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Differential Evolution

  • Chapter
Handbook of Optimization

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 38))

Abstract

After an introduction that includes a discussion of the classic random walk, this paper presents a step-by-step development of the differential evolution (DE) global numerical optimization algorithm. Five fundamental DE strategies, each more complex than the last, are evaluated based on their conformance to invariance and symmetry principles, degree of control parameter dependence, computational efficiency and response to randomization. Optimal control parameter settings for the family of convex, quadratic functions are empirically derived.

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References

  1. Storn, R., Price, K.V.: Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Price, K.V., Storn, R.: Differential evolution. Dr. Dobb’s Journal 264, 18–24 (1997)

    Google Scholar 

  3. Price, K.V., Storn, R., Lampinen, J.: Differential Evolution – A Practical Approach to Global Optimization. Springer, Heidelberg (2001)

    Google Scholar 

  4. Storn, R.: Differential evolution web site, http://www.icsi.berkeley.edu/~storn

  5. Qing, A.: Differential Evolution: Fundamentals and Applications in Electrical Engineering. John Wiley and Sons, Singapore (2009)

    Google Scholar 

  6. Feoktistov, V.: Differential evolution. In: Search of Solutions. Springer Science + Business Media, LLC (2006)

    Google Scholar 

  7. Zhang, J., Sanderson, A.: Adaptive Differential Evolution: A Robust Approach to Multimodal Problem Optimization. Springer, Heidelberg (2009)

    Google Scholar 

  8. Price, K.V., et al.: Differential evolution, Part Two. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 79–158. McGraw-Hill, Berkshire (1999)

    Google Scholar 

  9. Das, S., Suganthan, P.N., Coello Coello, C.A.: Special issue on differential evolution. IEEE Transactions on Evolutionary Computation 15(1) (2011)

    Google Scholar 

  10. Rönkkönen, J.: Continuous multimodal global optimization with differential evolution-based methods. Doctoral Thesis, Lappeenranta University of Technology, Lappeenranta, Finland (2009)

    Google Scholar 

  11. Onwubolu, G., Davendra, D.: Differential Evolution: A Handbook for Global Permutation-based Combinatorial Optimization. Springer, Heidelberg (2009)

    Book  MATH  Google Scholar 

  12. Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man and Cybernetics: Part B 26(1), 29–41 (1996)

    Article  Google Scholar 

  13. Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)

    Google Scholar 

  14. Dasgupta, D., Attoh-Okine, N.: Immunity-based systems: a survey. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Orlando, Florida, October 12-15, vol. 1, pp. 369–374 (1997)

    Google Scholar 

  15. Eberhart, R.C., Shi, Y.: Special issue on particle swarm optimization. IEEE Transactions on Evolutionary Computation 8(3) (2004)

    Google Scholar 

  16. Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Transactions on Evolutionary Computation 15(1), 4–31 (2011)

    Article  Google Scholar 

  17. Neri, F., Tirronen, V.: Recent advances in differential evolution: a survey and experimental analysis. Artif. Intell. Rev. 33(1-2), 61–106 (2010)

    Article  Google Scholar 

  18. Zeilinski, K., Laur, R.: Stopping criteria for differential evolution in constrained single-objective optimization. In: Chakraborty, U. (ed.) Advances in Differential Evolution, pp. 111–138. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Wang, H., Rahnamayan, S., Wu, Z.: Adaptive differential evolution with variable population size for solving high dimensional problems. In: Proceedings of the 2011 IEEE Congress on Evolutionary Computation, New Orleans, June 5-8, pp. 2626–2632 (2011)

    Google Scholar 

  20. Zhang, C., Chen, J., Xin, B., Cai, T., Chen, C.: Differential evolution with adaptive population size combining lifetime and extinction mechanisms. In: Proceedings of the Eight Asian Control Conference, Kaohsiung, May 15-18, pp. 1221–1226 (2011)

    Google Scholar 

  21. Salomon, R.: Reevaluating 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 

  22. Price, K.V.: Eliminating drift bias from the differential evolution algorithm. In: Chakraborty, U. (ed.) Advances in Differential Evolution, pp. 33–88. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Lampinen, J., Zelinka, I.: On stagnation of the differential evolution algorithm. In: Proceedings of the Sixth International Mendel Conference on Soft Computing, pp. 76–83 (2000)

    Google Scholar 

  24. Abbass, H.: The self-adaptive Pareto differential evolution algorithm. In: Proceedings of the Congress on Evolutionary Computation, vol. 1, pp. 831–836 (2002)

    Google Scholar 

  25. Thangraj, R., Pant, M., Abraham, A., Deep, K.: Differential evolution using a localized Cauchy mutation operator. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Istanbul, October 10-13, pp. 3710–3716 (2010)

    Google Scholar 

  26. Fu, X., Yu, J.: A hybrid algorithm based on extremal optimization with adaptive Levy mutation and differential evolution and application. In: Proceedings of the Fifth International Conference on Natural Computation, Tianjian, China, August 14-16, vol. 1, pp. 12–16 (2009)

    Google Scholar 

  27. Pant, M., Thangaraj, R., Abraham, A., Grosan, C.: Differential evolution with Laplace mutation operator. In: Proceedings of the 2009 IEEE Congress on Evolutionary Computation, Trondheim, May 18-21, pp. 2841–2849 (2009)

    Google Scholar 

  28. Liu, G., Li, Y., Nie, X., Sun, Y.: Improving clustering-based differential evolution with chaotic sequences and new mutation operator. International Journal of Advancements in Computing Technology 3(6), 276–286 (2011)

    Article  Google Scholar 

  29. Price, K.V., Rönkkönen, J.: Comparing the unimodal scaling performance of global and local selection in a mutation-only algorithm. In: Proceedings of the 2006 World Congress on Computational; Intelligence, Vancouver, July 16-21, pp. 7387–7394 (2006)

    Google Scholar 

  30. Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive models for the breeder genetic algorithm I. Evolutionary Computation 1(1), 25–50 (1993)

    Article  Google Scholar 

  31. Zhang, J., Sanderson, A.C.: JADE: adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation 13(5), 945–958 (2009)

    Article  Google Scholar 

  32. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transaction on Evolutionary Computation 13(2), 398–417 (2009)

    Article  Google Scholar 

  33. 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 Transactions on Evolutionary Computation 10(6), 646–657 (2006)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Pacific Bell, Vacaville, U.S.A.

    Kenneth V. Price

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  1. Kenneth V. Price
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Correspondence to Kenneth V. Price .

Editor information

Editors and Affiliations

  1. Technical University of Ostrava, 17. listopadu 15, Ostrava-Porub, 708 33, Czech Republic

    Ivan Zelinka

  2. , Faculty of Electrical Engineering and, Technical University of Ostrava, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Václav Snášel

  3. Auburn, 98071, USA

    Ajith Abraham

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Price, K.V. (2013). Differential Evolution. In: Zelinka, I., Snášel, V., Abraham, A. (eds) Handbook of Optimization. Intelligent Systems Reference Library, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30504-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-30504-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30503-0

  • Online ISBN: 978-3-642-30504-7

  • eBook Packages: EngineeringEngineering (R0)

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