Skip to main content
SpringerLink
Log in

Population size reduction for the differential evolution algorithm

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper studies the efficiency of a recently defined population-based direct global optimization method called Differential Evolution with self-adaptive control parameters. The original version uses fixed population size but a method for gradually reducing population size is proposed in this paper. It improves the efficiency and robustness of the algorithm and can be applied to any variant of a Differential Evolution algorithm. The proposed modification is tested on commonly used benchmark problems for unconstrained optimization and compared with other optimization methods such as Evolutionary Algorithms and Evolution Strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ali MM, Törn A (2004) Population set-based global optimization algorithms: some modifications and numerical studies. Comput Oper Res 31(10):1703–1725

    Article  MATH  MathSciNet  Google Scholar 

  2. Bäck T (2002) Adaptive business intelligence based on evolution strategies: some application examples of self-adaptive software. Inf Sci 148:113–121

    Article  MATH  Google Scholar 

  3. Bäck T, Fogel DB, Michalewicz Z (eds) (1997) Handbook of evolutionary computation. Institute of Physics Publishing and Oxford University Press, Oxford

    MATH  Google Scholar 

  4. Bäck T (1996) Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, New York

    MATH  Google Scholar 

  5. Brest J, Bošković B, Greiner S, Žumer V, Sepesy Maučec M (2007) Performance comparison of self-adaptive and adaptive differential evolution algorithms. Soft Comput—Fusion Found Methodol Appl 11(7):617–629. DOI: 10.1007/s00500-006-0124-0

    MATH  Google Scholar 

  6. 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):646–657. DOI: 10.1109/TEVC.2006.87213

    Article  Google Scholar 

  7. Brest J, Žumer V, Sepesy Maučec M (2006) Self-adaptive differential evolution algorithm in constrained real-parameter optimization. In: The 2006 IEEE congress on evolutionary computation CEC2006. IEEE Press, pp 919–926

  8. Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Natural computing. Springer, Berlin

    Google Scholar 

  9. Eiben AE, Marchiori E, Valko VA (2004) Evolutionary algorithms with on-the-fly population size adjustment. In: Proceedings of the 8th international conference on parallel problem solving from nature. Lecture Notes in Computer Science, vol 3242. Springer, New York, pp 41–50

    Google Scholar 

  10. Fan H-Y, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Global Optim 27(1):105–129

    Article  MATH  MathSciNet  Google Scholar 

  11. Feoktistov V (2006) Differential evolution: in search of solutions. Springer, New York

    MATH  Google Scholar 

  12. Fernandes C, Rosa A (2006) Self-regulated population size in evolutionary algorithms. In: Proceedings of the 9th international conference on parallel problem solving from nature. Lecture notes in computer science, vol 4193. Springer, New York

    Chapter  Google Scholar 

  13. Goldberg DE, Deb K, Clark JH (1992) Genetic algorithms, noise, and the sizing of populations. Complex Syst 6:333–362

    MATH  Google Scholar 

  14. Jansen T, De Jong KA, Wegener I (2005) On the choice of the offspring population size in evolutionary algorithms. Evol Comput 13(4):413–440

    Article  Google Scholar 

  15. Jiao Y-C, Dang C, Leung Y, Hao Y (2006) A modification to the new version of the price’s algorithm for continuous global optimization problems. J Global Optim 36(4):609–626. DOI: 10.1007/s10898-006-9030-3

    Article  MATH  MathSciNet  Google Scholar 

  16. Lee CY, Yao X (2004) Evolutionary programming using mutations based on the Lévy probability distribution. IEEE Trans Evol Comput 8(1):1–13

    Article  Google Scholar 

  17. Liang K-H, Yao X, Newton CS (2001) Adapting self-adaptive parameters in evolutionary algorithms. Appl Intell 15(3):171–180

    Article  MATH  Google Scholar 

  18. Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput—Fusion Found Methodol Appl 9(6):448–462

    MATH  Google Scholar 

  19. Lobo FG, Lima CF (2005) A review of adaptive population sizing schemes in genetic algorithms. In: Proceedings of the 2005 workshops on genetic and evolutionary computation, genetic and evolutionary computation conference. ACM Press, pp 228–234

  20. Mezura-Montes E, Velázquez-Reyes J, Coello Coello CA (2006) A comparative study of differential evolution variants for global optimization. In: GECCO, pp 485–492

  21. Ohkura K, Matsumura Y, Ueda K (2001) Robust evolution strategies. Appl Intell 15(3):153–169

    Article  MATH  Google Scholar 

  22. Price KV, Storn RM, Lampinen JA (2005) Differential evolution. A practical approach to global optimization. Springer, New York

    MATH  Google Scholar 

  23. Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: The 2005 IEEE congress on evolutionary computation CEC2005, September 2005, vol 2. IEEE Press, pp 1785–1791. DOI: 10.1109/CEC.2005.1554904

  24. Rönkkönen J, Kukkonen S, Price KV (2005) Real-parameter optimization with differential evolution. In: The 2005 IEEE congress on evolutionary computation CEC2005, September 2005, vol 1. IEEE Press, pp 506–513

  25. Shang Y-W, Qiu Y-H (2006) A note on the extended rosenbrock function. Evol Comput 14(1):119–126. DOI: 10.1162/106365606776022733

    Article  Google Scholar 

  26. Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report TR-95-012, Berkeley

  27. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359

    Article  MATH  MathSciNet  Google Scholar 

  28. Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput—Fusion Found Methodol Appl 10(8):673–686. DOI: 10.1007/s00500-005-0537-1

    Google Scholar 

  29. Tvrdík J (2006) Competitive differential evolution. In: MENDEL’06, 12th international conference on soft computing, pp 7–12

  30. Yao X, Liu Y, Lin G (July 1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering and Computer Science, University of Maribor, Maribor, Slovenia

    Janez Brest & Mirjam Sepesy Maučec

Authors
  1. Janez Brest
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mirjam Sepesy Maučec
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Janez Brest.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brest, J., Sepesy Maučec, M. Population size reduction for the differential evolution algorithm. Appl Intell 29, 228–247 (2008). https://doi.org/10.1007/s10489-007-0091-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-007-0091-x

Keywords

Search

Navigation