Skip to main content

Multimodal Container Planning: A QUBO Formulation and Implementation on a Quantum Annealer

  • Conference paper
  • First Online:
Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12747))

Included in the following conference series:

Abstract

Quantum computing is developing fast. Real world applications are within reach in the coming years. One of the most promising areas is combinatorial optimisation, where the Quadratic Unconstrained Binary Optimisation (QUBO) problem formulation is used to get good approximate solutions. Both the universal quantum computer as well as the quantum annealer can handle this kind of problems well. In this paper, we present an application on multimodal container planning. We show how to map this problem to a QUBO problem formulation and how the practical implementation can be done on the quantum annealer produced by D-Wave Systems.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://www.dwavesys.com/news/d-wave-systems-sells-its-first-quantum-computing-system-lockheed-martin-corporation.

  2. 2.

    https://www.dwavesys.com/press-releases/d-wave%C2%A0announces%C2%A0d-wave-2000q-quantum-computer-and-first-system-order.

  3. 3.

    https://www.dwavesys.com/press-releases/d-wave-previews-next-generation-quantum-computing-platform.

  4. 4.

    https://support.dwavesys.com/hc/en-us/community/posts/360034852633-High-Chain-Break-Fractions.

  5. 5.

    We used the D-Wave 2000 system. Only recently, D-Wave presented the 5000 qubit version.

References

  1. Andersen, J., Crainic, T.G., Christiansen, M.: Service network design with management and coordination of multiple fleets. Eur. J. Oper. Res. 193(2), 377–389 (2009)

    Article  MathSciNet  Google Scholar 

  2. Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

    Article  Google Scholar 

  3. Booth, M., Reinhardt, S.P., Roy, A.: Partitioning optimization problems for hybrid classical/quantum execution. Technical report, D-Wave Systems (September 2017)

    Google Scholar 

  4. Cao, Y., Jiang, S., Perouli, D., Kais, S.: Solving set cover with pairs problem using quantum annealing. Sci. Rep. 6(1), 33957 (2016)

    Article  Google Scholar 

  5. Chapuis, G., Djidjev, H., Hahn, G., Rizk, G.: Finding maximum cliques on the d-wave quantum annealer. J. Sig. Process. Syst. 91(3–4), 363–377 (2018)

    Google Scholar 

  6. Chiscop, I., Nauta, J., Veerman, B., Phillipson, F.: A hybrid solution method for the multi-service location set covering problem. In: International Conference On Computational Science (ICCS) (2020)

    Google Scholar 

  7. Coffrin, C.J.: Challenges with chains: Testing the limits of a d-wave quantum annealer for discrete optimization. Technical report, Los Alamos National Laboratory, U.S. (2019)

    Google Scholar 

  8. De Juncker, M.A.M., Huizing, D., del Vecchyo, M.R.O., Phillipson, F., Sangers, A.: Framework of synchromodal transportation problems. ICCL 2017. LNCS, vol. 10572, pp. 383–403. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68496-3_26

    Chapter  Google Scholar 

  9. Ding, B., Yu, J.X., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proceedings of the 11th International Conference on Extending Database Technology: Advances in Database Technology, pp. 205–216. ACM (2008)

    Google Scholar 

  10. Even, S., Itai, A., Shamir, A.: On the complexity of time table and multi-commodity flow problems. In: 16th Annual Symposium on Foundations of Computer Science, SFCS 1975, pp. 184–193. IEEE (1975)

    Google Scholar 

  11. Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014)

  12. Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106v1 (2000)

  13. Feld, S., et al.: A hybrid solution method for the capacitated vehicle routing problem using a quantum annealer. Front. ICT 6, 13 (2019)

    Article  Google Scholar 

  14. Foster, R.C., Weaver, B., Gattiker, J.: Applications of quantum annealing in statistics. arXiv preprint arXiv:1904.06819 (2019)

  15. Glover, F., Kochenberger, G., Du, Y.: A tutorial on formulating and using QUBO models. arXiv preprint arXiv:1811.11538 (2018)

  16. Huizing, D.: General methods for synchromodal planning of freight containers and transports. Master’s thesis, Delft University of Technology, The Netherlands (2017)

    Google Scholar 

  17. Jiang, S., Britt, K.A., McCaskey, A.J., Humble, T.S., Kais, S.: Quantum annealing for prime factorization. Sci. Rep. 8(1), 17667 (2018)

    Article  Google Scholar 

  18. Johnson, M.W., et al.: Quantum annealing with manufactured spins. Nature 473(7346), 194–198 (2011)

    Article  Google Scholar 

  19. Kalicharan, K., Phillipson, F., Sangers, A., De Juncker, M.: Reduction of variables for solving logistic flow problems. In: 2019 6th International Physical Internet Conference (IPIC) (2019)

    Google Scholar 

  20. Lucas, A.: Ising formulations of many NP problems. Front. Phys. 2, 5 (2014)

    Article  Google Scholar 

  21. McGeoch, C.C.: Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice. Synthesis Lectures on Quantum Computing, vol. 5, no. 2, pp. 1–93 (2014)

    Google Scholar 

  22. Mes, M.R.K., Iacob, M.E.: Synchromodal transport planning at a logistics service provider. In: Zijm, H., Klumpp, M., Clausen, U., Hompel, M. (eds.) Logistics and Supply Chain Innovation. Lecture Notes in Logistics. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-22288-2_2

  23. Neukart, F., Compostella, G., Seidel, C., Dollen, D.V., Yarkoni, S., Parney, B.: Traffic flow optimization using a quantum annealer. Front. ICT 4, 29 (2017)

    Article  Google Scholar 

  24. Pelofske, E., Hahn, G., Djidjev, H.: Solving large minimum vertex cover problems on a quantum annealer. In: Proceedings of the 16th ACM International Conference on Computing Frontiers, CF 2019, pp. 76–84. ACM, New York (2019)

    Google Scholar 

  25. Piattini, M., et al.: The Talavera manifesto for quantum software engineering and programming. In: Proceedings of the 1st QANSWER Workshop (2020)

    Google Scholar 

  26. Rieffel, E.G., Venturelli, D., O’Gorman, B., Do, M.B., Prystay, E.M., Smelyanskiy, V.N.: A case study in programming a quantum annealer for hard operational planning problems. Quantum Inf. Process. 14(1), 1–36 (2014). https://doi.org/10.1007/s11128-014-0892-x

    Article  MATH  Google Scholar 

  27. van Riessen, B., Negenborn, R.R., Dekker, R.: Synchromodal container transportation: an overview of current topics and research opportunities. In: Corman, F., Voß, S., Negenborn, R.R. (eds.) ICCL 2015. LNCS, vol. 9335, pp. 386–397. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24264-4_27

    Chapter  Google Scholar 

  28. SteadieSeifi, M., Dellaert, N.P., Nuijten, W., Van Woensel, T., Raoufi, R.: Multimodal freight transportation planning: a literature review. Eur. J. Oper. Res. 233(1), 1–15 (2014)

    Article  Google Scholar 

  29. Zweers, B.G., Bhulai, S., van der Mei, R.D.: Optimizing barge utilization in hinterland container transportation. Nav. Res. Logistics (NRL) 66(3), 253–271 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. Phillipson .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Phillipson, F., Chiscop, I. (2021). Multimodal Container Planning: A QUBO Formulation and Implementation on a Quantum Annealer. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham. https://doi.org/10.1007/978-3-030-77980-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-77980-1_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77979-5

  • Online ISBN: 978-3-030-77980-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics