Frontiers of Computer Science

, Volume 12, Issue 2, pp 297–315 | Cite as

On the selection of solutions for mutation in differential evolution

  • Yong Wang
  • Zhi-Zhong Liu
  • Jianbin Li
  • Han-Xiong Li
  • Jiahai Wang
Research Article


Differential evolution (DE) is a kind of evolutionary algorithms, which is suitable for solving complex optimization problems. Mutation is a crucial step in DE that generates new solutions from old ones. It was argued and has been commonly adopted in DE that the solutions selected for mutation should have mutually different indices. This restrained condition, however, has not been verified either theoretically or empirically yet. In this paper, we empirically investigate the selection of solutions for mutation in DE. From the observation of the extensive experiments, we suggest that the restrained condition could be relaxed for some classical DE versions as well as some advanced DE variants. Moreover, relaxing the restrained condition may also be useful in designing better future DE algorithms.


differential evolution mutation the selection of solutions for mutation evolutionary algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to thank the anonymous reviewers for their very constructive and helpful suggestions. This work was supported in part by the National Basic Research Program (973 Program) of China (2011CB013104), in part by the Innovation-driven Plan in Central South University (2015CXS012 and 2015CX007), in part by the National Natural Science Foundation of China (Grant Nos. 61273314 and 61673397), in part by the EU Horizon 2020 Marie Skłodowska-Curie Individual Fellowships (Project ID: 661327), in part by the Hunan Provincial Natural Science Fund for Distinguished Young Scholars (2016JJ1018), in part by the Program for New Century Excellent Talents in University (NCET-13-0596), and in part by State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology.

Supplementary material

11704_2016_5353_MOESM1_ESM.ppt (190 kb)
Supplementary material, approximately 190 KB.


