Skip to main content
SpringerLink
Log in

An adaptive mutation strategy correction framework for differential evolution

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Differential evolution (DE) is an efficient global optimization algorithm. However, due to its random properties, some individuals may mutate in the direction of deviating from the theoretical global optima, failing to evolve and wasting a lot of computing resources. Moreover, there is an imbalance between exploration and exploitation in mutation strategies. For these shortcomings, we propose an adaptive mutation strategy correction framework (AMSC) for DEs. In this framework, the population is firstly split into superior subpopulation and disadvantaged subpopulation. Two types of auxiliary mutant vectors based on the direction information are designed to respectively enhance the exploration ability and exploitation ability of these two subpopulations, so as to improve the search efficiency. Moreover, for achieving the proper balance between exploration and exploitation in DEs, we propose an adaptive cooperative rule for the above two auxiliary vectors based on the actual crossover rates. This rule controls the relative size of two subgroups to determine the proportion of two types of auxiliary vectors used in the whole population. To evaluate the performance of AMSC framework, we have introduced into eight original DEs and carried out comparative experiments on four practical problems and 59 test functions from CEC 2014 and CEC 2017 benchmark suites. The experiments demonstrate that the AMSC framework can increase DEs’ performance dramatically.

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

Similar content being viewed by others

Data availability

All of data generated or analyzed during our study are included in this paper and the supplementary material file.

References

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

    MATH  MathSciNet  Google Scholar 

  2. Zhang Y, Gong D, Gao X, Tian T, Sun X (2020) Binary differential evolution with self-learning for multi-objective feature selection. Inform Sci 507:67–85

    MATH  MathSciNet  Google Scholar 

  3. Deng W, Shang S, Cai X, Zhao H, Zhou Y, Chen H, Deng W (2021) Quantum differential evolution with cooperative coevolution framework and hybrid mutation strategy for large scale optimization. Knowl-Based Syst 224:107080

    Google Scholar 

  4. Wang J, Weng T, Zhang Q (2018) A two-stage multiobjective evolutionary algorithm for multiobjective multidepot vehicle routing problem with time windows. IEEE Transact Cybernet 49(7):2467–2478

    Google Scholar 

  5. Arce F, Zamora E, Sossa H, Barrón R (2018) Differential evolution training algorithm for dendrite morphological neural networks. Appl Soft Comput 68:303–313

    Google Scholar 

  6. Ahmad MF, Isa NAM, Lim WH, Ang KM. Differential evolution: A recent review based on state-of-the-art works, Alex Eng J

  7. Mohamed AW, Hadi AA, Mohamed AK (2021) Differential evolution mutations: Taxonomy, comparison and convergence analysis. IEEE Access 9:68629–68662

    Google Scholar 

  8. Sun G, Peng J, Zhao R (2018) Differential evolution with individual-dependent and dynamic parameter adjustment. Soft Comput 22(17):5747–5773

    Google Scholar 

  9. Sun G, Yang B, Yang Z, Xu G (2020) An adaptive differential evolution with combined strategy for global numerical optimization. Soft Comput 24(9):6277–6296

    Google Scholar 

  10. Gupta S, Su R (2022) An efficient differential evolution with fitness-based dynamic mutation strategy and control parameters. Knowl-Based Syst 251:109280

    Google Scholar 

  11. Hu H, Kantardzic M, Sethi TS (2020) No Free Lunch Theorem for concept drift detection in streaming data classification: A review. Wiley Interdisciplinary Rev: Data Mining Knowl Discov 10(2):e1327

    Google Scholar 

  12. Li X, Ma S, Hu J (2017) Multi-search differential evolution algorithm. Appl Intell 47(1):231–256

    Google Scholar 

  13. Xu B, Chen X, Tao L (2018) Differential evolution with adaptive trial vector generation strategy and cluster-replacement-based feasibility rule for constrained optimization. Inform Sci 435:240–262

    MATH  MathSciNet  Google Scholar 

  14. Jiang R, Shankaran R, Wang S, Chao T (2022) A proportional, integral and derivative differential evolution algorithm for global optimization. Expert Syst Appl 206:117669

    Google Scholar 

  15. Wang Y, Li T, Liu X, Yao J (2022) An adaptive clonal selection algorithm with multiple differential evolution strategies. Inform Sci 604:142–169

