Differential Evolution Algorithm: Foundations and Perspectives

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


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.


Differential Evolution Differential Evolution Algorithm Target Vector Trial Vector Donor Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Back, T., Fogel, D.B., Michalewicz, Z.: Handbook of Evolutionary Computation. IOP and Oxford University Press, Bristol (1997)Google Scholar
  2. 2.
    Fogel, D.B.: Evolutionary Computation. IEEE Press, Piscataway (1995)Google Scholar
  3. 3.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1992)zbMATHGoogle Scholar
  4. 4.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  5. 5.
    Goldberg, D.E.: Genetic algorithms in search. In: Optimization and Machine Learning. Addison-Wesley, Reading (1989)Google Scholar
  6. 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),
  7. 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)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)zbMATHGoogle Scholar
  9. 9.
    Avriel, M.: Nonlinear Programming: Analysis and Methods. Dover Publishing (2003)Google Scholar
  10. 10.
    Price, W.L.: Global optimization by controlled random search. Computer Journal 20(4), 367–370 (1977)zbMATHCrossRefGoogle Scholar
  11. 11.
    Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence through Simulated Evolution. John Wiley, Chichester (1966)zbMATHGoogle Scholar
  12. 12.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  13. 13.
    Price, K., Storn, R., Lampinen, J.: Differential Evolution - A Practical Approach to Global Optimization. Springer, Berlin (2005)zbMATHGoogle Scholar
  14. 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. 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. 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)CrossRefGoogle Scholar
  17. 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)zbMATHGoogle Scholar
  18. 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. 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. 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. 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. 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. 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. 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)CrossRefGoogle Scholar
  25. 25.
    Teo, J.: Exploring dynamic self-adaptive populations in differential evolution. Soft Computing - A Fusion of Foundations, Methodologies and Applications (2006)Google Scholar
  26. 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. 27.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1, 67 (1997)CrossRefGoogle Scholar
  28. 28.
    Fan, H.-Y., Lampinen, J.: A trigonometric mutation operation to differential evolution. International Journal of Global Optimization 27(1), 105–129 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Ashlock, D.: Evolutionary Computation for Modeling and Optimization. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  30. 30.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  31. 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)CrossRefGoogle Scholar
  32. 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. 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. 34.
    Tizhoosh, H.R.: Opposition-based reinforcement learning. Journal of Advanced Computational Intelligence and Intelligent Informatics 10(3) (2006)Google Scholar
  35. 35.
    Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation 12(1), 64–79 (2008)CrossRefGoogle Scholar
  36. 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. 37.
    Pampara, G., Engelbrecht, A.P., Franken, N.: Binary differential evolution. In: IEEE Congress on Evolutionary Computation. CEC 2006 (2006)Google Scholar
  38. 38.
    Proakis, J.G., Salehi, M.: Communication System Engineering, 2nd edn. Prentice Hall Publishers, Englewood Cliffs (2002)Google Scholar
  39. 39.
    Noman, N., Iba, H.: Accelerating Differential Evolution Using an Adaptive Local Search. IEEE Transactions on Evolutionary Computation 12(1), 107–125 (2008)CrossRefGoogle Scholar
  40. 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. 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. 42.
    Ong, Y.-S., Keane, A.J.: Meta-lamarckian learning in memetic algorithms. IEEE Transactions on Evolutionary Computation 8(2), 99–110 (2004)CrossRefGoogle Scholar
  43. 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.2008.927706Google Scholar
  44. 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. 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. 46.
    Mendes, R., Kennedy, J.: The fully informed particle swarm: simpler, maybe better. IEEE Transactions of Evolutionary Computation 8(3) (2004)Google Scholar
  47. 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. 48.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. Addison-Wesley, Reading (1983)zbMATHGoogle Scholar
  49. 49.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms, 1st edn. MIT Press and McGraw-Hill (1990)Google Scholar
  50. 50.
    Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation 3(2), 82–102 (1999)CrossRefGoogle Scholar
  51. 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. 52.
    Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Berlin (1999)Google Scholar
  53. 53.
    Flury, B.: A First Course in Multivariate Statistics, vol. 28. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  54. 54.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)Google Scholar
  55. 55.
    Passino, K.M.: Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Systems Magazine, 52–67 (2002)Google Scholar
  56. 56.
    Kirkpatrik, S., Gelatt, C., Vecchi, M.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  57. 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. 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. 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. 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

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