Skip to main content

The Confidence Constraint: A Step Towards Stochastic CP Solvers

  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

  • 1550 Accesses

Abstract

We introduce the Confidence constraint, a chance constraint that ensures, with probability \(\gamma \), that a set of variables are no smaller than random variables for which the probability distribution is given. This constraint is useful in stochastic optimization to ensure that a solution is robust to external random events. It allows to control the trade-off between optimizing the objective function and ensuring the satisfiability of the solution under random parameters. We present a filtering algorithm for this constraint with explanations. We apply the constraint to a case study, an industrial scheduling problem where tasks have random processing times due to possible breakdowns during their execution. We evaluate our solutions with simulations and show that this new constraint allows robust solutions in decent computation time.

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

References

  1. Mercier-Aubin, A., Gaudreault, J., Quimper, C.G.: Leveraging constraint scheduling: a case study to the textile industry. In: 17th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Vienna, Austria. Springer, Heidelberg (2020)

    Google Scholar 

  2. Baptiste, P., Le Pape, C.: Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems. Constraints 5(1), 119–139 (2000). https://doi.org/10.1023/A:1009822502231

    Article  MathSciNet  MATH  Google Scholar 

  3. Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling. Kluwer Academic Publishers, Dordrecht (2001)

    Book  Google Scholar 

  4. Chakrabortty, R.K., Sarker, R.A., Essam, D.L.: Resource constrained project scheduling with uncertain activity durations. Comput. Ind. Eng. 112, 537–550 (2017)

    Article  Google Scholar 

  5. Chu, G., Stuckey, P.J., Schutt, A., Ehlers, T., Gange, G., Francis, K.: Chuffed, a lazy clause generation solver (2018)

    Google Scholar 

  6. Derrien, A., Petit, T., Zampelli, S.: A declarative paradigm for robust cumulative scheduling. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 298–306. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_23

    Chapter  Google Scholar 

  7. Fahimi, H.: Efficient algorithms to solve scheduling problems with a variety of optimization criteria. Ph.D. thesis, Université Laval (2016)

    Google Scholar 

  8. Grimmett, G., Welsh, D.: Probability: An Introduction. Oxford University Press, Oxford (2014)

    MATH  Google Scholar 

  9. Hebrard, E., Walsh, T.: Improved algorithm for finding (a,b)-super solutions. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, p. 848. Springer, Heidelberg (2005). https://doi.org/10.1007/11564751_86

    Chapter  Google Scholar 

  10. Kall, P., Mayer, J.: Stochastic Linear Programming. Springer, Boston (2011). https://doi.org/10.1007/978-1-4419-7729-8

    Book  MATH  Google Scholar 

  11. Lombardi, M., Milano, M.: A precedence constraint posting approach for the RCPSP with time lags and variable durations. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 569–583. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04244-7_45

    Chapter  Google Scholar 

  12. Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74970-7_38

    Chapter  Google Scholar 

  13. Rendl, A., Tack, G., Stuckey, P.J.: Stochastic MiniZinc. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 636–645. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_46

    Chapter  Google Scholar 

  14. Rossi, R., Tarim, S., Hnich, B., Pestwich, S.: A global chance-constraint for stochastic inventory systems under service level constraints. Constraints 13(4), 490–517 (2008). https://doi.org/10.1007/s10601-007-9038-4

    Article  MathSciNet  MATH  Google Scholar 

  15. Schling, B.: The Boost C++ Libraries. XML Press, Laguna Hills (2011)

    Google Scholar 

  16. Shishmarev, M., Mears, C., Tack, G., Garcia de la Banda, M.: Learning from learning solvers. In: Rueher, M. (ed.) CP 2016. LNCS, vol. 9892, pp. 455–472. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44953-1_29

    Chapter  Google Scholar 

  17. Stuckey, P.J., Feydy, T., Schutt, A., Tack, G., Fischer, J.: The minizinc challenge 2008–2013. AI Mag. 35(2), 55–60 (2014)

    Article  Google Scholar 

  18. Walsh, T.: Stochastic constraint programming. In: Proceedings of the 15th European Conference on Artificial Intelligence (ECAI-2002), pp. 111–115 (2009)

    Google Scholar 

  19. Zaayman, G., Innamorato, A.: The application of simio scheduling in industry 4.0. In: 2017 Winter Simulation Conference (WSC), pp. 4425–4434 (2017)

    Google Scholar 

  20. Zghidi, I., Hnich, B., Rebaï, A.: Modeling uncertainties with chance constraints. Constraints 23(2), 196–209 (2018). https://doi.org/10.1007/s10601-018-9283-8

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexandre Mercier-Aubin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mercier-Aubin, A., Dumetz, L., Gaudreault, J., Quimper, CG. (2020). The Confidence Constraint: A Step Towards Stochastic CP Solvers. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-58475-7_44

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58474-0

  • Online ISBN: 978-3-030-58475-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics