Skip to main content
Log in

A new hybrid differential evolution algorithm with self-adaptation for function optimization

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this study, a new hybrid algorithm, hDEBSA, is proposed with the aid of two evolutionary algorithms, Differential Evolution (DE) and Backtracking Search Optimization Algorithm (BSA). The control parameters of both algorithms are simultaneously considered as a self-adaptation basis such that the values of the parameters update automatically during the optimization process to improve performance and convergence speed. To validate the proposed algorithm, twenty-eight CEC2013 test functions are considered. The performance results of hDEBSA are validated by comparing them with several state-of-the-art algorithms that are available in literature. Finally, hDEBSA is applied to solve four real-world optimization problems, and the results are compared with the other algorithms, where it was found that the hDEBSA performance is better than that of the other algorithms.

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

Access this article

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

References

  1. Akay B, Karaboga D (2012) Artificial bee colony algorithm for large-scale problem and engineering design optimization. J Intell Manuf 23:1001–1014

    Article  Google Scholar 

  2. Smuc T (2002) Sensitivity of differential evolution algorithm to value of control parameters. In: Proceedings of the international conference on artificial intelligence, pp 108–1093

    Google Scholar 

  3. Smuc T (2002) Improving convergence properties of the differential evolution algorithm. In: Proceedings of MENDEL 2002, 8th international Mendel conference on soft computing, pp 80–86

    Google Scholar 

  4. Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219(14):8121–8144

    MathSciNet  MATH  Google Scholar 

  5. Liang JJ, Qu BY, Suganthan P, Hernández-Díaz AG (2013) Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session on Real-Parameter Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session on Real-Parameter Optimization, Technical Report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China And Technical Report, Nanyang Technological University, Singapore

  6. Eberhart R, Shi Y (2001) Particle swarm optimization: Developments, Applications and resources. In: Proceedings of the 2001 congress on evolutionary computation, vol 81, pp 81–86

    Google Scholar 

  7. Gong W, Cai Z (2013) Differential evolution with ranking based mutation operators. IEEE Trans Cybern 43(5):2066–2081

    Article  Google Scholar 

  8. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press

  9. Zaharie D (2009) Influence of crossover on the behavior of differential evolution algorithms. Appl Soft Comput 9(3):1126– 1138

    Article  Google Scholar 

  10. Lampinen J, Zelinka I (2000) On stagnation of the differential evolution algorithm. In: Proceedings of MENDEL 2000, 6th international Mendel conference on soft computing, pp 76–83

    Google Scholar 

  11. Wang L, Zhong Y, Yin Y, Zhao W, Wang B, Xu Y (2015) A hybrid backtracking search optimization algorithm with differential evolution. In: Mathematical problems in engineering, Volume 2015, Article ID 769245, https://doi.org/10.1155/2015/769245

  12. Gämperle R, Müller SD, Koumoutsakos P (2002) A parameter study for differential evolution. Adv Intell Syst Fuzzy Syst Evol Comput 10:293–298

    Google Scholar 

  13. Ronkkonen J, Kukkonen S, Price K (2005) Real-parameter optimization with differential evolution. Proc IEEE CEC 1:506–513

    Google Scholar 

  14. Storn R (1996) On the usage of differential evolution for function optimization. In: Biennial conference of the North American fuzzy information processing society (NAFIPS). IEEE, Berkeley, pp 519–523

    Chapter  Google Scholar 

  15. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence

  16. Zhang C, Ning J, Lu S, Ouyang D, Ding T (2009) A novel hybrid differential evolution and particle swarm optimization algorithm for unconstrained optimization. Oper Res Lett 37:117– 122

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang L, Li H, Jiao Y-C, Zhang F-S (2009) Hybrid differential evolution and the simplified quadratic interpolation for global optimization, Copyright is held by the author/owner(s). GEC’09. ACM, Shanghai, pp 12–14. 978-1-60558-326-6/09/06

    Google Scholar 

  19. Pant M, Thangaraj R (2011) DE-PSO: A new hybrid meta-heuristic for solving global optimization problems. Math Nat Comput 7(3):363–381

    Article  MathSciNet  Google Scholar 

  20. Omran M, Engelbrecht AP, Salman A (2008) Bare bones differential evolution. Eur J Oper Res 196 (1):128–139

    Article  MathSciNet  MATH  Google Scholar 

  21. Gong W, Cai Z, Ling CX (2010) DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput 15(4):645–665

    Article  Google Scholar 

  22. Wen-Yi L (2010) A GA–DE hybrid evolutionary algorithm for path synthesis off our- bar linkage. Mech Mach Theory 45:1096–1107

    Article  MATH  Google Scholar 

  23. Rao RV, Savsani VJ (2012) Mechanical design optimization using advanced optimization technique. Springer, London

    Book  Google Scholar 

  24. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713

    Article  Google Scholar 

  25. Abbass H (2002) The self-adaptive pareto differential evolution algorithm. In: Proceedings of 2002 congress on evolutionary computation, vol 1, pp 831–836

    Google Scholar 

  26. Brest J, Greiner S, Boškovic 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 (5):646–657

    Article  Google Scholar 

  27. Zhang J, Sanderson A (2009) JADE: Adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. Mallipeddi R, Suganthan P, Pan Q, Tasgetiren M (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696