  1. 1.
    Storn R, Price K. Differential evolution — a simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley, CA: International Computer Science Institute. Technical Report TR-95-012. 1995Google Scholar
  2. 2.
    Storn R, Price K. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 1997, 11(4): 341–359MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fan H, Lampinen J. A trigonometric mutation operation to differential evolution. Journal of Global Optimization, 2003, 27(1): 105–129MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Zhang J, Sanderson A. JADE: adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 2009, 13(5): 945–958CrossRefGoogle Scholar
  5. 5.
    Das S, Abraham A. Differential evolution using a neighborhood-based mutation operator. IEEE Transactions on Evolutionary Computation, 2009, 13(3): 526–553CrossRefGoogle Scholar
  6. 6.
    Wang Y, Cai Z X, Zhang Q F. Enhancing the search ability of differential evolution through orthogonal crossover. Information Sciences, 2012, 185(1): 153–177MathSciNetCrossRefGoogle Scholar
  7. 7.
    Guo S M, Yang C C. Enhancing differential evolution utilizing eigenvector-based crossover operator. IEEE Transactions on Evolutionary Computation, 2015, 19(1): 31–49MathSciNetCrossRefGoogle Scholar
  8. 8.
    Wang Y, Li H X, Huang T W, Li L. Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Applied Soft Computing, 2014, 18: 232–247CrossRefGoogle Scholar
  9. 9.
    Liu J H, Lampinen J. A fuzzy adaptive differential evolution algorithm. Soft Computing, 2005, 9(6): 448–462CrossRefzbMATHGoogle Scholar
  10. 10.
    Brest J, Greiner S, Boskovic B, Mernik M, Zumer V. Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation, 2006, 10(6): 646–657CrossRefGoogle Scholar
  11. 11.
    Noman N, Iba H. Accelerating differential evolution using an adaptive local search. IEEE Transactions on Evolutionary Computation, 2008, 12(1): 107–125CrossRefGoogle Scholar
  12. 12.
    Rahnamayan S, Tizhoosh H R, Salama M M A. Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation, 2008, 12(1): 64–79CrossRefGoogle Scholar
  13. 13.
    Sun J Y, Zhang Q F, Tsang E P K. DE/EDA: a new evolutionary algorithm for global optimization. Information Sciences, 2003, 169(3–4): 249–262MathSciNetGoogle Scholar
  14. 14.
    Qin A K, Huang V L, Suganthan P N. Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transactions on Evolutionary Computation, 2009, 13(2): 398–417CrossRefGoogle Scholar
  15. 15.
    Mallipeddi R, Suganthan P N, Pan Q, Tasgetiren M. Differential evolution algorithm with ensemble of parameters and mutation strategies. Applied Soft Computing, 2011, 11(2): 1679–1696CrossRefGoogle Scholar
  16. 16.
    Wang Y, Cai Z X, Zhang Q F. Differential evolution with composite trial vector generation strategies and control parameters. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 55–66CrossRefGoogle Scholar
  17. 17.
    Das S, Suganthan P N. Differential evolution: a survey of the state-ofthe- art. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 4–31CrossRefGoogle Scholar
  18. 18.
    Wang Y, Wang B C, Li H X, Yen G G. Incorporating objective function information into the feasibility rule for constrained evolutionary optimization. IEEE Transactions on Cybernetics, 2016, doi: 10.1109/TCYB.2015.2493239Google Scholar
  19. 19.
    Wang Y, Li H X, Yen G G, Song W. MOMMOP: multiobjective optimization for locating multiple optimal solutions of multimodal optimization problems. IEEE Transactions on Cybernetics, 2015, 45(4): 830–843CrossRefGoogle Scholar
  20. 20.
    Tvrdík J. Modifications of differential evolution with composite trial vector generation strategies. In: Snášel V, Abraham A, Corchado E S, eds. Soft Computing Models in Industrial and Environmental Applications. Advances in Intelligent Systems and Computing, Vol 188. Berlin: Springer,2013, 113–122CrossRefGoogle Scholar
  21. 21.
    Price K, Storn R, Lampinen J. Differential Evolution-A Practical Approach to Global Optimization. Berlin: Springer-Verlag,2005zbMATHGoogle Scholar
  22. 22.
    Liu H, Huang H, Liu S S. Explore influence of differential operator in DE mutation with unrestrained method to generate mutant vector. In: Rutkowski L, Korytkowski M, Scherer R, et al. eds. Swarm and Evolutionary Computation. Lecture Notes in Computer Science, Vol 7269. Berlin: Springer, 2012, 292–300CrossRefGoogle Scholar
  23. 23.
    Suganthan P N, Hansen N, Liang J, Deb K, Chen Y P, Auger A, Tiwari S. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL Report 2005005. 2005Google Scholar
  24. 24.
    Liang J J, Qu B Y, Suganthan P N, Hernández-Diaz A. Problem definitions and evaluation criteria for the CEC 2013 special session and competition on real-parameter optimization. Zhengzhou: Zhengzhou University. Technical Report. 2013Google Scholar
  25. 25.
    Tanabe R, Fukunaga A. Improving the search performance of shade using linear population size reduction. In: Proceeding of IEEE Congress on Evolutionary Computation. 2014, 1658–1665Google Scholar
  26. 26.
    Yang Z Y, Tang K, Yao X. Large scale evolutionary optimization using cooperative coevolution. Information Sciences, 2008, 87(15): 2985–2999MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yong Wang
    • 1
    • 2
  • Zhi-Zhong Liu
    • 1
  • Jianbin Li
    • 3
  • Han-Xiong Li
    • 4
    • 5
  • Jiahai Wang
    • 6
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina
  2. 2.School of Computer Science and InformaticsDe Montfort UniversityLeicesterUK
  3. 3.Institute of Information Security and Big DataCentral South UniversityChangshaChina
  4. 4.Department of Systems Engineering and Engineering ManagementCity University of Hong KongHong KongChina
  5. 5.State Key Laboratory of High Performance Complex ManufacturingCentral South UniversityChangshaChina
  6. 6.School of Data and Computer ScienceSun Yat-sen UniversityGuangzhouChina

Personalised recommendations