Skip to main content

Dynamic Multi-Armed Bandits and Extreme Value-Based Rewards for Adaptive Operator Selection in Evolutionary Algorithms

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5851))

Abstract

The performance of many efficient algorithms critically depends on the tuning of their parameters, which on turn depends on the problem at hand. For example, the performance of Evolutionary Algorithms critically depends on the judicious setting of the operator rates. The Adaptive Operator Selection (AOS) heuristic that is proposed here rewards each operator based on the extreme value of the fitness improvement lately incurred by this operator, and uses a Multi-Armed Bandit (MAB) selection process based on those rewards to choose which operator to apply next. This Extreme-based Multi-Armed Bandit approach is experimentally validated against the Average-based MAB method, and is shown to outperform previously published methods, whether using a classical Average-based rewarding technique or the same Extreme-based mechanism. The validation test suite includes the easy One-Max problem and a family of hard problems known as “Long k-paths”.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Grefenstette, J.: Optimization of control parameters for genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics 16(1), 122–128 (1986)

    Article  Google Scholar 

  2. Lobo, F., Lima, C., Michalewicz, Z. (eds.): Parameter Setting in Evolutionary Algorithms. Studies in Computational Intelligence, vol. 54. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  3. Davis, L.: Adapting operator probabilities in genetic algorithms. In: Schaffer, J.D. (ed.) Proc. ICGA 1989, pp. 61–69. Morgan Kaufmann, San Francisco (1989)

    Google Scholar 

  4. Da Costa, L., Fialho, A., Schoenauer, M., Sebag, M.: Adaptive operator selection with dynamic multi-armed bandits. In: Keijzer, M. (ed.) Proc. GECCO 2008, pp. 913–920. ACM Press, New York (2008)

    Chapter  Google Scholar 

  5. Fialho, A., Da Costa, L., Schoenauer, M., Sebag, M.: Extreme value based adaptive operator selection. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 175–184. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Machine Learning 47(2-3), 235–256 (2002)

    Article  MATH  Google Scholar 

  7. Hinkley, D.: Inference about the change point from cumulative sum-tests. Biometrika 58(3), 509–523 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  8. Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovac (1997)

    Google Scholar 

  9. Eiben, A.E., Hinterding, R., Michalewicz, Z.: Parameter control in Evolutionary Algorithms. IEEE Transactions on Evolutionary Computation 3(2), 124–141 (1999)

    Article  Google Scholar 

  10. Eiben, A.E., Michalewicz, Z., Schoenauer, M., Smith, J.E.: Parameter control in Evolutionary Algorithms. In: Lobo, F.G., et al. (eds.) Parameter Setting in Evolutionary Algorithms, pp. 19–46. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Birattari, M., Stützle, T., Paquete, L., Varrentrapp, K.: A racing algorithm for configuring metaheuristics. In: Langdon, W.B., et al. (eds.) Proc. GECCO 2002, pp. 11–18. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  12. Yuan, B., Gallagher, M.: Statistical racing techniques for improved empirical evaluation of evolutionary algorithms. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 172–181. Springer, Heidelberg (2004)

    Google Scholar 

  13. Bartz-Beielstein, T., Lasarczyk, C., Preuss, M.: Sequential parameter optimization. In: McKay, B. (ed.) Proc. CEC 2005, pp. 773–780. IEEE Press, Los Alamitos (2005)

    Google Scholar 

  14. Nannen, V., Eiben, A.E.: Relevance estimation and value calibration of evolutionary algorithm parameters. In: Veloso, M. (ed.) Proc. IJCAI 2007, pp. 975–980 (2007)

    Google Scholar 

  15. De Jong, K.: Parameter Setting in EAs: a 30 Year Perspective. In: Lobo, F.G., et al. (eds.) Parameter Setting in Evolutionary Algorithms, pp. 1–18. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Lobo, F., Goldberg, D.: Decision making in a hybrid genetic algorithm. In: Porto, B. (ed.) Proc. ICEC 1997, pp. 121–125. IEEE Press, Los Alamitos (1997)

    Google Scholar 

  17. Tuson, A., Ross, P.: Adapting operator settings in genetic algorithms. Evolutionary Computation 6(2), 161–184 (1998)

    Article  Google Scholar 

  18. Barbosa, H.J.C., Sá, A.M.: On adaptive operator probabilities in real coded genetic algorithms. In: Workshop on Advances and Trends in AI for Problem Solving – SCCC 2000 (2000)

    Google Scholar 

  19. Julstrom, B.A.: What have you done for me lately? Adapting operator probabilities in a steady-state genetic algorithm on genetic algorithms. In: Eshelman, L.J. (ed.) Proc. ICGA 1995, pp. 81–87. Morgan Kaufmann, San Francisco (1995)

    Google Scholar 

  20. Maturana, J., Saubion, F.: A compass to guide genetic algorithms. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 256–265. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Whitacre, J.M., Pham, T.Q., Sarker, R.A.: Use of statistical outlier detection method in adaptive evolutionary algorithms. In: Keijzer, M. (ed.) Proc. GECCO 2006, pp. 1345–1352. ACM Press, New York (2006)

    Chapter  Google Scholar 

  22. Goldberg, D.E.: Probability matching, the magnitude of reinforcement, and classifier system bidding. Machine Learning 5(4), 407–425 (1990)

    Google Scholar 

  23. Thierens, D.: An adaptive pursuit strategy for allocating operator probabilities. In: Beyer, H.G. (ed.) Proc. GECCO 2005, pp. 1539–1546. ACM Press, New York (2005)

    Chapter  Google Scholar 

  24. Wong, Y.Y., Lee, K.H., Leung, K.S., Ho, C.W.: A novel approach in parameter adaptation and diversity maintenance for genetic algorithms. Soft Computing 7(8), 506–515 (2003)

    Google Scholar 

  25. Lai, T., Robbins, H.: Asymptotically efficient adaptive allocation rules. Advances in Applied Mathematics 6(1), 4–22 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  26. Horn, J., Goldberg, D.E., Deb, K.: Long path problems. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 149–158. Springer, Heidelberg (1994)

    Google Scholar 

  27. Garnier, J., Kallel, L.: Statistical distribution of the convergence time of evolutionary algorithms for long-path problems. IEEE Transactions on Evolutionary Computation 4(1), 16–30 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fialho, Á., Da Costa, L., Schoenauer, M., Sebag, M. (2009). Dynamic Multi-Armed Bandits and Extreme Value-Based Rewards for Adaptive Operator Selection in Evolutionary Algorithms. In: Stützle, T. (eds) Learning and Intelligent Optimization. LION 2009. Lecture Notes in Computer Science, vol 5851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11169-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11169-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11168-6

  • Online ISBN: 978-3-642-11169-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics