Skip to main content

Reevaluating Exponential Crossover in Differential Evolution

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8672))

Abstract

Exponential crossover in Differential Evolution (DE), which is similar to 1-point crossover in genetic algorithms, continues to be used today as a default crossover operator for DE. We demonstrate that exponential crossover exploits an unnatural feature of some widely used synthetic benchmarks such as the Rosenbrock function – dependencies between adjacent variables. We show that for standard DE as well as state-of-the-art adaptive DE, exponential crossover performs quite poorly on benchmarks without this artificial feature. We also show that shuffled exponential crossover, which removes this kind of search bias, significantly outperforms exponential crossover.

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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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. Bouzarkouna, Z., Auger, A., Ding, D.Y.: Local-meta-model CMA-ES for partially separable functions. In: GECCO, pp. 869–876 (2011)

    Google Scholar 

  2. Brest, J., Greiner, S., Bošković, B., Mernik, M., Žumer, V.: Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems. IEEE Tran. Evol. Comput. 10(6), 646–657 (2006)

    Article  Google Scholar 

  3. Brest, J., Maučec, M.S.: Self-adaptive differential evolution algorithm using population size reduction and three strategies. Soft Comput. 15(11), 2157–2174 (2011)

    Article  Google Scholar 

  4. Caruana, R., Eshelman, L.J., Schaffer, J.D.: Representation and Hidden Bias II: Eliminating Defining Length Bias in Genetic Search via Shuffle Crossover. In: IJCAI, pp. 750–755 (1989)

    Google Scholar 

  5. Hansen, N.: GECCO BBOB (2014), http://coco.gforge.inria.fr/doku.php

  6. Hansen, N., Kern, S.: Evaluating the CMA Evolution Strategy on Multimodal Test Functions. In: Yao, X., et al. (eds.) PPSN VIII. LNCS, vol. 3242, pp. 282–291. Springer, Heidelberg (2004)

    Google Scholar 

  7. Herrera, F., Lozano, M., Molina, D.: Components and parameters of de, real-coded chc, and g-cmaes. Technical report, Univ. of Granada (2010)

    Google Scholar 

  8. Herrera, F., Lozano, M., Molina, D.: Test suite for the spec. iss. of Soft Computing on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems. Technical report, Univ. of Granada (2010)

    Google Scholar 

  9. LaTorre, A., Muelas, S., Peña, J.M.: A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: A scalability test. Soft Comput. 15(11), 2187–2199 (2011)

    Article  Google Scholar 

  10. Liang, J.J., Qu, B.Y., Suganthan, P.N.: Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization. Technical report, Zhengzhou Univ. and Nanyang Technological Univ. (2013)

    Google Scholar 

  11. Liang, J.J., Suganthan, P.N., Deb, K.: Novel Composition Test Functions for Numerical Global Optimization. In: Swarm Intell. Symp., pp. 68–75 (2005)

    Google Scholar 

  12. Lin, C., Qing, A., Feng, Q.: A comparative study of crossover in differential evolution. J. Heuristics 17(6), 675–703 (2011)

    Article  MATH  Google Scholar 

  13. Noman, N., Iba, H.: Accelerating Differential Evolution Using an Adaptive Local Search. IEEE Tran. Evol. Comput. 12(1), 107–125 (2008)

    Article  Google Scholar 

  14. Price, K.V., Storn, R.N., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer (2005)

    Google Scholar 

  15. Salomon, R.: Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms. BioSystems 39(3), 263–278 (1996)

    Article  Google Scholar 

  16. Storn, R., Price, K.: Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report, International Computer Science Institute, Berkeley, CA (1995)

    Google Scholar 

  17. Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.P., Auger, A., Tiwari, S.: Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Technical report, Nanyang Technological Univ. (2005)

    Google Scholar 

  18. Tanabe, R., Fukunaga, A.: Success-History Based Parameter Adaptation for Differential Evolution. In: IEEE CEC, pp. 71–78 (2013)

    Google Scholar 

  19. Tanabe, R., Fukunaga, A.: Supplemental material (2014), https://sites.google.com/site/tanaberyoji/home/ppsn2014-supplement.pdf

  20. Tang, K., Li, X., Suganthan, P.N., Yang, Z., Weise, T.: Benchmark Functions for the CEC 2010 Special Session and Competition on Large-Scale Global Optimization. Technical report, Univ. of Science and Technology of China (2010)

    Google Scholar 

  21. Whitley, D., Mathias, K., Rana, S., Dzubera, J.: Evaluating evolutionary algorithms. Artificial Intelligence 85, 245–276 (1996)

    Article  Google Scholar 

  22. Yao, X., Liu, Y., Lin, G.: Evolutionary Programming Made Faster. IEEE Tran. Evol. Comput. 3(2), 82–102 (1999)

    Article  Google Scholar 

  23. Zhang, J., Sanderson, A.C.: JADE: Adaptive Differential Evolution With Optional External Archive. IEEE Tran. Evol. Comput. 13(5), 945–958 (2009)

    Article  Google Scholar 

  24. Zhao, S., Suganthan, P.N.: Empirical investigations into the exponential crossover of differential evolutions. Swarm and Evol. Comput. 9, 27–36 (2013)

    Article  Google Scholar 

  25. Zhao, S., Suganthan, P.N., Das, S.: Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Comput. 15(11), 2175–2185 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Tanabe, R., Fukunaga, A. (2014). Reevaluating Exponential Crossover in Differential Evolution. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10762-2_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10761-5

  • Online ISBN: 978-3-319-10762-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics