Skip to main content
SpringerLink
Log in

Adaptive differential evolution with directional strategy and cloud model

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Recently, many studies have focused on differential evolution (DE), which is arguably one of the most powerful stochastic real-parameter optimization algorithms. Prominent variants of this approach largely optimize the DE algorithm; however, almost all the DE algorithms still suffer from problems like difficult parameter setting, slow convergence rate, and premature convergence. This paper presents a novel adaptive DE algorithm by constructing a trial vector generation pool, and dynamically setting control parameters according to current fitness information. The proposed algorithm adopts a distributed topology, which means the whole population is divided into three subgroups with different mutation and crossover operations used for each subgroup. However, a uniform selection strategy is employed. To improve convergence speed, a directional strategy is introduced based on the greedy strategy, which means that an individual with good performance can evolve rapidly in the optimal evolution direction. It is well known that the faster an algorithm converges, the greater the probability of premature convergence. Aimed at solving the local optimum problem, the proposed algorithm introduces a new mathematical tool in the selection process, called the membership cloud model. In essence, the cloud model improves the diversity of the population by randomly generating cloud droplets. Experimental results from executing typical benchmark functions show high quality performance of the proposed algorithm in terms of convergence, stability, and precision. They also indicate that this improved differential evolutionary algorithm can overcome the shortcoming of conventional differential evolutionary algorithms of low efficiency, while effectively avoiding falling into a local optimum.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Brest J, Mauec MS (2008) Population size reduction for the differential evolution algorithm. Appl Intell 29(3):228–247

    Article  Google Scholar 

  2. Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657

    Article  Google Scholar 

  3. Cai YQ, Wang JH (2013) Differential evolutionwith neighborhood and direction information for numerical optimization. IEEE Trans on Cybernetics 43(6):2202–2215

    Article  Google Scholar 

  4. Das S, Suganthan PN (2011) Differential evolution: A survey of the state-of-the-art. Evol Comput 15(1):4–31

    Article  Google Scholar 

  5. Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighborhood based mutation operator. IEEE Trans Evol Comput 13(3):526–553

    Article  Google Scholar 

  6. Ding JL, Liu J, Chowdhury KR, Zhang WS, Hu QP, Lei J (2014) A particle swarm optimization using local stochastic search and enhancing diversity for continuous optimization. Neurocomputing 137(0):261–267

    Article  Google Scholar 

  7. Dorronsoro B, Bouvry P (2011) Improving classical and decentralized differential evolution with new mutation operator and population topologies. IEEE Trans Evol Comput 15(1):67– 98

    Article  Google Scholar 

  8. Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141

    Article  Google Scholar 

  9. Gao XZ, Wang XL, Ovaska SJ (2009) Fusion of clonal selection algorithm and differential evolution method in training cascade-correlation neural network. Neurocomputing 72(10–12):2483–2490

    Article  Google Scholar 

  10. Gao Y (2009) An optimization algorithm based on cloud model. In: 2009 International Conference on Computational Intelligence and Security, pp 84–87

  11. Li DY, Du Y (2005) Artificial Intelligence with Uncertainty (in Chinese). National Defense Industry Press, Beijing

    Google Scholar 

  12. Li D Y, Liu C Y (2005) Study on the universality of the normal cloud model. Eng Sci 3(2):18–24

    Google Scholar 

  13. Li DY, Meng HJ, Shi XM (1995) Membership clouds and membership cloud generators (in chinese). Journal of Computer Research and Development 32(6):15–20

    Google Scholar 

  14. Li DY, Liu CY, Gan WY (2009) A new cognitive model: Cloud model. Int J Intell Syst 24(3):357–375

    Article  MATH  Google Scholar 

  15. Liang JJ, Qu BY, Suganthan PN, Hernández-Díaz AG (2013) Problem definitions and evaluation criteria for the cec 2013 special session on real-parameter optimization. Tech. rep., Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China

    Google Scholar 

  16. Liu G, Li YX, Nie X, Zheng H (2012) A novel clustering-based differential evolution with 2 multi-parent crossovers for global optimization. Appl Soft Comput 12(2):663–681

    Article  Google Scholar 

  17. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696

    Article  Google Scholar 

  18. Omran MGH, Salman A, Engelbrecht AP (2005) Self-adaptive differential evolution. Springer, Berlin Heidelberg, pp 192–199. chap International Conference, CIS 2005, Xian, China, December 15–19, 2005, Proceedings Part I

