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A fluctuant population strategy for differential evolution

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Abstract

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for global numerical optimization, which has been used in a wide range of application fields. The parameter of population size usually has important influence on the performance of DE, but it is not widely studied in the scope of DE. Based on the relationship between the population size and the exploration/exploitation ability of DE, we propose a novel fluctuant population (FP) strategy for automatically adjusting the value of population size during the runs. More specifically, the FP strategy mainly contains three parts: a monotone decreasing function is used to coordinate the focus between the exploration ability and exploitation ability, which can cause the FP strategy to decrease progressively at the macro level; a periodic function is applied to control the population diversity, which leads to the fluctuant feature of FP strategy at micro level; a rearranging and auto-grouping operation is used for removing and adding individual when the population size is changed. To evaluate the effect of the fluctuant population strategy on DE algorithm, based on 30 benchmark functions, we compare six selected DE algorithms with and without the FP strategy. The simulation results show that the fluctuant population strategy can significantly improve the performance of the six DE algorithms.

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References

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

    Article  MATH  Google Scholar 

  2. Das S, Mullick S, Suganthan P (2016) Recent advances in differential evolution—an updated survey. Swarm Evolut Comput 27:1–30

    Article  Google Scholar 

  3. Mohamed A (2018) A novel differential evolution algorithm for solving constrained engineering optimization problems. J Intell Manuf 29:659–692

    Article  Google Scholar 

  4. Zhu T, Hao Y, Luo W, Ning H (2018) Learning enhanced differential evolution for tracking optimaldecisions in dynamic power systems. Appl Soft Comput 67:812–821

    Article  Google Scholar 

  5. Qiu X, Xu J, Xu Y, Tan K (2018) A new differential evolution algorithm for minimax optimization in robust design. IEEE Trans Cybern 48:1355–1368

    Article  Google Scholar 

  6. Gotmare A, Bhattacharjee S, Patidar R, George N (2017) Swarm and evolutionary computing algorithms for system identification and filter design: a comprehensive review. Swarm Evolut Comput 32:68–84

    Article  Google Scholar 

  7. Das S, Suganthan P (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evolut Comput 15:4–31

    Article  Google Scholar 

  8. Opara K, Arabas J (2018) Comparison of mutation strategies in differential evolution—a probabilistic perspective. Swarm Evolut Comput 39:53–69

    Article  Google Scholar 

  9. Dorronsoro B, Bouvry P (2011) Improving classical and decentralized differential evolution with new mutation operator and population topologies. IEEE Trans Evolut Comput 15:67–98

    Article  Google Scholar 

  10. Iacca G, Mininno E, Neri F (2011) Composed compact differential evolution. Evolut Intell 4:17–29

    Article  MATH  Google Scholar 

  11. Fua C, Jiang C, Chen G, Liu Q (2017) An adaptive differential evolution algorithm with an aging leader and challengers mechanism. Appl Soft Comput 57:60–73

    Article  Google Scholar 

  12. Lu X, Tang K, Sendhoff B, Yao X (2014) A new self-adaptation scheme for differential evolution. Neurocomputing 146:2–16

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Sun G (2018) Differential evolution with adaptive parameter strategy for continuous optimization problems. J Uncertain Syst 12:256–266

    Google Scholar 

  15. Wang S, Li Y, Yang H (2017) Self-adaptive differential evolution algorithm with improved mutation mode. Appl Intell 47:644–658

    Article  Google Scholar 

  16. Dragoi E, Dafinescu V (2016) Parameter control and hybridization techniques in differential evolution: a survey. Artif Intell Rev 45:447–470

    Article  Google Scholar 

  17. Yu W, Shen M, Chen W, Zhan Z, Gong Y, Lin Y, Liu O, Zhang J (2014) Differential evolution with two-level parameter adaptation. IEEE Trans Cybern 44:1080–1099

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Sun G, Yang B, Yang Z, Xu G (2019) An adaptive differential evolution with combined strategy for global numerical optimization. Soft Comput. https://doi.org/10.1007/s00500-019-03934-3

    Article  Google Scholar 

  20. Piotrowski A (2017) Review of differential evolution population size. Swarm Evolut Comput 32:1–24

    Article  Google Scholar 

  21. Das S, Abraham A, Chakraboty U, Konar A (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evolut Comput 13:526–553

    Article  Google Scholar 

  22. Kotyrba M, Volna E, Bujok P (2015) Unconventional modelling of complex system via cellular automata and differential evolution. Swarm Evolut Comput 25:52–62

