Cutting Planes from Wide Split Disjunctions

  • Pierre Bonami
  • Andrea LodiEmail author
  • Andrea Tramontani
  • Sven Wiese
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)


In this paper, we discuss an extension of split cuts that is based on widening the underlying disjunctions. That the formula for deriving intersection cuts based on splits can be adapted to this case has been known for a decade now. For the first time though, we present applications and computational results. We further provide some theory that supports our findings, discuss extensions with respect to cut strengthening procedures and present some ideas on how to use the wider disjunctions also in branching.


Integer Variable Wide Split Integrality Requirement Split Disjunction Auxiliary Binary Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Andersen, K., Cornuéjols, G., Li, Y.: Reduce-and-split cuts: Improving the performance of mixed-integer Gomory cuts. Manag. Sci. 51, 1720–1732 (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    Andersen, K., Cornuéjols, G., Li, Y.: Split closure and intersection cuts. Math. Program. 102, 457–493 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Balas, E.: Intersection cuts-a new type of cutting planes for integer programming. Oper. Res. 19, 19–39 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Balas, E., Jeroslow, R.G.: Strengthening cuts for mixed integer programs. Eur. J. Oper. Res. 4, 224–234 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Belhaiza, S., Hansen, P., Laporte, G.: A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows. Comput. Oper. Res. 52, 269–281 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cook, W., Kannan, R., Schrijver, A.: Chvátal closures for mixed integer programming problems. Math. Program. 47, 155–174 (1990)CrossRefzbMATHGoogle Scholar
  7. 7.
    Coughlan, E.T., Lübbecke, M.E., Schulz, J.: A Branch-and-price algorithm for multi-mode resource leveling. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 226–238. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13193-6_20 CrossRefGoogle Scholar
  8. 8.
    Furini, F., Ljubić, I., Sinnl, M.: ILP and CP formulations for the lazy bureaucrat problem. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 255–270. Springer, Cham (2015). doi: 10.1007/978-3-319-18008-3_18 Google Scholar
  9. 9.
    Gomory, R.E.: An algorithm for integer solutions to linear programs. In: Graves, R.L., Wolfe, P. (eds.) Recent Advances in Mathematical Programming, pp. 269–302. McGraw-Hill, New York (1963)Google Scholar
  10. 10.
    Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0–1 knapsack problem. Manag. Sci. 45, 414–424 (1999)CrossRefzbMATHGoogle Scholar
  11. 11.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, UK (1990)zbMATHGoogle Scholar
  12. 12.
    Pisinger, D.: Accessed 19 Feb 2016
  13. 13.
    Wiese, S: On the interplay of Mixed Integer Linear, Mixed Integer Nonlinear and Constraint Programming. Ph.D. thesis, University of Bologna (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Pierre Bonami
    • 1
  • Andrea Lodi
    • 2
    Email author
  • Andrea Tramontani
    • 3
  • Sven Wiese
    • 4
  1. 1.CPLEX Optimization, IBM SpainMadridSpain
  2. 2.CERC - École Polytechnique de MontrealMontrealCanada
  3. 3.CPLEX Optimization, IBM ItalyBolognaItaly
  4. 4.DEI - University of Bologna, and OPTIT srlBolognaItaly

Personalised recommendations