Skip to main content
SpringerLink
Log in

Transferring Information Across Restarts in MIP

  • Conference paper
  • First Online:
Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13292))

Abstract

Restarting a solver gives us the chance to learn from things that went good or bad in the search until the restart point. The benefits of restarts are often justified with being able to employ different, better strategies and explore different, more promising parts of the search space. In that light, it is an interesting question to evaluate whether carrying over detected structures and collected statistics across a restart benefits the subsequent search, or even counteracts the anticipated diversification from the previous, unsuccessful search.

In this paper, we will discuss four different types of global information that can potentially be re-used after a restart of a mixed-integer programming (MIP) solver, present technical details of how to carry them through a represolve after a restart, and show how such an information transfer can help to speed up the state-of-the-art commercial MIP solver FICO Xpress by 7% on the instances where a restart is performed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

References

  1. Achterberg, T.: Conflict analysis in mixed integer programming. Discrete Optim. 4(1), 4–20 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Achterberg, T.: Constraint integer programming. Ph.D. thesis, Technische Universität Berlin (2007)

    Google Scholar 

  3. Achterberg, T.: SCIP: solving constraint integer programs. Math. Programm. Comput. 1(1), 1–41 (2009). https://doi.org/10.1007/s12532-008-0001-1

    Article  MathSciNet  MATH  Google Scholar 

  4. Achterberg, T., Bixby, R.E., Gu, Z., Rothberg, E., Weninger, D.: Presolve reductions in mixed integer programming. Informs J. Comput. 32(2), 473–506 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Achterberg, T., Koch, T., Martin, A.: Branching rules revisited. Oper. Res. Lett. 33(1), 42–54 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Anderson, D., Hendel, G., Le Bodic, P., Viernickel, M.: Clairvoyant restarts in branch-and-bound search using online tree-size estimation. Proc. AAAI Conf. Artif. Intell. 33(01), 1427–1434 (2019)

    Google Scholar 

  7. Atamtürk, A., Nemhauser, G.L., Savelsbergh, M.W.: Conflict graphs in solving integer programming problems. Eur. J. Ope. Res. 121(1), 40–55 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bénichou, M., Gauthier, J.M., Girodet, P., Hentges, G., Ribière, G., Vincent, O.: Experiments in mixed-integer programming. Math. Programm. 1, 76–94 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  9. Berthold, T., Feydy, T., Stuckey, P.J.: Rapid learning for binary programs. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 51–55. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13520-0_8

    Chapter  MATH  Google Scholar 

  10. Berthold, T., Hendel, G.: Learning to scale mixed-integer programs. Proc. AAAI Conf. Artif. Intell. 35(5), 3661–3668 (2021)

    Google Scholar 

  11. FICO Xpress Optimization (2021). https://www.fico.com/en/products/fico-xpress-optimization

  12. Gamrath, G.: Enhanced predictions and structure exploitation in branch-and-bound. Ph.D. thesis, Technical University Berlin (2020)

    Google Scholar 

  13. Gamrath, G., et al.: The SCIP Optimization Suite 7.0. Technical report 20–10, ZIB (2020)

    Google Scholar 

  14. Gamrath, G., Berthold, T., Heinz, S., Winkler, M.: Structure-driven fix-and-propagate heuristics for mixed integer programming. Math. Programm. Comput. 11(4), 675–702 (2019). https://doi.org/10.1007/s12532-019-00159-1

    Article  MathSciNet  MATH  Google Scholar 

  15. Hendel, G.: Enhancing MIP branching decisions by using the sample variance of pseudo costs. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 199–214. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18008-3_14

    Chapter  MATH  Google Scholar 

  16. Hendel, G., Anderson, D., Le Bodic, P., Pfetsch, M.E.: Estimating the size of branch-and-bound trees. Informs J. Comput. 34(2), 934–952 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hu, X., Shonkwiler, R., Spruill, M.C.: Random restarts in global optimization. Technical report, Georgia Institute of Technology (2009)

    Google Scholar 

  18. ILOG CPLEX Optimization Studio 12.10.0 (2019). https://www.ibm.com/docs/en/icos/12.10.0?topic=v12100-changes-log

  19. Lodi, A., Tramontani, A.: Performance variability in mixed-integer programming. In: Theory Driven by Influential Applications, pp. 1–12. INFORMS (2013)

    Google Scholar 

  20. Marchand, H., Martin, A., Weismantel, R., Wolsey, L.A.: Cutting planes in integer and mixed integer programming. Discrete Appl. Math. 123(124), 391–440 (2002)

    MathSciNet  MATH  Google Scholar 

  21. Moskewicz, M.H., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Annual Design Automation Conference, pp. 530–535. DAC 2001. Association for Computing Machinery (2001)

    Google Scholar 

  22. Nemhauser, G.L., Wolsey, L.A.: Integer programming and combinatorial optimization Wiley. Chichester. GL Nemhauser, MWP Savelsbergh, GS Sigismondi (1992).Constraint Classification for Mixed Integer Programming Formulations. COAL Bulletin, vol. 20, pp. 8–12 (1988)

    Google Scholar 

  23. Pokutta, Sebastian: Restarting algorithms: sometimes there is free lunch. In: Hebrard, Emmanuel, Musliu, Nysret (eds.) CPAIOR 2020. LNCS, vol. 12296, pp. 22–38. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58942-4_2

    Chapter  Google Scholar 

  24. Savelsbergh, M.W.P.: Preprocessing and probing techniques for mixed integer programming problems. ORSA J. Comput. 6(4), 445–454 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  25. Savelsbergh, M.W.P., Sigismondi, G.C., Nemhauser, G.L.: Functional description of MINTO, a mixed integer optimizer. Technische Universiteit Eindhoven (1991)

    Google Scholar 

  26. Tomlin, J.A.: On scaling linear programming problems. In: Balinski, M.L., Hellerman, E. (eds) Computational practice in mathematical programming. Mathematical Programming Studies vol. 4, pp. 146–166. Springer, Berlin, Heidelberg (1975). https://doi.org/10.1007/BFb0120718

  27. Tramontani, A.: Enhanced mixed integer programming techniques and routing problems. Ph.D. thesis, Springer (2011). https://doi.org/10.1007/s10288-010-0140-x

  28. Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics Bull. 1, 80–83 (1945)

    Article  Google Scholar 

  29. Witzig, J., Berthold, T., Heinz, S.: Experiments with conflict analysis in mixed integer programming. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 211–220. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59776-8_17

    Chapter  MATH  Google Scholar 

  30. Wolter, K.: Implementation of cutting plane separators for mixed integer programs. Master’s thesis, Technische Universität Berlin (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fair Isaac Germany GmbH, Stubenwald -Allee 19, 64625, Bensheim, Germany

    Timo Berthold & Gregor Hendel

  2. University of Padova, Via Gradenigo 6/B, 35131, Padova, Italy

    Domenico Salvagnin

Authors
  1. Timo Berthold
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gregor Hendel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Domenico Salvagnin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Timo Berthold .

Editor information

Editors and Affiliations

  1. UCLouvain, Louvain-la-Neuve, Belgium

    Pierre Schaus

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Berthold, T., Hendel, G., Salvagnin, D. (2022). Transferring Information Across Restarts in MIP. In: Schaus, P. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2022. Lecture Notes in Computer Science, vol 13292. Springer, Cham. https://doi.org/10.1007/978-3-031-08011-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-08011-1_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08010-4

  • Online ISBN: 978-3-031-08011-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation