A random perturbation modified differential evolution algorithm for unconstrained optimization problems

  • Zhaokun Wei
  • Xinlian Xie
  • Tiantian Bao
  • Yue Yu
Methodologies and Application


To solve unconstrained optimization problems, a random search differential evolution algorithm (RPMDE) is designed based on a modified differential evolution algorithm. The efficiency of an evolutionary algorithm usually depends on its exploration competence and development capability. Considering these characteristics, an effective difference operator called ‘DE/M_pBest-best/1’ is designed, which originates from ‘DE/best/1/’ and ‘DE/current-pbest/1’. The operator makes use of information from the best population of individuals to generate new solutions for the development of RPMDE and guarantee swarm quality during the later evolution of the algorithm, which improves its searching ability. To prevent the solutions from falling into local optima, RPMDE also adopts random perturbation to update the current solution with a better solution after difference mutation and crossover are competed. Furthermore, a levy distribution is employed to adjust the scale factor as a control parameter. All designed operators are beneficial to improve the exploration competence and the diversity of the whole population. Last, a large number of computational experiments and comparisons are conducted by employing 15 benchmark functions. The experimental results indicate that the designed algorithm, RPMDE, is more effective than other differential evolution variants in dealing with unconstrained optimization problems.


Improved differential evolution algorithm Difference strategy Random perturbation Levy distribution Parameter adjustment 



This research work has been supported by the National Key Research and Development Program of China [2017YFC0805309] and the Fundamental Research Funds for the Central Universities (3132016358). The authors are also grateful to the anonymous reviewers and editors for their comments and constructive suggestions.

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.


