Soft Computing

, Volume 15, Issue 11, pp 2109–2126 | Cite as

Role differentiation and malleable mating for differential evolution: an analysis on large-scale optimisation

  • Carlos García-MartínezEmail author
  • Francisco J. Rodríguez
  • Manuel Lozano


Differential Evolution is a simple yet powerful algorithm for continuous optimisation problems. Traditionally, its operators combine the information of randomly chosen vectors of the population. However, four different roles are clearly identified from their formulations: receiving, placing, leading, and correcting vectors. In this work, we propose two mechanisms that emphasise the proper selection of vectors for each role in crossover and mutation operations: (1) the role differentiation mechanism defines the attributes for which vectors are selected for each role; (2) malleable mating allows placing vectors to adapt their mating trends to ensure some similarity relations with the leading and correcting vectors. In addition, we propose a new differential evolution approach that combines these two mechanisms. We have performed experiments on a testbed composed of 19 benchmark functions and five dimensions, ranging from 50 variables to 1,000. Results show that both mechanisms allow differential evolution to statistically improve its results, and that our proposal becomes competitive with regard to representative methods for continuous optimisation.


Differential evolution Large-scale optimisation Real-parameter optimisation Role differentiation Malleable mating Mutation operation 



This work was supported by the Research Projects TIN2008-05854 and P08-TIC-4173.


  1. Abbass H (2002) The self-adaptive pareto differential evolution algorithm. In: Proceedings of the congress on evolutionary computation, pp 831–836Google Scholar
  2. Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: IEEE congress on evolutionary computation, pp 1769–1776Google Scholar
  3. Bäck T (1994) Selective pressure in evolutionary algorithms: a characterization of selection mechanisms. In: Michalewicz Z (ed) IEEE congress on evolutionary computation. IEEE Press, pp 57–62Google Scholar
  4. Bäck T, Fogel DB, Michalewicz Z (1997) Handbook of evolutionary computation. Institute of Physics PublishersGoogle Scholar
  5. Brest J, Greiner S, Boškovic B, Mernik M, Žumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657CrossRefGoogle Scholar
  6. Brest J, Zamuda A, Boškovic B, Maučec MS, Žumer V (2009) Dynamic optimization using self-adaptive differential evolution. In: Proceedings of the congress on evolutionary computation, pp 415–422Google Scholar
  7. Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighbourhood-based mutation operator. IEEE Trans Evol Comput 13(3):526–553CrossRefGoogle Scholar
  8. Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Springer, BerlinGoogle Scholar
  9. Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141CrossRefGoogle Scholar
  10. Eiben G, Schut MC (2008) New ways to calibrate evolutionary algorithms. In: Siarry P, Michalewicz Z (eds) Advances in metaheuristics for hard optimization. Springer, Berlin, pp 153–177Google Scholar
  11. Eshelman LJ (1991) The CHC adaptive search algorithm: how to have safe search when engaging in nontraditional genetic recombination, foundations of genetic algorithms, vol 1. Morgan Kaufmann, pp 265–283Google Scholar
  12. Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Whitley LD (ed) Foundations of genetic algorithms, vol 2. Morgan Kaufmann, pp 187–202Google Scholar
  13. Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Global Optim 27(1):105–129MathSciNetzbMATHCrossRefGoogle Scholar
  14. Fernandes C, Rosa A (2001) A study on non-random mating and varying population size in genetic algorithms using a royal road function. In: Proceedings of the congress on evolutionary computation. IEEE Press, pp 60–66Google Scholar
  15. Fernandes C, Rosa AC (2008) Self-adjusting the intensity of assortative mating in genetic algorithms. Soft Comput 12(10):955–979CrossRefGoogle Scholar
  16. Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32(200):675–701CrossRefGoogle Scholar
  17. Garcia S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617–644zbMATHCrossRefGoogle Scholar
  18. García-Martínez C, Lozano M, Herrera F, Molina D, Sánchez AM (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Oper Res 185(3):1088–1113zbMATHCrossRefGoogle Scholar
  19. Hansen N (2005) Compilation of results on the CEC benchmark function set. Technical report, Institute of Computational Science, ETH Zurich, SwitzerlandGoogle Scholar
  20. Herrera F, Lozano M, Molina D (2010a) Components and parameters of DE, real-coded CHC, and G-CMAES.
  21. Herrera F, Lozano M, Molina D (2010b) Test suite for the special issue of Soft Computing on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems.
  22. Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70MathSciNetzbMATHGoogle Scholar
  23. Iman RL, Davenport JM (1980) Approximations of the critical region of the Friedman statistic. Commun Stat Theor Meth A9(6):571–595Google Scholar
  24. Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680MathSciNetCrossRefGoogle Scholar
  25. Langdon WB, Poli R (2007) Evolving problems to learn about particle swarm optimizers and other search algorithms. IEEE Trans Evol Comput 11(5):561–578CrossRefGoogle Scholar
  26. Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462zbMATHCrossRefGoogle Scholar
  27. Lozano M, Herrera F (2009) Special issue of soft computing: a fusion of foundations, methodologies and applications on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems.
  28. Mezura-Montes E, Velázquez-Reyes J, Coello CA (2006) Modified differential evolution for constrained optimization. In: Proceedings of the congress on evolutionary computation, pp 332–339Google Scholar
  29. Neri F, Tirronen V (2009) Scale factor local search in differential evolution. Memetic Comput 1:153–171CrossRefGoogle Scholar
  30. Omran M, Salman A, Engelbrecht AP (2005) Self-adaptive differential evolution, computational intelligence and security. Lecture notes in artificial intelligence, vol 3801. Springer, Berlin, pp 192–199Google Scholar
  31. Price KV, Storn R, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, BerlinGoogle Scholar
  32. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417CrossRefGoogle Scholar
  33. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359MathSciNetzbMATHCrossRefGoogle Scholar
  34. Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput: Fusion Found, Methodologies Applicat 10(8):673–686Google Scholar
  35. Whitley D, Rana S, Dzubera J, Mathias E (1996) Evaluating evolutionary algorithms. Artif Intell 85:245–276CrossRefGoogle Scholar
  36. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80–83CrossRefGoogle Scholar
  37. Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999MathSciNetCrossRefGoogle Scholar
  38. Zaharie D, Petcu D (2004) Adaptive pareto differential evolution and its parallelization. In: Parallel processing and applied mathematics. Lecture notes in computer science, vol 3019, pp 261–268Google Scholar
  39. Zhang J, Sanderson AC (2009) JADE: Adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Carlos García-Martínez
    • 1
    Email author
  • Francisco J. Rodríguez
    • 2
  • Manuel Lozano
    • 2
  1. 1.Department of Computing and Numerical AnalysisUniversity of CórdobaCórdobaSpain
  2. 2.Department of Computer Science and Artificial Intelligence (CITIC-UGR)University of GranadaGranadaSpain

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