Skip to main content
SpringerLink
Log in

A note on the selection of Benders’ cuts

  • Full Length Paper
  • Series B
  • Published:
Mathematical Programming Submit manuscript

Abstract

A new cut selection criterion for Benders’ cuts is proposed and computationally analyzed. The results show that the new criterion is more robust—and often considerably faster—than the standard ones.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amaldi E., Pfetsch M.E., Trotter L.E. Jr: On the maximum feasible subsystem problem, IISs and IIS-hypergraphs. Math. Program. 95(3), 533–554 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Atamtürk A., Nemhauser G.L., Savelsbergh M.W.P.: Valid inequalities for problems with additive variable upper bounds. Math. Program. 91, 145–162 (2001)

    MATH  MathSciNet  Google Scholar 

  3. Atamturk A., Rajan D.: On splittable and unsplittable flow capacitated network design arc-set polyhedra. Math. Program. 92, 315–333 (2002)

    Article  MathSciNet  Google Scholar 

  4. Balas E., Ceria S., Cornuéjols G.: Mixed 0–1 programming by lift-and-project in a branch-and-cut framework. Manage. Sci. 42, 1229–1246 (1996)

    Article  MATH  Google Scholar 

  5. Benders J.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cadoux F.: Computing deep facet-defining disjunctive cuts for mixed-integer programming. Math. Program. 122(2), 197–223 (2009)

    Article  MathSciNet  Google Scholar 

  7. Cornuéjols G.: Valid inequalities for mixed integer linear programs. Math. Program. Ser. B 112(1), 3–44 (2008)

    Article  MATH  Google Scholar 

  8. Cornuéjols G., Lemaréchal C.: A convex analysis perspective on disjunctive cuts. Math. Program. 106(3), 567–586 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Costa A.M.: A survey on Benders decomposition applied to fixed-charge network design problems. Comput. Oper. Res. 32(6), 1429–1450 (2005)

    Article  MathSciNet  Google Scholar 

  10. Fukuda K., Liebling T.M., Margot F.: Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron. Comput. Geome. 8, 1–12 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gleeson J., Ryan J.: Identifying minimally infeasible subsystems of inequalities. ORSA J. Comput. 2(1), 61–63 (1990)

    MATH  Google Scholar 

  12. Magnanti T., Wong R.: Accelerating Benders decomposition: algorithmic enhancement and model selection criteria. Oper. Res. 29, 464–484 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  13. McDaniel D., Devine M.: A modified Benders’ partitioning algorithm for mixed integer programming. Manage. Sci. 4, 312–319 (1977)

    Article  Google Scholar 

  14. Rei W., Cordeau J.F., Gendreau M., Soriano P.: Accelerating Benders decomposition by local branching. INFORMS J. Comput. 21, 333–345 (2009)

    Article  MathSciNet  Google Scholar 

  15. Wentges P.: Accelerating Benders’ decomposition for the capacitated facility location problem. Math. Methods Oper. Res. 44, 267–290 (1996)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DEI, University of Padova, Padua, Italy

    Matteo Fischetti

  2. DMPA, University of Padova, Padua, Italy

    Domenico Salvagnin & Arrigo Zanette

Authors
  1. Matteo Fischetti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Domenico Salvagnin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arrigo Zanette
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matteo Fischetti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fischetti, M., Salvagnin, D. & Zanette, A. A note on the selection of Benders’ cuts. Math. Program. 124, 175–182 (2010). https://doi.org/10.1007/s10107-010-0365-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-010-0365-7

Keywords

Mathematics Subject Classification (2000)

Search

Navigation