Skip to main content
SpringerLink
Log in

Cellular differential evolutionary algorithm with double-stage external population-leading and its application

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This paper aims to address the problem of poor diversity and convergence for traditional evolutionary algorithms in solving multi-objective optimization problems and proposes a cellular differential evolutionary algorithm with double-stage external population-leading. This algorithm divides the maintenance of external population diversity into double stages and introduces new disturbance in the mutation operation to avoid the algorithm falling into a local optimum. In the first stage, the external population is maintained according to the rank and k-nearest neighbor distance. The second stage adopts the external population retention strategy of multi-objective cellular differential algorithm that only retains non-dominated solutions. In both stages, the external population has complete feedback, which means the solutions from the external population randomly replace existing individuals in the two-dimensional grid population after every iteration. Tests on fifteen benchmark functions show that the new algorithm can obtain more uniform Pareto front and competitive convergence results than the other four typical algorithms. Finally, the feasibility and effectiveness of this algorithm are verified by the case study of cycloid speed reducer.

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
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Giagkiozis I, Fleming PJ (2015) Methods for multi-objective optimization: an analysis. Inf Sci 293:338–350

    Article  MathSciNet  Google Scholar 

  2. Gomes GF, de Almeida FA, da Sliva Lopes Alexandrino P, da Cunha SS, de Sousa BS, Ancelotti AC (2019) A multiobjective sensor placement optimization for SHM systems considering fisher information matrix and mode shape interpolation. Eng Comput 35(2):519–535

    Article  Google Scholar 

  3. Hassan RA, Crossley WA (2003) Multi-objective optimization of communication satellites with two-branch tournament genetic algorithm. J Spacecr Rockets 40(2):266–272

    Article  Google Scholar 

  4. Chen G, Sun Y, Lu L, Chen W (2016) A new static accuracy design method for ultra-precision machine tool based on global optimisation and error sensitivity analysis. Int J Nanomanuf 12(2):167–180

    Article  Google Scholar 

  5. Chen G, Sun Y, Zhang F, Lu L, Chen W, Yu N (2018) Dynamic accuracy design method of ultra-precision machine tool. Chin J Mech Eng 31(1):8

    Article  Google Scholar 

  6. Liu Z, Li X, Wu D, Qian Z, Feng P, Rong Y (2018) The development of a hybrid firefly algorithm for multi-pass grinding process optimization. J Intell Manuf 30:2457–2472

    Article  Google Scholar 

  7. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  8. Zitzler E, Laumanns M, Thiele L (2002) SPEA2: improving the strength pareto evolutionary algorithm. In: Proceedings of evolutionary methods for design, optimization, and control with application to industrial problems. Athens, Greece, pp 95–100

  9. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolution algorithm based on decomposition. IEEE Trans Evol Comput 6(11):712–731

    Article  Google Scholar 

  10. Alexandrino PDSL, Gomes GF, Cunha SS Jr (2019) A robust optimization for damage detection using multiobjective genetic algorithm, neural network and fuzzy decision making. Inverse Probl Sci Eng 28(1):1741–5977

    MathSciNet  Google Scholar 

  11. Gomes GF, Almeida FAD (2020) Tuning metaheuristic algorithms using mixture design: application of sunflower optimization for structural damage identification. Adv Eng Softw 149:102877

    Article  Google Scholar 

  12. Lim DK, Woo DK, Yeo HK, Jung SY, Ro JS, Jung HK (2015) A novel surrogate-assisted multi-objective optimization algorithm for an electromagnetic machine design. IEEE Trans Magn 51(3):1–4

    Article  Google Scholar 

  13. Tian HX, Shuai MW, Li K (2019) Optimization study of line planning for high speed railway based on an improved multi-objective differential evolution algorithm. IEEE Access 7:137731–137743

    Article  Google Scholar 

  14. Paula TID, Gomes GF, Freitas Gomes JHD, Paiva APD (2019) A mixture design of experiments approach for genetic algorithm tuning applied to multi-objective optimization. In: World congress on global optimization. Metz, France, pp 600–610

  15. Nebro AJ, Durillo JJ, Luna F, Dorronsoro B, Alba E (2009) Mocell: a cellular genetic algorithm for multiobjective optimization. Int J Intell Syst 24(7):726–746

    Article  Google Scholar 

  16. Canyurt OE, Hajela P (2010) Cellular genetic algorithm technique for the multicriterion design optimization. Struct Multidiscip 40:201–214

    Article  Google Scholar 

  17. Alba E, Dorronsoro B (2008) Cellular genetic algorithms. Springer, New York

    Book  Google Scholar 

  18. Giacobini M, Tomassini M, Tettamanzi AGB, Alba E (2005) Selection intensity in cellular evolutionary algorithms for regular lattices. IEEE Trans Evol Comput 9(5):489–505

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Zhang H, Song S, Zhou GXZ (2015) A multiobjective cellular genetic algorithm based on 3D structure and cosine crowding measurement. Int J Mach Learn Cybern 6:487–500

