Skip to main content
Log in

\(\mu \)JADE: adaptive differential evolution with a small population

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript


This paper proposes a new differential evolution (DE) algorithm for unconstrained continuous optimisation problems, termed \(\mu \)JADE, that uses a small or ‘micro’ (\(\mu \)) population. The main contribution of the proposed DE is a new mutation operator, ‘current-by-rand-to-pbest.’ With a population size less than 10, \(\mu \)JADE is able to solve some classical multimodal benchmark problems of 30 and 100 dimensions as reliably as some state-of-the-art DE algorithms using conventionally sized populations. The algorithm also compares favourably to other small population DE variants and classical DE.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others


  • Brest J, Maučec M (2011) Self-adaptive differential evolution algorithm using population size reduction and three strategies. Soft Comput 15:2157–2174

    Article  Google Scholar 

  • Choi T, Ahn C (2014) An adaptive differential evolution algorithm with automatic population resizing for global numerical optimization. In: Pan L, Pǎun G, Pérez-Jiménez M, Song T (eds) Bio-Inspired Computing– Theories and Applications, Communications in Computer and Information Science, vol 472, Springer, pp 68–72

  • Das S, Suganthan P (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evolut Comput 15:4–31

    Article  Google Scholar 

  • Fajfar I, Puhan J, Tomažič S, Bűrmen A (2011) On selection in differential evolution. Elektrotehniški Vestnik 78:275–280

    Google Scholar 

  • Fajfar I, Tuma T, Puhan J, Olenšek J, Bűrmen A (2012) Towards smaller populations in differential evolution. J Microelectron Electron Compon Mater 42:152–163

    Google Scholar 

  • Gong W, Cai Z (2013) Differential evolution with ranking-based mutation operators. IEEE Trans Cybern 43:2066–2081

    Article  Google Scholar 

  • Gong W, Cai Z, Ling C (2011a) De/bbo: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput 15:645–665

    Article  Google Scholar 

  • Gong W, Cai Z, Ling C, Li H (2011b) Enhanced differential evolution with adaptive strategies for numerical optimization. IEEE Trans Syst Man Cybern Part B Cybern 41:397–413

    Article  Google Scholar 

  • Gong W, Cai Z, Wang Y (2014) Repairing the crossover rate in adaptive differential evolution. Appl Soft Comput 15:149–168

    Article  Google Scholar 

  • Kazimipour B, Li X, Qin A (2014) Effects of population initialization on differential evolution for large scale optimization. In: 2014 IEEE Congress on Evolutionary Computation, pp 2404–2411

  • Lampinen J, Zelinka I (2000) On stagnation of the differential evolution algorithm. In: 6th International Conference on Soft Computing MENDEL, pp 76–83

  • Mallipeddi R, Suganthan P (2008) Empirical study on the effect of population size on differential evolution algorithm. In: The 2008 IEEE Congress on Evolutionary Computation, pp 3663–3670

  • Mendes R, Mohais A (2005) DynDE: a differential evolution for dynamic optimization problems. In: The 2005 IEEE Congress on Evolutionary Computation, vol 3, pp 2808–2815

  • Mininno E, Neri F, Cupertino F, Naso D (2011) Compact differential evolution. IEEE Trans Evol Comput 15:32–54

    Article  Google Scholar 

  • Montgomery J, Chen S (2010) An analysis of the operation of differential evolution at high and low crossover rates. In: 2010 IEEE Congress on Evolutionary Computation, pp 1–8

  • Ren X, Chen Z, Ma Z (2010) Differential evolution using smaller population. In: 2010 Second International Conference on Machine Learning and Computing, pp 76–80

  • Ronkkonen J, Kukkonen S, Price K (2005) Real-parameter optimization with differential evolution. In: The 2005 IEEE Congress on Evolutionary Computation, vol 1, pp 506–513

  • Salehinejad H, Rahnamayan S, Tizhoosh H, Chen S (2014) Micro-differential evolution with vectorized random mutation factor. In: 2014 IEEE Congress on Evolutionary Computation, pp 2055–2062

  • Sharma H, Shrivastava P, Bansal J, Tiwari R (2014) Fitness based self adaptive differential evolution. In: Terrazas G, Otero F, Masagosa A (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2013), Studies in Computational Intelligence, vol 512, Springer, pp 71–84

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

    Article  MathSciNet  MATH  Google Scholar 

  • Teng N, Teo J, Hijazi M (2009) Self-adaptive population sizing for a tune-free differential evolution. Soft Comput 13:709–724

    Article  Google Scholar 

  • Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput 10:673–686

    Article  Google Scholar 

  • Wang X, Zhao S (2013) Differential evolution algorithm with self-adaptive population resizing mechanism. Math Probl Eng 419372

  • Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15:55–66

    Article  Google Scholar 

  • Yang M, Cai Z, Li C, Guan J (2013) An improved adaptive differential evolution algorithm with population adaptation. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, pp 145–152

  • Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102

    Article  Google Scholar 

  • Yu X, Huang D, Wang X, Jin Y (2008) DE-based neural network nonlinear model predictive control and its application for the pH neutralization reactor control. Chin Control Decis Conf 2008:1597–1602

    Google Scholar 

  • Zhang J, Sanderson A (2009a) Adaptive differential evolution: a robust approach to multimodal problem optimization adaptation learning and optimization. Springer, Berlin

    Book  Google Scholar 

  • Zhang J, Sanderson A (2009b) JADE: Adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 13:945–958

    Article  Google Scholar 

  • Zhao S, Wang X, Chen L, Zhu W (2014) A novel self-adaptive differential evolution algorithm with population size adjustment scheme. Arab J Science Eng 39:6149–6174

    Article  Google Scholar 

Download references


The authors would like to thank the anonymous reviewers for helping to improve this paper.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Yaochu Jin.

Additional information

Communicated by V. Loia.

This work was funded by Bosch Thermotechnology Ltd. and the Engineering and Physical Sciences Research Council (EPSRC) UK.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Brown, C., Jin, Y., Leach, M. et al. \(\mu \)JADE: adaptive differential evolution with a small population. Soft Comput 20, 4111–4120 (2016).

Download citation

  • Published:

  • Issue Date:

  • DOI: