Skip to main content
SpringerLink
Log in

A hybrid machine learning and evolutionary approach to material selection and design optimization for eco-friendly structures

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In an increasingly competitive and digital industrial environment, the optimization of structures is a key point not only to reduce costs but also to reduce the consumption of natural resources. To this end, different approaches have emerged throughout history based on the tools available at the time. With the current rise of artificial intelligence and the concept of machine learning, revolutionary ideas are emerging that allow an optimal dimensioning of structures in record time. This work presents the use of variational autoencoders and mixed-variable solvers as a proposal for structural optimization and material selection. It has expanded upon previous research by advancing in three directions: (1) incorporating more material attributes, particularly relevant for environmental considerations; (2) analyzing in more detail aspects of VAEs such as the dimensionality of the latent space; and (3) a two-step hybrid approach to select the optimal candidate: preliminary filtering with VAE and final design via mixed-variable model. Various examples demonstrate the applicability of the proposed method.

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
Algorithm 1
Algorithm 2
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Algorithm 3
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Ashby MF (2011) Material selection in mechanical design. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Barjhoux P-J, Diouane Y, Grihon S, Bettebghor D, Morlier J (2020) A bi-level methodology for solving large-scale mixed categorical structural optimization. Struct Multidisc Optim 62(1):337–351

    Article  MathSciNet  Google Scholar 

  • Barjhoux P-J, Diouane Y, Grihon S, Morlier J (2022) An outer approximation bi-level framework for mixed categorical structural optimization problems. Struct Multidisc Optim 65(8):214

    Article  MathSciNet  Google Scholar 

  • Blank J, Deb K (2020) Pymoo: multi-objective optimization in python. IEEE Access 8:89497–89509

    Article  Google Scholar 

  • Burda Y, Grosse R, Salakhutdinov R (2015) Importance weighted autoencoders. arXiv Preprint. arXiv:1509.00519

  • Chandrasekhar A, Sridhara S, Suresh K (2022) Integrating material selection with design optimization via neural networks. Eng Comput 38(5):4715–4730

    Article  Google Scholar 

  • Ching E, Carstensen JV (2022) Truss topology optimization of timber–steel structures for reduced embodied carbon design. Eng Struct 252:113540

    Article  Google Scholar 

  • Diederik PK, Ba JL (2015) Adam: a method for stochastic optimization. In: ICLR 2015—conference track proceedings. International conference on learning representations

  • Diederik PK, Welling M (2013) Auto-encoding variational bayes. arXiv Preprint. http://arxiv.org/abs/1312.6114

  • Duriez E, Morlier J, Azzaro-Pantel C, Charlotte M (2022) Ecodesign with topology optimization. Procedia CIRP 109:454–459

    Article  Google Scholar 

  • Duriez E, Azzaro-Pantel C, Morlier J, Charlotte M (2023a) A fast method of material, design and process eco-selection via topology optimization, for additive manufactured structures. Clean Environ Syst 9:100114

    Article  Google Scholar 

  • Duriez E, Martín VMG, Joseph M (2023b) CO2 footprint minimization of solar-powered hale using MDO and eco-material selection. Sci Rep 13(1):11994

    Article  Google Scholar 

  • Eggert R (2005) Engineering design. Pearson/Prentice Hall, Upper Saddle River

    Google Scholar 

  • GitHub code: structural material selection using deep learning. https://github.com/mid2SUPAERO/HybML-EvoMatDesEco. Accessed 16 Aug 2023

  • Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge

    Google Scholar 

  • Jahan A, Ismail MY, Sapuan SM, Mustapha F (2010) Material screening and choosing methods—a review. Mater Des 31(2):696–705

    Article  Google Scholar 

  • Kingma DP, Welling M. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114

  • Kingma DP, Welling M et al (2019) An introduction to variational autoencoders. Found Trends® Mach Learn 12(4):307–392

    Article  Google Scholar 

  • Manson JA, Chamberlain TW, Bourne RA (2021) MVMOO: mixed variable multi-objective optimisation. J Glob Optim 80(4):865–886

    Article  MathSciNet  Google Scholar 

  • NSGA-II: non-dominated sorting genetic algorithm. https://pymoo.org/algorithms/moo/nsga2.html. Accessed 29 July 2023

  • Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A (2019) PyTorch: an imperative style, high-performance deep learning library. In: Advances in neural information processing systems, 32

  • Rakshit S, Ananthasuresh GK (2008) Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization. Struct Multidisc Optim 35:55–68

    Article  Google Scholar 

  • Tawarmalani M, Sahinidis NV (2005) A polyhedral branch-and-cut approach to global optimization. Math Progr 103(2):225–249

    Article  MathSciNet  Google Scholar 

  • Venkata Rao R (2006) A material selection model using graph theory and matrix approach. Mater Sci Eng A 431(1–2):248–255

    Google Scholar 

  • Zhou C-C, Yin G-F, Xiao-Bing H (2009) Multi-objective optimization of material selection for sustainable products: artificial neural networks and genetic algorithm approach. Mater Des 30(4):1209–1215

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the assistance from Associate Professor Israel G. García, Departamento de Mecánica de Medios Continuos y Teoría de Estructuras, E.T.S. Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n,41092, Seville, Spain

Author information

Authors and Affiliations

  1. ICA, Université de Toulouse, ISAE-SUPAERO, MINES ALBI, UPS, INSA, CNRS, Toulouse, France

    Joseph Morlier

  2. ISAE-SUPAERO, Université de Toulouse, Toulouse, France

    Luis Yepes Llorente

  3. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, USA

    Saketh Sridhara & Krishnan Suresh

Authors
  1. Luis Yepes Llorente
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph Morlier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saketh Sridhara
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Krishnan Suresh
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.M. devised the original research project and proposed the global methodology. L.Y.L. designed the computational framework and analyzed the data. L.Y.L. wrote the draft manuscript with the inputs from all authors. K.S and S.S. revised the draft manuscript and proposed additional experiments: three dimensions and latent space of environmental attributes. All authors reviewed the results and approved the final version of the manuscript.

Corresponding author

Correspondence to Joseph Morlier.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Replication of results

https://github.com/mid2SUPAERO/HybML-EvoMatDesEco.

Additional information

Responsible Editor: Zequn Wang

Publisher's Note

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

Appendices

Appendix A: Annexed figures

See Figs. 22 and 23.

Fig. 22
figure 22

Comparison in the distribution of yield strength values in the latent space for different numbers of neurons

Full size image
Fig. 23
figure 23

Material representation in a two-dimensional latent space comparison for different values of \(\beta \) parameter. Note that the map enlarges

Full size image

Appendix B: annexed tables

See Tables 11, 12, and 13.

Table 11 Comparison of error for different values of the \(\beta \) parameter
Full size table
Table 12 Available objective functions
Full size table
Table 13 Available constraints
Full size table

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

Yepes Llorente, L., Morlier, J., Sridhara, S. et al. A hybrid machine learning and evolutionary approach to material selection and design optimization for eco-friendly structures. Struct Multidisc Optim 67, 69 (2024). https://doi.org/10.1007/s00158-024-03777-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00158-024-03777-z

Keywords

Search

Navigation