Skip to main content

Alternating Direction Method and Deep Learning for Discrete Control with Storage

  • Conference paper
  • First Online:
Combinatorial Optimization (ISCO 2024)

Abstract

This paper deals with scheduling the operations in systems with storage modeled as a mixed integer nonlinear program (MINLP). Due to time interdependency induced by storage, discrete control, and nonlinear operational conditions, computing even a feasible solution may require an unaffordable computational burden. We exploit a property common to a broad class of these problems to devise a decomposition algorithm related to alternating direction methods, which progressively adjusts the operations to the storage state profile. We also design a deep learning model to predict the continuous storage states to start the algorithm instead of the discrete decisions, as commonly done in the literature. This enables search diversification through a multi-start mechanism and prediction using scaling in the absence of a training set. Numerical experiments on the pump scheduling problem in water networks show the effectiveness of this hybrid learning/decomposition algorithm in computing near-optimal strict-feasible solutions in more reasonable times than other approaches.

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

Access this chapter

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

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    https://github.com/sofdem/gopslpnlpbb.

References

  1. Bonvin, G., Demassey, S.: Extended linear formulation of the pump scheduling problem in water distribution networks. In: 9th International Network Optimization Conference, pp. 13–18 (2019)

    Google Scholar 

  2. Bonvin, G., Demassey, S., Lodi, A.: Pump scheduling in drinking water distribution networks with an LP/NLP-based B &B. Optim. Engin. 22, 1275–1313 (2021)

    Article  Google Scholar 

  3. Borovykh, A., Bohte, S., Oosterlee, C.W.: Conditional time series forecasting with convolutional neural networks. preprint: arXiv:1703.04691 (2017)

  4. Demassey, S., Sessa, V., Tavakoli, A.: Strengthening mathematical models for pump scheduling in water distribution. In: 14th International Conference on Applied Energy (2022)

    Google Scholar 

  5. Ding, J.Y., et al.: Accelerating primal solution findings for mixed integer programs based on solution prediction. In: AAAI Conference on Artificial Intelligence, vol. 34, pp. 1452–1459 (2020)

    Google Scholar 

  6. Gal, Y., Ghahramani, Z.: Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In: 33rd International Conference Machine Learning, vol. 48, pp. 1050–1059 (2016)

    Google Scholar 

  7. Geißler, B., Morsi, A., Schewe, L., Schmidt, M.: Penalty alternating direction methods for mixed-integer optimization: a new view on feasibility pumps. SIAM J. Optim. 27(3), 1611–1636 (2017)

    Article  MathSciNet  Google Scholar 

  8. Ghaddar, B., Naoum-Sawaya, J., Kishimoto, A., Taheri, N., Eck, B.: A Lagrangian decomposition approach for the pump scheduling problem in water networks. Eur. J. Oper. Res. 241(2), 490–501 (2015)

    Article  MathSciNet  Google Scholar 

  9. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016). http://www.deeplearningbook.org

  10. Gorski, J., Pfeuffer, F., Klamroth, K.: Biconvex sets and optimization with biconvex functions: a survey and extensions. Math. Meth. Oper. Res. 66, 373–407 (2007)

    Article  MathSciNet  Google Scholar 

  11. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. preprint: arXiv:1412.6980 (2014)

  12. Kleinert, T., Schmidt, M.: Computing feasible points of bilevel problems with a penalty alternating direction method. INFORMS J. Comput. 33, 198–215 (2020)

    Article  MathSciNet  Google Scholar 

  13. Kool, W., Van Hoof, H., Welling, M.: Attention, learn to solve routing problems! preprint: arXiv:1803.08475 (2018)

  14. Mackle, G.: Application of genetic algorithms to pump scheduling for water supply. In: International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, pp. 400–405 (1995)

    Google Scholar 

  15. Naoum-Sawaya, J., Ghaddar, B., Arandia, E., Eck, B.: Simulation-optimization approaches for water pump scheduling and pipe replacement problems. Eur. J. Oper. Res. 246, 293–306 (2015)

    Article  Google Scholar 

  16. Rockafellar, R.T.: Network Flows and Monotropic Optimization. Athena Scientific, Nashua (1999)

    Google Scholar 

  17. Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(1), 1929–1958 (2014)

    MathSciNet  Google Scholar 

  18. Todini, E., Pilati, S.: A gradient algorithm for the analysis of pipe networks. In: Computer Applications in Water Supply, vol. 1. Research Studies Press Ltd. (1988)

    Google Scholar 

  19. Van Zyl, J.E., Savic, D.A., Walters, G.A.: Operational optimization of water distribution systems using a hybrid genetic algorithm. J. Water Res. Plan. Manage. 130(2), 160–170 (2004)

    Article  Google Scholar 

  20. Wang, Y., Yin, W., Zeng, J.: Global convergence of ADMM in nonconvex Nonsmooth optimization. J. Sci. Comput. 78, 29–63 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgement

This work is supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sophie Demassey .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Demassey, S., Sessa, V., Tavakoli, A. (2024). Alternating Direction Method and Deep Learning for Discrete Control with Storage. In: Basu, A., Mahjoub, A.R., Salazar González, J.J. (eds) Combinatorial Optimization. ISCO 2024. Lecture Notes in Computer Science, vol 14594. Springer, Cham. https://doi.org/10.1007/978-3-031-60924-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-60924-4_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-60923-7

  • Online ISBN: 978-3-031-60924-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics