Skip to main content

Differential Evolution Algorithm: Foundations and Perspectives

  • Chapter
Book cover Metaheuristic Clustering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 178))

Abstract

Differential Evolution (DE) has recently emerged as simple and efficient algorithm for global optimization over continuous spaces.DE shares many features of the classical Genetic Algorithms (GA). But it is much easier to implement than GA and applies a kind of differential mutation operator on parent chromosomes to generate the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world, resulting in a lot of variants of the basic algorithm, with improved performance. This chapter begins with a conceptual outline of classical DE and then presents several significant variants of the algorithm in greater details.

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 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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. Back, T., Fogel, D.B., Michalewicz, Z.: Handbook of Evolutionary Computation. IOP and Oxford University Press, Bristol (1997)

    Google Scholar 

  2. Fogel, D.B.: Evolutionary Computation. IEEE Press, Piscataway (1995)

    Google Scholar 

  3. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1992)

    MATH  Google Scholar 

  4. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  5. Goldberg, D.E.: Genetic algorithms in search. In: Optimization and Machine Learning. Addison-Wesley, Reading (1989)

    Google Scholar 

  6. Storn, R., Price, K.: Differential Evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012, ICSI (1995), http://http.icsi.berkeley.edu/~storn/litera.html

  7. Storn, R., Price, K.: Differential evolution – A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)

    MATH  Google Scholar 

  9. Avriel, M.: Nonlinear Programming: Analysis and Methods. Dover Publishing (2003)

    Google Scholar 

  10. Price, W.L.: Global optimization by controlled random search. Computer Journal 20(4), 367–370 (1977)

    Article  MATH  Google Scholar 

  11. Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence through Simulated Evolution. John Wiley, Chichester (1966)

    MATH  Google Scholar 

  12. Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  13. Price, K., Storn, R., Lampinen, J.: Differential Evolution - A Practical Approach to Global Optimization. Springer, Berlin (2005)

    MATH  Google Scholar 

  14. Price, K.V.: An introduction to differential evolution. In: Corne, D., Dorigo, M., Glover, V. (eds.) New Ideas in Optimization, pp. 79–108. Mc Graw-Hill, UK (1999)

    Google Scholar 

  15. Gamperle, R., Muller, S.D., Koumoutsakos, A.: Parameter study for differential evolution. In: WSEAS NNA-FSFS-EC 2002, Interlaken, Switzerland, Feburary 11-15 (2002)

    Google Scholar 

  16. Ronkkonen, J., Kukkonen, S., Price, K.V.: Real parameter optimization with differential evolution. In: The 2005 IEEE Congress on Evolutionary Computation (CEC 2005), vol. 1, pp. 506–513. IEEE Press, Los Alamitos (2005)

    Chapter  Google Scholar 

  17. Liu, J., Lampinen, J.: A Fuzzy adaptive differential evolution algorithm. Soft computing- A Fusion of Foundations, Methodologies and Applications 9(6), 448–462 (2005)

    MATH  Google Scholar 

  18. Qin, A.K., Suganthan, P.N.: Self-adaptive differential evolution algorithm for numerical optimization. In: IEEE Congress on Evolutionary Computation, pp. 1785–1791 (2005)

    Google Scholar 

  19. Zaharie, D.: Control of population diversity and adaptation in differential evolution algorithms. In: Matousek, D., Osmera, P. (eds.) Proc. of MENDEL 2003 9th International Conference on Soft Computing, Brno, Czech Republic, pp. 41–46 (June 2003)

    Google Scholar 

  20. Zaharie, D., Petcu, D.: Adaptive pareto differential evolution and its parallelization. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2004. LNCS, vol. 3019, pp. 261–268. Springer, Heidelberg (2004)

    Google Scholar 

  21. Abbass, H.: The Self-Adaptive pareto differential evolution algorithm., In: Proceedings of the 2002 Congress on Evolutionary Computation, pp. 831–836 (2002)

    Google Scholar 

  22. Beyer, H.G.: On the dynamics of EAs without selection. In: Banzaf, W., Reeves, C. (eds.) Foundations of genetic algorithms, pp. 5–26. Morgan Kaufmann, San Mateo (1999)

    Google Scholar 

  23. Zaharie, D.: Critical Values for the Control Parameters of Differential Evolution Algorithms. In: Matousek, R., Osmera, P. (eds.) Proc. of Mendel 2002, 8th International Conference on Soft Computing, Brno, Czech Republic, pp. 62–67 (2002)

    Google Scholar 

  24. Omran, M., Salman, A., Engelbrecht, A.P.: Self-adaptive differential evolution. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS, vol. 3801, pp. 192–199. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Teo, J.: Exploring dynamic self-adaptive populations in differential evolution. Soft Computing - A Fusion of Foundations, Methodologies and Applications (2006)

    Google Scholar 

  26. Das, S., Konar, A., Chakraborty, U.K.: Two improved differential evolution schemes for faster global search. In: ACM-SIGEVO Proceedings of GECCO, Washington D.C., pp. 991–998 (June 2005)

    Google Scholar 

  27. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1, 67 (1997)

    Article  Google Scholar 

  28. Fan, H.-Y., Lampinen, J.: A trigonometric mutation operation to differential evolution. International Journal of Global Optimization 27(1), 105–129 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  29. Ashlock, D.: Evolutionary Computation for Modeling and Optimization. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  30. Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  31. 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 

  32. Tizhoosh, H.R.: Opposition-Based Learning: A New Scheme for Machine Intelligence. In: Int. Conf. on Computational Intelligence for Modeling Control and Automation - CIMCA 2005, Vienna, Austria, vol. I, pp. 695–701 (2005)

    Google Scholar 

  33. Tizhoosh, H.R.: Reinforcement learning based on actions and opposite actions. In: ICGST International Conference on Artificial Intelligence and Machine Learning (AIML 2005), Cairo, Egypt (2005)

    Google Scholar 

  34. Tizhoosh, H.R.: Opposition-based reinforcement learning. Journal of Advanced Computational Intelligence and Intelligent Informatics 10(3) (2006)

    Google Scholar 

  35. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation 12(1), 64–79 (2008)

    Article  Google Scholar 

  36. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution for optimization of noisy problems. In: Proc. 2006 IEEE Congress on Evolutionary Computation (CEC 2006), Vancouver, pp. 1865–1872 (July 2006)

    Google Scholar 

  37. Pampara, G., Engelbrecht, A.P., Franken, N.: Binary differential evolution. In: IEEE Congress on Evolutionary Computation. CEC 2006 (2006)

    Google Scholar 

  38. Proakis, J.G., Salehi, M.: Communication System Engineering, 2nd edn. Prentice Hall Publishers, Englewood Cliffs (2002)

    Google Scholar 

  39. Noman, N., Iba, H.: Accelerating Differential Evolution Using an Adaptive Local Search. IEEE Transactions on Evolutionary Computation 12(1), 107–125 (2008)

    Article  Google Scholar 

  40. Tsutsui, S., Yamamura, M., Higuchi, T.: Multi-parent recombination with simplex crossover in real coded genetic algorithms. In: Proc. Genetic Evol. Comput. Conf (GECCO 1999), pp. 657–664 (July 1999)

    Google Scholar 

  41. 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 University, Singapore, and KanGAL Report #2005005, IIT Kanpur, India (May 2005)

    Google Scholar 

  42. Ong, Y.-S., Keane, A.J.: Meta-lamarckian learning in memetic algorithms. IEEE Transactions on Evolutionary Computation 8(2), 99–110 (2004)

    Article  Google Scholar 

  43. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transactions on Evolutionary Computations (2009), doi:10.1109/TEVC.2008.927706

    Google Scholar 

  44. Mezura-Montes, E., Velázquez-Reyes, J., Coello, C.A.C.: A comparative study of differential evolution variants for global optimization. In: Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 485–492 (2006)

    Google Scholar 

  45. Das, S., Abraham, A., Chakraborty, U.K., Konar, A.: Differential Evolution Using a Neighborhood based Mutation Operator. IEEE Transactions on Evolutionary Computation (accepted, 2008)

    Google Scholar 

  46. Mendes, R., Kennedy, J.: The fully informed particle swarm: simpler, maybe better. IEEE Transactions of Evolutionary Computation 8(3) (2004)

    Google Scholar 

  47. Zielinski, K., Peters, D., Laur, R.: Run time analysis regarding stopping criteria for differential evolution and particle swarm optimization. In: Proc. of the 1st International Conference on Experiments/Process/System Modelling/Simulation/Optimization, Athens, Greece (2005)

    Google Scholar 

  48. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. Addison-Wesley, Reading (1983)

    MATH  Google Scholar 

  49. Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms, 1st edn. MIT Press and McGraw-Hill (1990)

    Google Scholar 

  50. Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation 3(2), 82–102 (1999)

    Article  Google Scholar 

  51. Yang, Z., He, J., Yao, X.: Making a Difference to Differential Evolution. In: Michalewicz, Z., Siarry, P. (eds.) Advances in Metaheuristics for Hard Optimization, pp. 415–432. Springer, Heidelberg (2007)

    Google Scholar 

  52. Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Berlin (1999)

    Google Scholar 

  53. Flury, B.: A First Course in Multivariate Statistics, vol. 28. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  54. Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  55. Passino, K.M.: Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Systems Magazine, 52–67 (2002)

    Google Scholar 

  56. Kirkpatrik, S., Gelatt, C., Vecchi, M.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  57. Zhang, W.-J., Xie, X.-F.: DEPSO: Hybrid particle swarm with differential evolution operator. In: Proc. IEEE Int. Conf. Syst., Man, Cybern., pp. 3816–3821 (2003)

    Google Scholar 

  58. Das, S., Konar, A., Chakraborty, U.K.: Annealed Differential Evolution. In: IEEE Congress in Evolutionary Computation, CEC 2007. IEEE press, USA (2007)

    Google Scholar 

  59. Biswas, A., Dasgupta, S., Das, S., Abraham, A.: A Synergy of Differential Evolution and Bacterial Foraging Algorithm for Global Optimization. Neural Network World 17(6), 607–626 (2007)

    Google Scholar 

  60. Das, S., Konar, A., Chakraborty, U.K.: Improving particle swarm optimization with differentially perturbed velocity. In: Proc. Genetic Evol. Comput. Conf. (GECCO), pp. 177–184 (June 2005)

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Das, S., Abraham, A., Konar, A. (2009). Differential Evolution Algorithm: Foundations and Perspectives . In: Metaheuristic Clustering. Studies in Computational Intelligence, vol 178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93964-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-93964-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92172-1

  • Online ISBN: 978-3-540-93964-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics