IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3451-d1213636.html
   My bibliography  Save this article

A Symbolic Approach to Discrete Structural Optimization Using Quantum Annealing

Author

Listed:
  • Kevin Wils

    (Department of Aerospace Structures and Materials, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands)

  • Boyang Chen

    (Department of Aerospace Structures and Materials, Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands)

Abstract

With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem is the discrete truss sizing problem—the goal is to select the best size for each truss member so as to minimize a stress-based objective function. To make the problem compatible with quantum annealing devices, the objective function must be translated into a quadratic unconstrained binary optimization (QUBO) form. This work focuses on exploring the feasibility of making this translation. The practicality of using a quantum annealer for such optimization problems is also assessed. A method is eventually established to translate the objective function into a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger problems faces some challenges that would require further research to address.

Suggested Citation

  • Kevin Wils & Boyang Chen, 2023. "A Symbolic Approach to Discrete Structural Optimization Using Quantum Annealing," Mathematics, MDPI, vol. 11(16), pages 1-29, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3451-:d:1213636
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3451/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3451/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    2. M. W. Johnson & M. H. S. Amin & S. Gildert & T. Lanting & F. Hamze & N. Dickson & R. Harris & A. J. Berkley & J. Johansson & P. Bunyk & E. M. Chapple & C. Enderud & J. P. Hilton & K. Karimi & E. Ladiz, 2011. "Quantum annealing with manufactured spins," Nature, Nature, vol. 473(7346), pages 194-198, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabian Key & Lukas Freinberger, 2024. "A Formulation of Structural Design Optimization Problems for Quantum Annealing," Mathematics, MDPI, vol. 12(3), pages 1-18, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andreas Wichert, 2022. "Quantum Tree Search with Qiskit," Mathematics, MDPI, vol. 10(17), pages 1-28, August.
    2. Aufenanger, Tobias, 2018. "Treatment allocation for linear models," FAU Discussion Papers in Economics 14/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2018.
    3. Michele Samorani & Yang Wang & Yang Wang & Zhipeng Lv & Fred Glover, 2019. "Clustering-driven evolutionary algorithms: an application of path relinking to the quadratic unconstrained binary optimization problem," Journal of Heuristics, Springer, vol. 25(4), pages 629-642, October.
    4. Bahram Alidaee & Haibo Wang, 2017. "A note on heuristic approach based on UBQP formulation of the maximum diversity problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 102-110, January.
    5. Fred Glover & Jin-Kao Hao, 2016. "f-Flip strategies for unconstrained binary quadratic programming," Annals of Operations Research, Springer, vol. 238(1), pages 651-657, March.
    6. Yang Wang & Jin-Kao Hao & Fred Glover & Zhipeng Lü & Qinghua Wu, 2016. "Solving the maximum vertex weight clique problem via binary quadratic programming," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 531-549, August.
    7. Wang, Haibo & Alidaee, Bahram, 2019. "Effective heuristic for large-scale unrelated parallel machines scheduling problems," Omega, Elsevier, vol. 83(C), pages 261-274.
    8. Aritra Sarkar & Zaid Al-Ars & Koen Bertels, 2021. "QuASeR: Quantum Accelerated de novo DNA sequence reconstruction," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-23, April.
    9. Marcello Calvanese Strinati & Claudio Conti, 2022. "Multidimensional hyperspin machine," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    10. Fred Glover & Gary Kochenberger & Rick Hennig & Yu Du, 2022. "Quantum bridge analytics I: a tutorial on formulating and using QUBO models," Annals of Operations Research, Springer, vol. 314(1), pages 141-183, July.
    11. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.
    12. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    13. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    14. Mark W. Lewis & Amit Verma & Todd T. Eckdahl, 2021. "Qfold: a new modeling paradigm for the RNA folding problem," Journal of Heuristics, Springer, vol. 27(4), pages 695-717, August.
    15. Ricardo N. Liang & Eduardo A. J. Anacleto & Cláudio N. Meneses, 2022. "Data structures for speeding up Tabu Search when solving sparse quadratic unconstrained binary optimization problems," Journal of Heuristics, Springer, vol. 28(4), pages 433-479, August.
    16. Juntao Wang & Daniel Ebler & K. Y. Michael Wong & David Shui Wing Hui & Jie Sun, 2023. "Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    17. Leonardo Lozano & David Bergman & J. Cole Smith, 2020. "On the Consistent Path Problem," Operations Research, INFORMS, vol. 68(6), pages 1913-1931, November.
    18. Bin Yan & Nikolai A. Sinitsyn, 2022. "Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    19. Yitian Qian & Shaohua Pan & Shujun Bi, 2023. "A matrix nonconvex relaxation approach to unconstrained binary polynomial programs," Computational Optimization and Applications, Springer, vol. 84(3), pages 875-919, April.
    20. Fabian Böhm & Diego Alonso-Urquijo & Guy Verschaffelt & Guy Van der Sande, 2022. "Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning," Nature Communications, Nature, vol. 13(1), pages 1-13, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3451-:d:1213636. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.