  1. Angira R, Santosh A (2007) Optimization of dynamic systems: a trigonometric differential evolution approach. Comput Chem Eng 31(9):1055–1063CrossRefGoogle Scholar
  2. Baatar N, Zhang D, Koh CS (2013) An improved differential evolution algorithm adopting lambda—best mutation strategy for global optimization of electromagnetic devices. IEEE Trans Magn 49(5):2097–2100CrossRefGoogle Scholar
  3. Balaji G, Balamurugan R, Lakshminarasimman L (2016) Mathematical approach assisted differential evolution for generator maintenance scheduling. Int J Elec Power 82:508–518CrossRefGoogle Scholar
  4. Basu M (2016) Quasi-oppositional differential evolution for optimal reactive power dispatch. Int J Electr Power 78:29–40CrossRefGoogle Scholar
  5. Brest J, Greiner S, Bošković 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(6):646–657CrossRefGoogle Scholar
  6. Chen Y, Mahalec V, Chen Y, Liu X, He R, Sun K (2015) Reconfiguration of satellite orbit for cooperative observation using variable-size multi-objective differential evolution. Eur J Oper Res 242(1):10–20MathSciNetCrossRefzbMATHGoogle Scholar
  7. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE T Evol Comput 15(1):4–31CrossRefGoogle Scholar
  8. Deng CH, Zhao BY, Deng AY, Hu RX (2009) New differential evolution algorithm with a second enhanced mutation operator. In: IEEE international workshop on intelligent systems and applications. IEEE, pp 1–4Google Scholar
  9. Elsayed SM, Sarker RA, Essasm DL (2013) An improved self-adaptive differential evolution algorithm for optimization problems. IEEE Trans Ind Inf 9(1):89–99CrossRefGoogle Scholar
  10. Gong W, Cai Z, Ling CX (2011) Enhanced differential evolution with adaptive strategies for numerical optimization. IEEE T Syst Man Cy B 41(2):397–413CrossRefGoogle Scholar
  11. Gong W, Cai Z (2013) Differential evolution with ranking-based mutation operators. IEEE Trans Cybernet 43(6):2066–2081CrossRefGoogle Scholar
  12. Gong W, Cai Z, Ling CX (2010) A real-coded biogeography-based optimization with mutation. App Math Comput 216(9):2749–2758MathSciNetCrossRefzbMATHGoogle Scholar
  13. Joshi R, Sanderson AC (1999) Minimal representation multi-sensor fusion using differential evolution. IEEE Trans Syst Man Cybern A, Syst Hum 29(1):63–76CrossRefGoogle Scholar
  14. Karaboga N (2005) Digital IIR filter design using differential evolution algorithm. EURASIP J Adv Signal Process 8:1269–1276zbMATHGoogle Scholar
  15. Kovačević D, Mladenović N, Petrović B, Milošević P (2014) DE-VNS: self-adaptive differential evolution with crossover neighborhood search for continuous global optimization. Comput Oper Res 52:157–169MathSciNetCrossRefzbMATHGoogle Scholar
  16. Lin Q, Zhu Q, Huang P, Chen J, Ming Z, Yu J (2015) A novel hybrid multi-objective immune algorithm with adaptive differential evolution. Comput Oper Res 62:95–111MathSciNetCrossRefzbMATHGoogle Scholar
  17. Liu W, Wang P, Qiao H (2012) Part-based adaptive detection of workpieces using differential evolution. Signal Process 92(2):301–307CrossRefGoogle Scholar
  18. Maio FD, Baronchelli S, Zio E (2014) Hierarchical differential evolution for minimal cut sets identification: application to nuclear safety systems. Eur J Oper Res 238(2):645–652MathSciNetCrossRefzbMATHGoogle Scholar
  19. Onwubolu G, Davendra D (2006) Scheduling flow shops using differential evolution algorithm. Eur J Oper Res 171(2):674–692CrossRefzbMATHGoogle Scholar
  20. Pan QK, Suganthan PN, Wang L, Gao L, Mallipeddi R (2011) A differential evolution algorithm with self-adapting strategy and control parameters. Comput Oper Res 38(1):394–408MathSciNetCrossRefzbMATHGoogle Scholar
  21. Price KV, Storn RM, Lampinen JA (2005) Differential evolution-a practical approach to global optimization. Springer, New YorkzbMATHGoogle Scholar
  22. Qin AK, Huan VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evolut Comput 13(2):398–417CrossRefGoogle Scholar
  23. Qu BY, Liang JJ, Wang ZY, Chen Q, Suganthan PN (2016) Novel benchmark functions for continuous multimodal optimization with comparative results. Swarm Evol Comput 26:23–34CrossRefGoogle Scholar
  24. Storn R, Price K (1996) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  25. Storn R (1996) Differential evolution design of an IIR-filter. In: IEEE international conference on evolutionary computation. IEEE, pp 268–273Google Scholar
  26. Tanabe R, Fukunaga A (2013) Evaluating the performace of SHADE on CEC 2013 benchmark problem. In: IEEE congress on evolutionary computation. IEEE, pp 1952–1959Google Scholar
  27. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66CrossRefGoogle Scholar
  28. Zhang J, Avasarala V, Sanderson AC, Mullen T (2008) Differential evolution for discrete optimization: An experimental study on Combinatorial Auction problems. In: IEEE world congress on computational intelligence. IEEE, pp 2794–2880Google Scholar
  29. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 13(5):945–958CrossRefGoogle Scholar
  30. Zio E, Viadana G (2011) Optimization of the inspection intervals of a safety system in a nuclear power plant by multi-objective differential evolution (MODE). Reliab Eng Syst Saf 96(11):1552–1563CrossRefGoogle Scholar
  31. Zou D, Wu J, Gao L, Li S (2013) A modified differential evolution algorithm for unconstrained optimization problems. Neurocomputing 120(6):469–481CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhaokun Wei
    • 1
  • Xinlian Xie
    • 1
  • Tiantian Bao
    • 1
  • Yue Yu
    • 1
  1. 1.Transportation Management College, Room 318Dalian Maritime UniversityDalianChina

Personalised recommendations