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Triangular Gaussian mutation to differential evolution

  • Jinglei Guo
  • Yong WuEmail author
  • Wei Xie
  • Shouyong Jiang
Methodologies and Application
  • 31 Downloads

Abstract

Differential evolution (DE) has been a popular algorithm for its simple structure and few control parameters. However, there are some open issues in DE regrading its mutation strategies. An interesting one is how to balance the exploration and exploitation behaviour when performing mutation, and this has attracted a growing number of research interests over a decade. To address this issue, this paper presents a triangular Gaussian mutation strategy. This strategy utilizes the physical positions and the fitness differences of the vertices in the triangular structure. Based on this strategy, a triangular Gaussian mutation to DE and its improved version (ITGDE) are suggested. Empirical studies are carried out on the 20 benchmark functions and show that, in comparison with several state-of-the-art DE variants, ITGDE obtains significantly better or at least comparable results, suggesting the proposed mutation strategy is promising for DE.

Keywords

Differential evolution Gaussian distribution Triangular structure Global optimum 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (61501198), Wuhan Youth Science and Technology Chenguang program (2014072704011248), Natural Science Foundation of Hubei Province (2014CFB461).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Brest J, Greiner S, Bošković 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):646–657Google Scholar
  2. Brest J, Maučec MS (2009) Population size reduction for the differential evolution algorithm. Appl Intell 29(3):228–247Google Scholar
  3. Darwin C (2009) On the origin of the species by means of natural selection or the preservation of favoured races in the struggle for life. Penguin Classics, LondonGoogle Scholar
  4. Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evol Comput. 13(3):526–553Google Scholar
  5. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31Google Scholar
  6. Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution—an updated survey. Swarm Evol Comput 27(1):1–30Google Scholar
  7. Epitropakis MG, Tasoulis DK, Pavlidis NG, Vrahatis MN (2011) Enhancing differential evolution utilizing proximity-based mutation operators. IEEE Trans Evol Comput 15(1):99–119Google Scholar
  8. Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27(1):105–129MathSciNetzbMATHGoogle Scholar
  9. Gamperle R, Muller SD, Koumoutsakos P (2002), A parameter study for differential evolution. In: Proceedings of internationaal conference on advances in intelligent systems, fuzzy systems, evolutionary computation, pp 293–298Google Scholar
  10. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617–644zbMATHGoogle Scholar
  11. García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Inf Sci 180(10):2044–2064Google Scholar
  12. Ghosh A, Das S, Chowdhury A, Giri R (2011) An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Inf Sci 181(18):3749–3765MathSciNetGoogle Scholar
  13. Gong W, Cai Z (2013) Differential evolution with ranking-based mutation operators. IEEE Trans Cybern 43(6):2066–2081Google Scholar
  14. Guo SM, Yang CC, Hsu PH, Tsai JC (2014) Improving differential evolution with successful-parent-selecting framework. IEEE Trans Evol Comput 19(5):717–730Google Scholar
  15. Kennedy J (2003) Bare bones particle swarms. In: Proceedings of IEEE swarm intelligence symposium , pp 80–87Google Scholar
  16. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696Google Scholar
  17. Price K, Storn RM, Lampinen JA (2006) Differential evolution: a practical approach to global optimization. Springer, BerlinzbMATHGoogle Scholar
  18. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417Google Scholar
  19. Rahnamayan S, Tizhoosh HR, Salama M (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79Google Scholar
  20. Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces, vol 3. ICSI, BerkeleyzbMATHGoogle Scholar
  21. Tanabe R, Fukunaga AS (2013) Success-history based parameter adaptation for differential evolution. In: Proceedings of 2013 IEEE congress on evolutionary computation, pp 71–78Google Scholar
  22. Tanabe R, Fukunaga AS (2014) Improving the search performance of shade using linear population size reduction. In: Proceedings of 2014 IEEE congress on evolutionary computation, pp 1658–1665Google Scholar
  23. Wang H, Wu ZJ, Liu Y, Jiang DZ, Chen LL (2009) Space transformation search: a new evolutionary technique. In: Proceedings of 1st ACM/SIGEVO summit on genetic and evolutionary computation, pp 537–544Google Scholar
  24. Wang H, Rahnamayan S, Sun H, Omran MG (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43(2):634–647Google Scholar
  25. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66Google Scholar
  26. Wang Y, Cai ZX, Zhang Q (2012) Enhancing the search ability of differential evolution through orthogonal crossover. Inf Sci 185(1):153–177MathSciNetGoogle Scholar
  27. Wang Y, Liu ZZ, Li J, Li HX, Yen GG (2016) Utilizing cumulative population distribution information in differential evolution. Appl Soft Comput 48(1):329–346Google Scholar
  28. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102Google Scholar
  29. Yildiz AR (2013) A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations. Appl Soft Comput 13(3):1561–1566Google Scholar
  30. Yu WJ, Shen M, Chen WN, Zhan ZH, Gong YJ, Lin Y, Liu O, Zhang J (2014) Differential evolution with two-level parameter adaptation. IEEE Trans Cybern 44(7):1080–1099Google Scholar
  31. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer ScienceCentral China Normal UniversityWuhanChina
  2. 2.School of AutomationWuhan University of TechnologyWuhanChina
  3. 3.School of Computing ScienceUniversity of LincolnLincolnUK

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