    Article  Google Scholar 

  30. 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  Google Scholar 

  31. Duan H, Luo Q (2014) Adaptive backtracking search algorithm for induction magnetometer optimization. IEEE Trans Magn 50(11):6001206

    Google Scholar 

  32. Liang JJ, Qin AK, Suganthan P, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transactions on Evolutionary Computation, 10(3)

  33. Van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8:225–239

    Article  Google Scholar 

  34. Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: Simpler, may be better. IEEE Trans Evol Comput 8:204–210

    Article  Google Scholar 

  35. Beightler CS, Phillips DT (1976) Applied geometric programming. Wiley, New York, p 1976

    Google Scholar 

  36. Das S, Suganthan P (2010) Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Technical Report, http://www.ntu.edu.sg/home/EPNSugan

  37. Wu G, Mallipeddi R, Suganthan PN, Wang R, Chen H (2016) Differential evolution with multi-population based ensemble of mutation strategies. Inf Sci 329:329–345

    Article  Google Scholar 

  38. Awad NH, Ali MZ, Suganthan PN, Reynolds RG (2017) CADE: A hybridization of cultural algorithm and differential evolution for numerical optimization. Inf Sci 378:215–241

    Article  Google Scholar 

  39. Nama S, Saha AK, Ghosh S (2016) Improved backtracking search algorithm for pseudo dynamic active earth pressure on retaining wall supporting c-Θ backfill. Appl Soft Comput 52:885–897

    Article  Google Scholar 

  40. Nama S, Saha AK, Ghosh S (2016) Improved symbiotic organisms search algorithm for solving unconstrained function optimization. Decis Sci Lett 5:361–380

    Article  Google Scholar 

  41. Tejani GG, Savsanin VJ, Patel VK (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Des Eng 3(3):226–249

    Google Scholar 

  42. Chen D, Zou F, Lu R, Wang P (2017) Learning backtracking search optimisation algorithm and its application. Inf Sci 376:71–94

    Article  Google Scholar 

  43. Lin Q, Gao L, Li X, Zhang C (2015) A hybrid backtracking search algorithm for permutation flow-shop scheduling problem, Computers & Industrial Engineering, https://doi.org/10.1016/j.cie.2015.04.009

  44. Askarzadeh A, Coelho LdS (2014) A backtracking search algorithm combined with Burger’s chaotic map for parameter estimation of PEMFC electrochemical model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2014.05.052

  45. Wang B, Wang L, Yin Y, Xu Y, Zhao W, Tang Y (2015) An improved neural network with random weights using backtracking search algorithm, Neural Process Letter, https://doi.org/10.1007/s11063-015-9480-z

  46. Nama S, Saha AK, Ghosh S (2016) A new ensemble algorithm of differential evolution and backtracking search optimization algorithm with adaptive control parameter for function optimization. Int J Indust Eng Comput 7:323–338

    Google Scholar 

  47. Wang L, Zhong Y, Yin Y, Zhao W, Wang B, Xu Y (2015) A hybrid backtracking search optimization algorithm with differential evolution. In: Mathematical problems in engineering, Volume 2015, Article ID 769245, https://doi.org/10.1155/2015/769245

  48. Guney K, Durmus A (2016) Elliptical antenna array synthesis using backtracking search optimisation algorithm. Def Sci J 66:272–277

    Article  Google Scholar 

  49. Modiri-Delshad M, Kaboli AghayS. Hr, Taslimi-Renani E, Abd Rahim N (2016) Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options. Energy 116:637–649

    Article  Google Scholar 

  50. Souza RR, Fadel Miguel L, lopez RH, Torii AJ, Miguel LFF (2016) A backtracking search algorithm for the simultaneous size, shape and topology optimization of trusses. Latin Amer J Solids Struct 13:2622–2651

    Article  Google Scholar 

  51. Khooban MH, Vafamand N, Liaghat A, Dragicevic T (2016) An optimal general type-2 fuzzy controller for Urban Traffic Network, ISA Transactions, https://doi.org/10.1016/j.isatra.2016.10.011i

  52. Song X, Zhang X, Zhao S, Li L (2015) Backtracking search algorithm for effective and efficient surface wave analysis. J Appl Geophys 114:19–31

    Article  Google Scholar 

  53. Wang S, Li Y, Yang H (2017) Self-adaptive differential evolution algorithm with improved mutation mode, Applied Intelligence, https://doi.org/ 10.1007/s10489-017-0914-3

  54. Li X, Ma S, Hu J (2017) Multi-search differential evolution algorithm, Applied Intelligence, https://doi.org/10.1007/s10489-016-0885-9

  55. Yi W, Gao L, Li X (2015) A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems. Appl Intell 42:642–660

    Article  Google Scholar 

Download references

Acknowledgments

The authors are extremely thankful to anonymous referees and the editor for their valuable comments towards improving the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Apu Kumar Saha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nama, S., Saha, A.K. A new hybrid differential evolution algorithm with self-adaptation for function optimization. Appl Intell 48, 1657–1671 (2018). https://doi.org/10.1007/s10489-017-1016-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-017-1016-y

Keywords

Navigation