Skip to main content
Log in

Many-objective evolutionary algorithms based on reference-point-selection strategy for application in reactor radiation-shielding design

  • Published:
Nuclear Science and Techniques Aims and scope Submit manuscript

Abstract

In recent years, the development of new types of nuclear reactors, such as transportable, marine, and space reactors, has presented new challenges for the optimization of reactor radiation-shielding design. Shielding structures typically need to be lightweight, miniaturized, and radiation-protected, which is a multi-parameter and multi-objective optimization problem. The conventional multi-objective (two or three objectives) optimization method for radiation-shielding design exhibits limitations for a number of optimization objectives and variable parameters, as well as a deficiency in achieving a global optimal solution, thereby failing to meet the requirements of shielding optimization for newly developed reactors. In this study, genetic and artificial bee-colony algorithms are combined with a reference-point-selection strategy and applied to the many-objective (having four or more objectives) optimal design of reactor radiation shielding. To validate the reliability of the methods, an optimization simulation is conducted on three-dimensional shielding structures and another complicated shielding-optimization problem. The numerical results demonstrate that the proposed algorithms outperform conventional shielding-design methods in terms of optimization performance, and they exhibit their reliability in practical engineering problems. The many-objective optimization algorithms developed in this study are proven to efficiently and consistently search for Pareto-front shielding schemes. Therefore, the algorithms proposed in this study offer novel insights into improving the shielding-design performance and shielding quality of new reactor types.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
€34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

Data availability

The data that support the findings of this study are openly available in Science Data Bank at https://cstr.cn/31253.11.sciencedb.j00186.00575 and https://doi.org/10.57760/sciencedb.j00186.00575.

References

  1. Y. Chen, B. Yan, The technology of shielding design for nuclear reactor: a review. Prog. Nucl. Energ. 161, 104741 (2023). https://doi.org/10.1016/j.pnucene.2023.104741

    Article  Google Scholar 

  2. N.M. Schaeffer, Reactor Shielding for Nuclear Engineers (US Atomic Energy Commission Office of Information Services, 1983). https://doi.org/10.2172/4479460

    Book  Google Scholar 

  3. S.F. Demuth, SP100 space reactor design. Prog. Nucl. Energ. 42(3), 323–59 (2003). https://doi.org/10.1016/S0149-1970(03)90003-5

    Article  Google Scholar 

  4. Y. Wang, Y. Tao, Y. Tao et al., Shielding design of a megawatt-scale heat pipe reactor core. Nucl. Tech. (in Chinese) 46(02), 020606 (2023). https://doi.org/10.11889/j.0253-3219.2023.hjs.46.020606.

    Article  Google Scholar 

  5. M.A. Sazali, N. Rashid, K. Hamzah, A preliminary study to metaheuristic approach in multilayer radiation shielding optimization. Mater. Sci. Eng. 298(1), 012042 (2018). https://doi.org/10.1088/1757-899X/298/1/012042/meta

    Article  Google Scholar 

  6. B.S. Skim, J.H. Moon, Use of a genetic algorithm in the search for a near-optimal shielding design. Ann. Nucl. Energy 37(2), 120–129 (2010). https://doi.org/10.1016/j.anucene.2009.11.014

    Article  Google Scholar 

  7. S. Zheng, Q. Pan, H. Lv et al., Semi-empirical and semi-quantitative lightweight shielding design method. Nucl. Sci. Tech. 34(3), 43 (2023). https://doi.org/10.1007/s41365-023-01187-2

    Article  Google Scholar 

  8. Z. Chen, Z. Zhang, J. Xie et al., Metaheuristic optimization method for compact reactor radiation shielding design based on genetic algorithm. Ann. Nucl. Energy 134, 318–329 (2019). https://doi.org/10.1016/j.anucene.2019.06.031

    Article  Google Scholar 

  9. J. Lei, C. Yang, H. Zhang et al., Radiation shielding optimization design research based on bare-bones particle swarm optimization algorithm. Nucl. Eng. Technol. 55(6), 2215–2221 (2023). https://doi.org/10.1016/j.net.2023.02.018

    Article  Google Scholar 

  10. Y. Song, J. Mao, Z. Zhang et al., A novel multi-objective shielding optimization method: DNN-PCA-NSGA-II. Ann. Nucl. Energy 161, 108461 (2021). https://doi.org/10.1016/j.anucene.2021.108461

    Article  Google Scholar 

  11. Z. Chen, Z. Zhang, J. Xie et al., Multi-objective optimization strategies for radiation shielding design with genetic algorithm. Comput. Phys. Commun. 260, 107267 (2021). https://doi.org/10.1016/j.cpc.2020.107267

    Article  MathSciNet  Google Scholar 

  12. C. He, X. Qiu, Z. Sun et al., Radiation shielding optimization of space reactor based on intelligent decision support system. Nucl. Tech. (in Chinese) 45(05), 050601 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.050601.

    Article  Google Scholar 

  13. K. Li, R. Wang, T. Zhang et al., Evolutionary many-objective optimization: A comparative study of the state-of-the-art. IEEE Access 6, 26194–26214 (2018). https://doi.org/10.1109/ACCESS.2018.2832181

    Article  Google Scholar 

  14. H. Chen, Y. Tian, W. Pedrycz et al., Hyperplane assisted evolutionary algorithm for many-objective optimization problems. IEEE T. Cybernetics. 50(7), 3367–3380 (2020). https://doi.org/10.1109/TCYB.2019.2899225

    Article  Google Scholar 

  15. K. Li, K. Deb, Q. Zhang et al., An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE T. Evolut. Comput. 19(5), 694–716 (2014). https://doi.org/10.1109/TEVC.2014.2373386

    Article  Google Scholar 

  16. H. Ishibuchi, N. Tsukamoto, Y. Nojima, Evolutionary many-objective optimization: A short review. IEEE C. Evol. Computat. pp. 2419-2426 (2008). https://doi.org/10.1109/CEC.2008.4631121

    Article  Google Scholar 

  17. G. Hu, H. Hu, Q. Yang et al., Study on the design and experimental verification of multilayer radiation shield against mixed neutrons and \(\gamma\)-rays. Nucl. Eng. Technol. 52(1), 178–184 (2020). https://doi.org/10.1016/j.net.2019.07.016

    Article  Google Scholar 

  18. H.O. Tekin, T. Manici, Simulations of mass attenuation coefficients for shielding materials using the MCNP-X code. Nucl. Sci. Tech. 28, 95 (2017). https://doi.org/10.1007/s41365-017-0253-4

    Article  Google Scholar 

  19. J. Zhou, Q. Zeng, Y. Xiong et al., Research on the shielding performance and optimization of new type foam metal matrix composite shielding materials. Nucl. Instrum. Meth. B. 516, 31–37 (2022). https://doi.org/10.1016/j.nimb.2022.02.005

    Article  ADS  Google Scholar 

  20. Y. Tian, X. Zhang, R. Cheng et al., Guiding evolutionary multiobjective optimization with generic front modeling. IEEE T. Cybernetics. 50, 1106–1119 (2020). https://doi.org/10.1109/TCYB.2018.2883914

    Article  Google Scholar 

  21. F. Chen, G. Li, M. Yang, Y. Han, R. Liang, Optimization research on neutron shielding material component based on genetic algorithm. Radiat. Prot. 40(1), 38–44 (2020). (in Chinese)

    Google Scholar 

  22. Y. Li, T. Yu, Z. Chen et al., Development and verification of radiation shielding optimization design platform for marine reactor. Nuclear Power Eng. 43(1), 221–228 (2022). https://doi.org/10.13832/j.jnpe.2022.01.0208 (in Chinese)

    Article  Google Scholar 

  23. L. Kuang, T. Yu, Z. Chen et al., CAD-based inversion visualization of monte Carlo Computational model based on SALOME. High Power Laser Particle Beams. 35(03), 168–174 (2023). https://doi.org/10.11884/HPLPB202335.220276 (in Chinese)

    Article  Google Scholar 

  24. Y. Hu, Y. Qiu, U. Fischer, Development and benchmarking of the Weight Window Mesh function for OpenMC. Fusion Eng. Des. 170, 112551 (2021). https://doi.org/10.1016/j.fusengdes.2021.112551

    Article  Google Scholar 

  25. I. Das, J.E. Dennis, Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. Siam. J. Optimiz. 134, 631–657 (1998). https://doi.org/10.1137/S1052623496307510

    Article  MathSciNet  Google Scholar 

  26. K. Deb, A. Pratap, S. Agarwal et al., A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE T. Evolue. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017

    Article  Google Scholar 

  27. K.S. Tang, K.F. Man, S. Kwong et al., Genetic algorithms and their applications. IEEE Signal. Proc. Mag. 13(6), 22–37 (1996). https://doi.org/10.1109/79.543973

    Article  ADS  Google Scholar 

  28. H. Zhang, Z. Chen, C. Liu et al., Study on many-objective optimization method for reactor 3D shielding structure based on genetic algorithm. Nucl. Tech. (in Chinese) 45(11), 110603 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.110603

    Article  Google Scholar 

  29. Y. Xiang, Y. Zhou, H. Liu, An elitism based multi-objective artificial bee colony algorithm. Eur. J. Oper. Re. 245(1), 168–193 (2015). https://doi.org/10.1016/j.ejor.2015.03.005

    Article  ADS  Google Scholar 

  30. R. Akbari, R. Hedayatzadeh, K. Ziarati et al., A multi-objective artificial bee colony algorithm. Swarm Evol. Comput. 2, 39–52 (2012). https://doi.org/10.1016/j.swevo.2011.08.001

    Article  Google Scholar 

  31. F. Neri, V. Tirronen, Recent advances in differential evolution: a survey and experimental analysis. Artif. Intell. Rev. 33, 61–106 (2010). https://doi.org/10.1007/s10462-009-9137-2

    Article  Google Scholar 

  32. E. Tanyildizi, G. Demir, Golden sine algorithm: A novel math-inspired algorithm. Adv. Electr. Comput. En. 17, 71–78 (2017). https://doi.org/10.4316/AECE.2017.02010

    Article  Google Scholar 

  33. Q. He, L. Wang, A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl. Math. Comput. 186(2), 1407–1422 (2007). https://doi.org/10.1016/j.amc.2006.07.134

    Article  MathSciNet  Google Scholar 

  34. H. Jain, K. Deb, An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach. Ieee. T. Evolue. Comput. 18(4), 602–622 (2013). https://doi.org/10.1109/TEVC.2013.2281534

    Article  Google Scholar 

  35. K. Deb, H. Jain, An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE T. Evolue. Comput. 18(4), 577–601 (2013). https://doi.org/10.1109/TEVC.2013.2281535

    Article  Google Scholar 

  36. D.A. Browm, M.B. Chadwick, R. Capote et al., ENDF/B-VIII. 0: the 8th major release of the nuclear reaction data library with CIELO-project cross sections, new standards and thermal scattering data. Nucl. Data Sheets 148, 1–142 (2018). https://doi.org/10.1016/j.nds.2018.02.001

    Article  ADS  Google Scholar 

  37. Y. Harima, An historical review and current status of buildup factor calculations and applications. Radiat. Phys. Chem. 41, 631–672 (1993). https://doi.org/10.1016/0969-806X(93)90317-N

    Article  ADS  Google Scholar 

  38. A. Sun, Z. Chen, T. Yu et al., Development and verification of a monte carlo calculation program magic for dose of boron neutron capture therapy. Modern Appl. Phys. 14(04), 41–48 (2023). https://doi.org/10.12061/j.issn.2095-6223.2023.040202 (in Chinese)

    Article  Google Scholar 

  39. Z. Yang, H. Wang, K. Yang, SMS-EMOA: Multiobjective selection based on dominated hypervolume. IEEE World Cong. Comput. Intel. pp. 282–288 (2016). https://doi.org/10.1109/FSKD.2016.7603187

    Article  Google Scholar 

  40. Q. Pan, N. An, T. Zhang et al., Single-step Monte Carlo criticality algorithm. Comput. Phys. Commun. 279, 108439 (2022). https://doi.org/10.1016/j.cpc.2022.108439

    Article  MathSciNet  Google Scholar 

  41. Q. Pan, H. Lv, S. Tang et al., Pointing probability driven semi-analytic Monte Carlo method (PDMC)-Part I: global variance reduction for large-scale radiation transport analysis. Comput. Phys. Commun. 291, 108850 (2023). https://doi.org/10.1016/j.cpc.2023.108850

    Article  Google Scholar 

  42. Q. Pan, T. Zhang, X. Liu et al., SP3-coupled global variance reduction method based on RMC code. Nucl. Sci. Tech. 32, 122 (2021). https://doi.org/10.1007/s41365-021-00973-0

    Article  Google Scholar 

  43. L. Li, S. Jiang, Z. Chen et al., Mesh-based activation analysis for structural materials in nuclear reactor. Nucl. Tech. (in Chinese) 45(08), 080601 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.080601.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Cheng-Wei Liu, Ai-Kou Sun, Hong-Yu Qu, and Zhen-Ping Chen. The first draft of the manuscript was written by Cheng-Wei Liu, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Zhen-Ping Chen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 12475174 and 12175101) and YueLuShan Center Industrial Innovation (No. 2024YCII0108).

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

Liu, CW., Sun, AK., Lei, JC. et al. Many-objective evolutionary algorithms based on reference-point-selection strategy for application in reactor radiation-shielding design. NUCL SCI TECH 36, 105 (2025). https://doi.org/10.1007/s41365-025-01683-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41365-025-01683-7

Keywords