  17. Teytaud, O., Gelly, S.: General lower bounds for evolutionary algorithms. In: Runarsson, T.P., Beyer, H.-G., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 21–31. Springer, Heidelberg (2006). https://doi.org/10.1007/11844297_3

    Chapter  Google Scholar 

  18. Ulmer, H., Streichert, F., Zell, A.: Model-assisted steady-state evolution strategies. In: Cantú-Paz, E. (ed.) GECCO 2003. LNCS, vol. 2723, pp. 610–621. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45105-6_72

    Chapter  Google Scholar 

Download references

Acknowledgements

This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Author information

Authors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada

    Arash Kayhani & Dirk V. Arnold

Authors
  1. Arash Kayhani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dirk V. Arnold
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dirk V. Arnold .

Editor information

Editors and Affiliations

  1. Inria Saclay, Palaiseau, France

    Anne Auger

  2. University of Coimbra, Coimbra, Portugal

    Carlos M. Fonseca

  3. University of Coimbra, Coimbra, Portugal

    Nuno Lourenço

  4. University of Coimbra, Coimbra, Portugal

    Penousal Machado

  5. University of Coimbra, Coimbra, Portugal

    Luís Paquete

  6. Colorado State University, Fort Collins, Colorado, USA

    Darrell Whitley

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kayhani, A., Arnold, D.V. (2018). Design of a Surrogate Model Assisted (1 + 1)-ES. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99253-2_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99252-5

  • Online ISBN: 978-3-319-99253-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation