Soft Computing

, Volume 21, Issue 8, pp 2105–2127 | Cite as

Differential Evolution with Grid-Based Parameter Adaptation

  • Vasileios A. Tatsis
  • Konstantinos E. Parsopoulos
Methodologies and Application


The reduction of human intervention in tuning metaheuristic optimization algorithms has been an ongoing research pursuit. Differential Evolution is a very popular algorithm that counts a large number of variants. However, its efficiency has been shown to depend on the type of its crossover operators (binomial or exponential), mutation operators, as well as on the two parameters that dominate these procedures. Making proper decisions on these parameters has proved to be a laborious, problem-dependent task. We propose a parameter adaptation technique that allows the algorithm to dynamically determine the most suitable crossover type and parameter values during its execution. The technique is based on a search procedure in the discretized parameter search space, using estimations of the algorithm’s performance. The proposed approach is tested and statistically validated on an established high-dimensional test suite. Also, comparisons with other algorithms are reported, verifying the competitiveness of the proposed approach.


Metaheuristic Optimization Dynamic Parameter Adaptation  Parameter Control Differential Evolution 


  1. Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 769–1776Google Scholar
  2. Bäck T (1996) Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, New YorkGoogle Scholar
  3. Brest J, Bošković B, Zamuda A (2012) Self-adaptive differential evolution algorithm with a small and varying population size. In: WCCI 2012 IEEE World congress on computational intelligenceGoogle Scholar
  4. Brest J, Greiner S, Bošković 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
  5. Brest J, Maucec MS (2011) Self-adaptive differential evolution algorithm using population size reduction and three strategies. Soft Comput 15:2157–2174CrossRefGoogle Scholar
  6. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31CrossRefGoogle Scholar
  7. de Oca MAM, Aydin D, Stützle T (2011) An incremental particle swarm for large-scale optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms. Soft Comput 15:2233–2255CrossRefGoogle Scholar
  8. Duarte A, Martí R, Gortazar F (2011) Path relinking for large scale global optimization. Soft Comput 15:2257–2273CrossRefGoogle 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 AE, Smit SK (2011) Evolutionary algorithm parameters and methods to tune them. In: Hamadi Y, Monfroy E, Saubion F (eds) Autonomous search, chap. 2. Springer, Berlin, pp 15–36Google Scholar
  11. Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. Found Genet Algorithms 2:187–202Google Scholar
  12. García-Martínez C, Rodríguez FJ, Lozano M (2011) Role differentiation and malleable mating for differential evolution: an analysis on large scale optimisation. Soft Comput 15:2109–2126CrossRefGoogle Scholar
  13. García-Nieto J, Alba E (2011) Restart particle swarm optimization with velocity modulation: a scalability test. Soft Comput 15:2221–2232CrossRefGoogle Scholar
  14. Gardeux V, Chelouah R, Siarry P, Glover F (2011) EM323: a line search based algorithm for solving high-dimensional continuous non-linear optimization problems. Soft Comput 15:2275–2285CrossRefGoogle Scholar
  15. Hoos HH (2011) Automated algorithm configuration and parameter tuning. In: Hamadi Y, Monfroy E, Saubion F (eds) Autonomous search, chap. 3. Springer, Berlin, pp 37–72Google Scholar
  16. LaTorre A, Muelas S, Peña J (2011) A MOS-based dynamic memetic differential evolution algorithm for continuous optimization a scalability test. Soft Comput 15:2187–2199CrossRefGoogle Scholar
  17. LaTorre A, Muelas S, Peña J (2012) Multiple offspring sampling in large scale global optimization. In: 2012 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–8Google Scholar
  18. Lozano M, Herrera F, Molina D (2010) Evolutionary algorithms and other metaheuristics for continuous optimization problems.
  19. Lozano M, Herrera F, Molina D (2011) Editorial scalability of evolutionary algorithms and other metaheuristics for large-scale continuous optimization problems. Soft Comput 15:2085–2087CrossRefGoogle Scholar