    Google Scholar 

  16. Dixit A, Mani A, Bansal R (2022) An adaptive mutation strategy for differential evolution algorithm based on particle swarm optimization. Evolutionary Intell 15(3):1571–1585

    Google Scholar 

  17. Tan Z, Li K, Wang Y (2021) Differential evolution with adaptive mutation strategy based on fitness landscape analysis. Inform Sci 549:142–163

    MATH  MathSciNet  Google Scholar 

  18. Deng W, Ni H, Liu Y, Chen H, Zhao H (2022) An adaptive differential evolution algorithm based on belief space and generalized opposition-based learning for resource allocation. Appl Soft Comput 127:109419

    Google Scholar 

  19. Deng L, Li C, Han R, Zhang L, Qiao L (2021) TPDE: A tri-population differential evolution based on zonal-constraint stepped division mechanism and multiple adaptive guided mutation strategies. Inform Sci 575:22–40

    MathSciNet  Google Scholar 

  20. Biswas PP, Suganthan PN (2020) Large initial population and neighborhood search incorporated in lshade to solve cec2020 benchmark problems, in, IEEE Congress on Evolutionary Computation (CEC). IEEE 1–7:2020

    Google Scholar 

  21. Singh SP (2018) New adaption based mutation operator on differential evolution algorithm. Intell Decis Technol 12(4):389–397

    Google Scholar 

  22. Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution, in, (2013) IEEE Congress on Evolutionary Computation. IEEE 71–78

  23. Deng L, Li C, Lan Y, Sun G, Shang C (2022) Differential evolution with dynamic combination based mutation operator and two-level parameter adaptation strategy. Expert Syst Appl 192:116298

    Google Scholar 

  24. Sun G, Lan Y, Zhao R (2019) Differential evolution with Gaussian mutation and dynamic parameter adjustment. Soft Comput 23(5):1615–1642

    Google Scholar 

  25. Xu Y, Yang X, Yang Z, Li X, Wang P, Ding R, Liu W (2021) An enhanced differential evolution algorithm with a new oppositional-mutual learning strategy. Neurocomputing 435:162–175

    Google Scholar 

  26. Sallam KM, Elsayed SM, Sarker RA (2016) Essam DL, Two-phase differential evolution framework for solving optimization problems, in, IEEE Symposium Series on Computational Intelligence (SSCI). IEEE 1–8:2016

    Google Scholar 

  27. Tarkhaneh O, Shen H (2019) An adaptive differential evolution algorithm to optimal multi-level thresholding for MRI brain image segmentation. Expert Syst Appl 138:112820

    Google Scholar 

  28. Wang J, Li S (2019) An improved grey wolf optimizer based on differential evolution and elimination mechanism. Sci Rep 9(1):1–21

    MathSciNet  Google Scholar 

  29. Yildizdan G, Baykan ÖK (2020) A novel modified bat algorithm hybridizing by differential evolution algorithm. Expert Syst Appl 141:112949

    Google Scholar 

  30. Gao S, Yu Y, Wang Y, Wang J, Cheng J, Zhou M (2019) Chaotic local search-based differential evolution algorithms for optimization. IEEE Transact Syst Man Cybernet: Syst 51(6):3954–3967

    Google Scholar 

  31. Sun G, Li C, Deng L (2021) An adaptive regeneration framework based on search space adjustment for differential evolution. Neural Comput Appl 33(15):9503–9519

    Google Scholar 

  32. Mohamed AW, Suganthan PN (2018) Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation. Soft Comput 22(10):3215–3235

    Google Scholar 

  33. Mohamed AW, Mohamed AK (2019) Adaptive guided differential evolution algorithm with novel mutation for numerical optimization. Inter J Mach Learn Cybernet 10(2):253–277

    Google Scholar 

  34. Tian M, Gao X, Yan X (2020) Performance-driven adaptive differential evolution with neighborhood topology for numerical optimization. Knowl-Based Syst 188:105008

    Google Scholar 

  35. Yan X, Tian M (2022) Differential evolution with two-level adaptive mechanism for numerical optimization. Knowl-Based Syst 241:108209

    Google Scholar 

  36. Cheng J, Pan Z, Liang H, Gao Z, Gao J (2021) Differential evolution algorithm with fitness and diversity ranking-based mutation operator. Swarm Evolutionary Comput 61:100816

    Google Scholar 

  37. Cao Z, Wang Z, Fu Y, Jia H, Tian F (2022) An adaptive differential evolution framework based on population feature information. Inform Sci 608:1416–1440

    Google Scholar 

  38. Ghosh A, Das S, Das AK, Senkerik R, Viktorin A, Zelinka I, Masegosa AD (2022) Using spatial neighborhoods for parameter adaptation: An improved success history based differential evolution. Swarm Evolutionary Comput 71:101057

    Google Scholar 

  39. Li Y, Wang S, Yang B, Chen H, Wu Z, Yang H (2022) Population reduction with individual similarity for differential evolution, Artifi Intell Rev. 1–63

  40. Zeng Z, Zhang M, Chen T, Hong Z (2021) A new selection operator for differential evolution algorithm. Knowl-Based Syst 226:107150

    Google Scholar 

  41. Zeng Z, Hong Z, Zhang H, Zhang M, Chen C (2022) Improving differential evolution using a best discarded vector selection strategy. Inform Sci 609:353–375

    Google Scholar 

  42. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Transact Evolutionary Comput 13(5):945–958

    Google Scholar 

  43. Liang JJ, Qu BY, Suganthan PN (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore 635:490

  44. Wu G, Mallipeddi R, Suganthan PN (2017) Problem definitions and evaluation criteria for the CEC 2017 competition on constrained real-parameter optimization, National University of Defense Technology, Changsha, Hunan, PR China and Kyungpook National University, Daegu, South Korea and Nanyang Technological University, Singapore, Technical Report

  45. Das S, Suganthan PN (2011) Problem definitions and evaluation criteria for CEC, competition on testing evolutionary algorithms on real world optimization problems. Jadavpur University, Nanyang Technological University, Kolkata 2010:341–359

  46. García-Martínez C, Lozano M, Herrera F, Molina D, Sánchez AM (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Operat Res 185(3):1088–1113

    MATH  Google Scholar 

  47. Herrera F, Lozano M (2000) Gradual distributed real-coded genetic algorithms. IEEE Transact Evolutionary Comput 4(1):43–63

    Google Scholar 

  48. Tanabe R, Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction, in, IEEE congress on evolutionary computation (CEC). IEEE 1658–1665:2014

    Google Scholar 

  49. Awad NH, Ali MZ, Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems, in, IEEE Congress on Evolutionary Computation (CEC). IEEE 372–379:2017

    Google Scholar 

  50. Zhao X, Feng S, Hao J, Zuo X, Zhang Y (2021) Neighborhood opposition-based differential evolution with Gaussian perturbation. Soft Comput 25(1):27–46

    Google Scholar 

  51. Guo S-M, Yang C-C, Hsu P-H, Tsai JS-H (2015) Improving differential evolution with a successful-parent-selecting framework. IEEE Transact Evolutionary Comput 19(5):717–730

    Google Scholar 

  52. Deng L, Zhang L, Fu N, Sun H, Qiao L (2020) ERG-DE: An elites regeneration framework for differential evolution. Inform Sci 539:81–103

    MATH  MathSciNet  Google Scholar 

  53. Corder GW, Foreman DI (2009) Nonparametric Statistics for Non-Statisticians, John Wiley & Sons

Download references

Acknowledgement

This work was supported by the National Natural Science Foundation of China under Grant 62176075, and project ZR2021MF063 supported by Shandong Provincial Natural Science Foundation.

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Harbin Institute of Technology, Weihai, China

    Libao Deng, Yifan Qin & Chunlei Li

  2. School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin, China

    Chunlei Li

  3. Insight Centre for Data Analytics, Dublin City University, Dublin, Ireland

    Lili Zhang

Authors
  1. Libao Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yifan Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chunlei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lili Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Libao Deng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary material

Below is the link to the electronic supplementary material.

Supplementary file 1 (PDF 5174 kb)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, L., Qin, Y., Li, C. et al. An adaptive mutation strategy correction framework for differential evolution. Neural Comput & Applic 35, 11161–11182 (2023). https://doi.org/10.1007/s00521-023-08291-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-023-08291-9

Keywords

Search

Navigation