    Article  Google Scholar 

  21. Alba E, Dorronsoro B, Giacobini M, Tomassini M (2007) Decentralized cellular evolutionary algorithms, handbook of bioinspired algorithms and applications. pp 103–120

  22. He Z, Yen GG (2017) Many-objective evolutionary algorithms based on coordinated selection strategy. IEEE Trans Evol Comput 21(2):220–223

    Article  Google Scholar 

  23. Kirley M (2001) MEA: a metapopulation evolutionary algorithm for multi-objective optimisation problems. In:  Congress on evolutionary computation (CEC). IEEE Press, Piscataway, NJ, pp 949–956

  24. Murata T, Ishibuchi H, Gen M (2001) Specification of genetic search directions in cellular multi-objective genetic algorithms. In: Proceedings of the first international conference on evolutionary multi-criterion optimization (EMO). Zurich, Switzerland, pp 82–95

  25. Janson S, Alba E, Dorronsoro B, Middendorf M (2006) Hierarchical cellular genetic algorithm. In: Evolutionary computation in combinatorial optimization: 6th European conference. Springer, Berlin, pp 111–112

  26. Dorronsoro B, Bouvry P (2013) Cellular genetic algorithms without additional parameters. J Supercomput 63(3):816–835

    Article  Google Scholar 

  27. Alba E, Dorronsoro B, Luna F, Nebro AJ (2007) A cellular multi-objective genetic algorithm for optimal broadcasting strategy in metropolitan MANETs. Comput Commun 30(4):685–697

    Article  Google Scholar 

  28. Durillo JJ, Nebro AJ, Luna F, Alba E (2008) Solving three-objective optimization problems using a new hybrid cellular genetic algorithm. In: Rudolph G., Jansen T., Beume N., Lucas S., Poloni C. (eds) Proceedings of 10th international conference on parallel problem solving from Nature. Springer, Berlin, pp 661–670

  29. 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  Google Scholar 

  30. Jolai F, Assadipour G (2010) A hybrid cellular genetic algorithm for multi-objective crew scheduling problem. In: International conference on hybrid artificial intelligence systems. Springer, Berlin, pp 359–367

  31. Ruiz P, Dorronsoro B, Valentini G, Pinel F, Bouvry P (2012) Optimisation of the enhanced distance based broadcasting protocol for MANETs. J Supercomput 62(3):1213–1240

    Article  Google Scholar 

  32. Wang Y, Qian Q, Chen Y, Qian Q, Chen Y, Jin S, Wang W, Feng D (2017) Design and application of cellular differential algorithm based on complete feedback from external population. Comput Integr Manuf Syst 23(8):1679–1691

    Google Scholar 

  33. Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10(5):477–506

    Article  Google Scholar 

  34. Huband S, Barone L, While L, Hingston P (2005) A scalable multi-objective test problem toolkit. In: Third international conference on evolutionary multicriterion optimization (EMO). Springer, Berlin, pp 280–295

  35. Zitzler E, Thiele L, Laumanns M, Fonseca CM, Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132

    Article  Google Scholar 

  36. Wang YN, Wu LH, Yuan XF (2010) Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure. Soft Comput 14(3):193–209

    Article  Google Scholar 

  37. Wang J, Luo S, Su D (2016) Multi-objective optimal design of cycloid speed reducer based on genetic algorithm. Mech Mach Theory 102:135–148

    Article  Google Scholar 

  38. Liu Y, Lin Z, Zhao K, Ye J, Huang X (2020) Multiobjective gearshift optimization with leagendre pseudospectral method for seamless two-speed transmission. Mech Mach Theory 145:103682

    Article  Google Scholar 

  39. Gamperle R, Muller SD, Koumoutsakos P (2002) A parameter study for differential evolution. In: Advances in intelligent systems, fuzzy systems, evolutionary computation. Wseas Press, Greece, pp 293–298

  40. Rao ZG (1994) Designing of planetary gearing. National Defense Industry Press, Beijing (in Chinese)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R&D Program of China (No. 2018YFB1308100), the Natural Science Foundation of Zhejiang Province of China (No. LY16G010013), and the National High-Tech R&D Program of China (No. 2015AA043002).

Author information

Authors and Affiliations

  1. Key Laboratory of Special Purpose Equipment and Advanced Processing Technology, Ministry of Education, Zhejiang University of Technology, Hangzhou, China

    Yaliang Wang, Chendi Ni, Xinyu Fan, Qijing Qian & Shousong Jin

Authors
  1. Yaliang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chendi Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinyu Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qijing Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shousong Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yaliang Wang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Ni, C., Fan, X. et al. Cellular differential evolutionary algorithm with double-stage external population-leading and its application. Engineering with Computers 38 (Suppl 3), 2101–2120 (2022). https://doi.org/10.1007/s00366-021-01311-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01311-z

Keywords

Search

Navigation