  20. Molina D, Lozano M, Sánchez AM, Herrera F (2011) Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains. Soft Comput 15:2201–2220CrossRefGoogle Scholar
  21. Neumaier A, Fendl H, Schilly H, Leitner T (2011) VXQR: derivative-free unconstrained optimization based on QR factorizations. Soft Comput 15:2287–2298CrossRefGoogle Scholar
  22. Parsopoulos K, Vrahatis M (2010) Particle swarm optimization and intelligence: advances and applications. Information Science Publishing (IGI Global)Google Scholar
  23. Piotrowski AP (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci 241:164–194CrossRefGoogle Scholar
  24. Poláková R, Tvrdík J, Bujok P (2014) Controlled restart in differential evolution applied to CEC2014 benchmark functions. In: IEEE congress on evolutionary computationGoogle Scholar
  25. Price K, Storn R (2009) Differential evolution (DE) for continuous function optimization (an algorithm by Kenneth Price and Rainer Storn).
  26. Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, BerlinMATHGoogle Scholar
  27. 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
  28. Qing A (2009) Differential evolution: fundamentals and applications in electrical engineering. Wiley-IEEE Press, New YorkGoogle Scholar
  29. Segura C, Coello CAC, Segredo E, León C (2015) On the adaptation of the mutation scale factor in differential evolution. Optim Lett 9(1):189–198MathSciNetCrossRefMATHGoogle Scholar
  30. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359MathSciNetCrossRefMATHGoogle Scholar
  31. Takahama T (1997) Sample source code of differential evolution (coded by T. Takahama).
  32. Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: IEEE congress on evolutionary computationGoogle Scholar
  33. Tanabe R, Fukunaga A (2014) Improving the search performance of SHADE using linear population size reduction. In: IEEE congress on evolutionary computationGoogle Scholar
  34. Tang K, Yao X, Suganthan PN, MacNish C, Chen YP, Chen CM, Yang Z (2007) Benchmark functions for the cec2008 special session and competition on large scale global optimization. Nature Inspired Computation and Applications Laboratory, USTC, China, pp 153–177Google Scholar
  35. Tvrdík J (2006) Competitive differential evolution. In: 12th international coference on soft computingGoogle Scholar
  36. Tvrdík J, Poláková R (2013) Competitive differential evolution applied to CEC 2013 problems. In: 2013 IEEE Congress on evolutionary computation (CEC). IEEE, pp 1651–1657Google Scholar
  37. Wang H, Wu Z, Rahnamayan S (2011) Enhanced opposition-based differential evolution for solving high-dimensional continuous optimization problems. Soft Comput 15:2127–2140CrossRefGoogle Scholar
  38. Weber M, Neri F, Tirronen V (2011) Shuffle or update parallel differential evolution for large scale optimization. Soft Comput 15:2089–2107CrossRefGoogle Scholar
  39. Weber M, Tirronen V, Neri F (2010) Scale factor inheritance mechanism in distributed differential evolution. Soft Comput 14:1187–1207CrossRefGoogle Scholar
  40. Yang Z, Tang K, Yao X (2011) Scalability of generalized adaptive differential evolution for large-scale continuous optimization. Soft Comput 15:2141–2155CrossRefGoogle Scholar
  41. Zaharie D (2007) A comparative analysis of crossover variants in differential evolution. In: Proceedings of IMCSIT, pp 171–181Google Scholar
  42. Zaharie D (2009) Influence of crossover on the behavior of differential evolution algorithms. Appl Soft Comput 9(3):1126–1138CrossRefGoogle Scholar
  43. Zaharie D, Petcu D (2005) Parallel implementation of multi-population differential evolution. In: Concurrent information processing and computing, pp 223–232Google Scholar
  44. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13:945–958CrossRefGoogle Scholar
  45. Zhao S, Suganthan P, Das S (2011) Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Comput 15(11):2175–2185CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Vasileios A. Tatsis
    • 1
  • Konstantinos E. Parsopoulos
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of IoanninaIoanninaGreece

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