    Google Scholar 

  19. Pan QK, Suganthan PN, Ling W, Liang G, Mallipeddi R (2011) A differential evolution algorithm with self-adapting strategy and control parameters. Comput Oper Res 38(1):394–408

    Article  MATH  MathSciNet  Google Scholar 

  20. Price KV (1999) An introduction to differential evolution. In: Corne D, Dorigo M, Glover F (eds) New ideas in optimization. McGraw-Hill, Ltd., UK, pp 79–108

  21. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398– 417

    Article  Google Scholar 

  22. Storn R, Price K (1997) Differential evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MATH  MathSciNet  Google Scholar 

  23. Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the cec 2005 special session on real-parameter optimization. Nanyang Technological University, Tech. rep.

    Google Scholar 

  24. Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: Evolutionary Computation (CEC), 2013 IEEE Congress on, pp 71–78

  25. Vafashoar R, Meybodi MR, Azandaryani AHM (2012) Cla-de: a hybrid model based on cellular learning automata for numerical optimization. Appl Intell 36(3):735–748

    Article  Google Scholar 

  26. Varadarajan M, Swarup KS (2008) Differential evolutionary algorithm for optimal reactive power dispatch. Electrical Power and Energy Systems 30(8):435–441

    Article  Google Scholar 

  27. Wang X, Zhao SG (2013) Differential evolution algorithm with self-adaptive population resizing mechanism. Math Probl Eng 2013(2013):1–14

    Google Scholar 

  28. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66

    Article  MathSciNet  Google Scholar 

  29. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics Bulletin 1(6):80–83

    Article  Google Scholar 

  30. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102

    Article  Google Scholar 

  31. Yildiz AR (2013) Hybrid taguchi-differential evolution algorithm for optimization of multi-pass turning operations. Appl Soft Comput 13(3):1433–1439

    Article  Google Scholar 

  32. Zaharie D (2003) Control of population diversity and adaptation in differential evolution algorithms. In: Matousek R, Osmera P (eds) In: 2003 9th international conference on soft computing, pp 41–46

    Google Scholar 

  33. Zhan ZH, Zhang J, Li Y, Shi YH (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evol Comput 15(6):832–847

    Article  Google Scholar 

  34. Zhang JQ, Sanderson AC (2009) Jade: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Article  Google Scholar 

  35. Zhang JZ, Ding XM (2011) A multi-swarm self-adaptive and cooperative particle swarm optimization. Eng Appl Artif Intell 24(6):958–967

    Article  Google Scholar 

  36. Zhao SZ, Suganthan PN, Das S (2011) Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Comput 15(11):2175–2185

    Article  Google Scholar 

  37. Zhao ZQ, Gou J, Wang J (2010) Directional evolutionary algorithm based on fitness gradient of individuals (in chinese). Pattern Recognit Artif Intell 23(1):29–37

    Google Scholar 

  38. Zheng YJ, Ling HF, Xue JY (2014) Ecogeography-based optimization: Enhancing biogeography-based optimization with ecogeographic barriers and differentiations. Comput Oper Res 50(0):115–127

    Article  Google Scholar 

  39. Zhu CM, Ni J (2012). Cloud model-based differential evolution algorithm for optimization problems. In: 2012 Sixth International Conference on Internet Computing for Science and Engineering, pp 55–59

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61103170, 51305142, 61305085), the Program for Prominent Young Talent in Fujian Province University (No. JA12005), the Program for Prominent Young Talent in Fujian Province University (No. JA12005), and the Promotion Program for Young andMiddle-aged Teachers in Science and Technology Research at Huaqiao University (No. ZQN-PY211).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Huaqiao University, Xiamen, 361021, China

    Jin Gou, Wang-Ping Guo, Feng Hou, Cheng Wang & Yi-Qiao Cai

Authors
  1. Jin Gou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang-Ping Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yi-Qiao Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin Gou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gou, J., Guo, WP., Hou, F. et al. Adaptive differential evolution with directional strategy and cloud model. Appl Intell 42, 369–388 (2015). https://doi.org/10.1007/s10489-014-0592-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-014-0592-3

Keywords

Search

Navigation