    Article  Google Scholar 

  23. Guo S, Yang C (2015) Enhancing differential evolution utilizing eigenvector-based crossover operator. IEEE Trans Evolut Comput 19:31–49

    Article  Google Scholar 

  24. Piotrowski A (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci 241:164–194

    Article  Google Scholar 

  25. Brest J, Maucec M (2008) Population size reduction for the differential evolution algorithm. Appl Intell 29:228–247

    Article  Google Scholar 

  26. Tanabe R, Fukunaga A (2014) Improving the search performance of SHADE using linear population size reduction. In: Proceedings of the IEEE congress on evolutionary computation, pp 1658–1665

  27. Ali M, Awad N, Suganthan P, Reynolds R (2017) An adaptive multipopulation differential evolution with dynamic population reduction. IEEE Trans Cybern 47:2768–2779

    Article  Google Scholar 

  28. Awad N, Ali M, Suganthan P (2018) Ensemble of parameters in a sinusoidal differential evolution with niching-based population reduction. Swarm Evolut Comput 39:141–156

    Article  Google Scholar 

  29. Zamuda A, Brest J (2015) Self-adaptive control parameters randomization frequency and propagations in differential evolution. Swarm Evolut Comput 25:72–99

    Article  Google Scholar 

  30. Tirronen V, Neri F (2009) Differential evolution with fitness diversity self-adaptation. In: Chiong R (ed) Nature-inspired algorithms for optimisation, SCI 193. Springer, Berlin, pp 199–234

    Chapter  Google Scholar 

  31. Penunuri F, Cab C, Carvente O, Zambrano-Arjona M, Tapia J (2016) A study of the classical differential evolution control parameters. Swarm Evolut Comput 26:86–96

    Article  Google Scholar 

  32. Zhu W, Tang Y, Fang J, Zhang W (2013) Adaptive population tuning scheme for differential evolution. Inf Sci 223:164–191

    Article  Google Scholar 

  33. Teng N, Teo J, Hijazi M (2009) Self-adaptive population sizing for a tune-free differential evolution. Soft Comput 13:709–724

    Article  Google Scholar 

  34. Guo S, Yang C, Hsu P, Tsai J (2015) Improving differential evolution with a successful-parent-selecting framework. IEEE Trans Evolut Comput 19:717–730

    Article  Google Scholar 

  35. Fan Q, Yan X (2016) Self-adaptive differential evolution algorithm with zoning evolution of control parameters and adaptive mutation strategies. IEEE Trans Cybern 46:219–232

    Article  Google Scholar 

  36. Qiu X, Xu J, Xu Y, Tan KC (2018) A new differential evolution algorithm for minimax optimization in robust design. IEEE Trans Cybern 48:1355–1368

    Article  Google Scholar 

  37. Liang J, Qu B, Suganthan P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Zhengzhou University, China, and Nanyang Technological University, Singapore

  38. Qin A, Huang V, Suganthan P (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evolut Comput 13:398–417

    Article  Google Scholar 

  39. Zhang J, Sanderson A (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 13:945–958

    Article  Google Scholar 

  40. Wang H, Rahnamayan S, Sun H, Omran M (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43:634–647

    Article  Google Scholar 

  41. Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: Proceedings of the IEEE congress on evolutionary computation, pp 71–78

  42. Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 71701187 and 61702389, and Research Project of Zhejiang Education Department under Grant No. Y201738184, and Yanta Scholars Foundation of Xi’an University of Finance and Economics.

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Authors and Affiliations

  1. College of Economic and Management, Zhejiang Normal University, Jinhua, 321004, China

    Gaoji Sun

  2. School of Statistics, Xi’an University of Finance and Economics, Xi’an, 710100, China

    Geni Xu

  3. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, China

    Rong Gao

  4. College of Mathematics and Statistics, Huanggang Normal University, Huanggang, 438000, China

    Jie Liu

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  1. Gaoji Sun
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  2. Geni Xu
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  3. Rong Gao
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  4. Jie Liu
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Correspondence to Gaoji Sun or Geni Xu.

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Sun, G., Xu, G., Gao, R. et al. A fluctuant population strategy for differential evolution. Evol. Intel. 16, 1747–1765 (2023). https://doi.org/10.1007/s12065-019-00287-6

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  • DOI: https://doi.org/10.1007/s12065-019-00287-6

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