Skip to main content
SpringerLink
Log in

A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

The differential evolution (DE) algorithm is a notably powerful evolutionary algorithm that has been applied in many areas. Therefore, the question of how to improve the algorithm’s performance has attracted considerable attention from researchers. The mutation operator largely impacts the performance of the DE algorithm The control parameters also have a significant influence on the performance. However, it is not an easy task to set a suitable control parameter for DE. One good method is to considering the mutation operator and control parameters simultaneously. Thus, this paper proposes a new DE algorithm with a hybrid mutation operator and self-adapting control parameters. To enhance the searching ability of the DE algorithm, the proposed method categorizes the population into two parts to process different types of mutation operators and self-adapting control parameters embedded in the proposed algorithm framework. Two famous benchmark sets (including 46 functions) are used to evaluate the performance of the proposed algorithm and comparisons with various other DE variants previously reported in the literature have also been conducted. Experimental results and statistical analysis indicate that the proposed algorithm has good performance on these functions.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(3):341–359

    Article  MATH  MathSciNet  Google Scholar 

  2. Onwubolu G, Davendra D (2006) Scheduling flow shops using differential evolution algorithm. Eur J Oper Res 171(2):674– 692

    Article  MATH  Google Scholar 

  3. Yildiz AR (2013) A new hybrid differential evolution algorithm for the selection optimal machining parameters in milling operations. Appl Soft Comput 13(3):1561–1566

    Article  Google Scholar 

  4. Storn R (1999) System design by constraint adaption and differential evolution. IEEE Trans Evol Comput 3(1):22–34

    Article  Google Scholar 

  5. Vafashoar R, Meybodi MR, Momeni Azandaryani AH (2012) CLA-DE: a hybrid model based on cellular learning automata for numerical optimization. Appl Intell 36(3):735–745

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

    Article  Google Scholar 

  7. Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1–2):61–106

    Article  Google Scholar 

  8. Islam SM, Das S, Ghosh S, Subhrajit Roy (2012) An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Trans Syst Man Cybern Part B: Cybern 42(2):482–500

    Article  Google Scholar 

  9. Ali MM (2011) Differential evolution with generalized differentials. J Comput Appl Math 235(80):2205–2216

    Article  MATH  MathSciNet  Google Scholar 

  10. Thangaraj R., Pant M., Abraham A. (2010) New mutation schemes for differential evolution algorithm and their application to the optimization of directional over-current relay settings. Appl Math Comput 216(5):532–544

    Article  MATH  MathSciNet  Google Scholar 

  11. Han MF, Liao SH, Chang JY, Lin CT (2013) Dynamic group-based differential evolution using a self-adaptive strategy for global optimization problems. Appl Intell 39(5):41–56

    Article  Google Scholar 

  12. Brest J., Greiner S., Boskovic B., Zemer V. (2006) Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(5):646–657

    Article  Google Scholar 

  13. Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(5):448–462

    Article  MATH  Google Scholar 

  14. Neri F, Tirronen V (2009) Scale factor local search in differential evolution. Memetic Comput 1(2):153–171

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Zhou Y, Li X, Gao L (2013) A differential evolution algorithm with intersect mutation operator. Appl Soft Comput 13(2):390–401

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. 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 

  19. Rahnamayan S, Tizhoosh HR, Salama MMA (2009) Opposition-based differential evolution. IEEE Trans Evol Comput 13(3):398–417

    Google Scholar 

  20. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(20):1679–1696

    Article  Google Scholar 

  21. Gamperle R, Muler S, Koumoutsakos P. (2002) A parameter study for differential evolution. In: Proc. WSEAS Int. Conf. Advances Intell Syst. Fussy Syst. Evol. Comput.

  22. Pan Quanke, Suganthan PN, Wang Ling, Gao Liang, Mallipeddi R (2011) A differential evolution algorithm with self-adaptive strategy and control parameters. Comput Oper Res 38(1):394– 408

    Article  MATH  MathSciNet  Google Scholar 

  23. Epitropakis MG, Tasoulis DK, Pavlidis NG., Vassilis PP, Vrahatis MN (2011) Enhancing differential evolution utilizing proximity-based mutation operators. IEEE Trans Evol Comput 15(1):99–119

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  25. Civicioglu P (2012) Transforming geocentric Cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput Geosci 46:229–247

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005 ) Problem definitions and evaluation criteria for CEC 2005 special session on real-parameter optimization, Nanyang Technol. Uni., Singapore. http://www.ntu.edu.sg/home/EPNSugan

Download references

Acknowledgments

This research work is supported by the National Basic Research Program of China (973 Program) under Grant no. 2011CB706804 and the Natural Science Foundation of China (NSFC) under Grant nos. 51375004 and 51435009.

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Author information

Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology, Wuhan, 430074, Peoples’s Republic of China

    Wenchao Yi, Liang Gao, Xinyu Li & Yinzhi Zhou

Authors
  1. Wenchao Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yinzhi Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinyu Li.

Appendices

Appendix A: Benchmark set 1

Table 7 The first twelve benchmark functions for benchmark set 2
Full size table

Appendix B: Benchmark set 2

The last thirteen benchmark functions in benchmark set 2 are hybrid composite functions, which consist of up to ten sub-functions. In the following, only the first twelve benchmark functions are listed. For more details on this benchmark set, please refer to Suganthan et al. [27]

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yi, W., Gao, L., Li, X. et al. A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems. Appl Intell 42, 642–660 (2015). https://doi.org/10.1007/s10489-014-0620-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-014-0620-3

Keywords

Search

Navigation