Skip to main content
SpringerLink
Log in

A Branch-and-cut Algorithm for Integer Bilevel Linear Programs

  • Conference paper
Operations Research and Cyber-Infrastructure

Part of the book series: Operations Research/Computer Science Interfaces ((ORCS,volume 47))

Abstract

We describe a rudimentary branch-and-cut algorithm for solving integer bilevel linear programs that extends existing techniques for standard integer linear programs to this very challenging computational setting. The algorithm improves on the branch-and-bound algorithm of Moore and Bard in that it uses cutting plane techniques to produce improved bounds, does not require specialized branching strategies, and can be implemented in a straightforward way using only linear solvers. An implementation built using software components available in the COIN-OR software repository is described and preliminary computational results presented.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Martin A (2005) Branching rules revisited. Operations Research Letters 33(1):42–54

    Article  MathSciNet  MATH  Google Scholar 

  • Bard J (1988) Convex two-level optimization. Mathematical Programming 40: 15–27

    Article  MathSciNet  MATH  Google Scholar 

  • Bard J, Moore J (1990) A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing 11(2):281–292

    Article  MathSciNet  MATH  Google Scholar 

  • Bard J, Moore J (1992) An algorithm for the discrete bilevel programming problem. Naval Research Logistics 39:419–435

    Article  MathSciNet  MATH  Google Scholar 

  • Cormican K, Morton D, Wood R (1998) Stochastic network interdiction. Operations Research 46(2):184–197

    Article  MATH  Google Scholar 

  • Cornuejols G (2008) Valid inequalities for mixed integer linear programs. Mathematical Programming B 112:3–44

    Article  MathSciNet  MATH  Google Scholar 

  • Dempe S (2001) Discrete bilevel optimization problems. Tech. Rep. D-04109, Institut fur Wirtschaftsinformatik, Universitat Leipzig, Leipzig, Germany

    Google Scholar 

  • DeNegre S, Ralphs T, Guzelsoy M (2008) A new class of valid inequalities for mixed integer bilevel linear programs. Tech. rep., Lehigh University

    Google Scholar 

  • Figueira J (2000) MCDM Numerical Instances Library. URL http://www.univvalenciennes.fr/ROAD/MCDM/ListMOKP.html

  • Ghare P, Montgomery D, Turner W (1971) Optimal interdiction policy for a flow network. Naval Research Logistics Quarterly 18:27–45

    Article  MathSciNet  Google Scholar 

  • Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical Computing 13(5):1194–1217

    Article  MathSciNet  MATH  Google Scholar 

  • Held H, Woodruff D (2005) Heuristics for multi-stage interdiction of stochastic networks. Journal of Heuristics 11(5-6);483–500

    Article  MATH  Google Scholar 

  • Israeli E, Wood R (2002) Shortest path network interdiction. Networks 40(2): 97–111

    Article  MathSciNet  MATH  Google Scholar 

  • Janjarassuk U, Linderoth J (2006) Reformulation and sampling to solve a stochastic network interdiction problem. Tech. Rep. 06T-001, Lehigh University

    Google Scholar 

  • Lim C, Smith J (2007) Algorithms for discrete and continuous multicommodity flow network interdiction problems. IIE Transactions 39(1):15–26

    Article  Google Scholar 

  • Loridan P, Morgan J (1996) Weak via strong stackelberg problem: New results. Journal of Global Optimization 8(3):263–287

    Article  MathSciNet  MATH  Google Scholar 

  • Lougee-Heimer R (2003) The Common OPtimization INterface for Operations Research. IBM Journal of Research and Development 47(1):57–66

    Article  Google Scholar 

  • McMasters A, Mustin T (1970) Optimal interdiction of a supply network. Naval Research Logistics Quarterly 17:261–268

    Article  MATH  Google Scholar 

  • Moore J, Bard J (1990) The mixed integer linear bilevel programming problem. Operations Research 38(5):911–921

    Article  MathSciNet  MATH  Google Scholar 

  • Morton D, Pan F, Saeger K (2007) Models for nuclear smuggling interdiction. IIE Transactions 39(1):3–14

    Article  Google Scholar 

  • Royset J, Wood R (2007) Solving the bi-objective maximum-flow network-interdiction problem. INFORMS Journal on Computing 19(2):175–184

    Article  MathSciNet  MATH  Google Scholar 

  • Vicente L, Savard G, Judice J (1994) Descent approaches for quadratic bilevel programming. Journal of Optimization Theory and Applications 81:379–399

    Article  MathSciNet  MATH  Google Scholar 

  • Wen U, Yang Y (1990) Algorithms for solving the mixed integer two-level linear programming problem. Computers & Operations Research 17(2):133–142

    Article  MathSciNet  MATH  Google Scholar 

  • Wollmer R (1964) Removing arcs from a network. Operations Research 12(6):934–940

    Article  MathSciNet  MATH  Google Scholar 

  • Wood R (1993) Deterministic network interdiction. Mathematical and Computer Modelling 17(2):1–18

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial & Systems Engineering,, Lehigh University, 200 W. Packer Avenue,, Bethlehem,, PA 18015,

    S. T. DeNegre & T. K. Ralphs

Authors
  1. S. T. DeNegre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. K. Ralphs
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. T. DeNegre .

Editor information

Editors and Affiliations

  1. Dept. Systems & Computer Engineering, Carleton University, Ottawa, ON, K1S 5B6, Canada

    John W. Chinneck

  2. Maximal Software, Inc., 2111 Wilson Blvd., Arlington, VA, 22201, USA

    Bjarni Kristjansson

  3. Dept. of Mathematical Sciences College of Engineering and Science, Clemson University, 340975, Clemson, SC, 29634, USA

    Matthew J. Saltzman

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this paper

Cite this paper

DeNegre, S.T., Ralphs, T.K. (2009). A Branch-and-cut Algorithm for Integer Bilevel Linear Programs. In: Chinneck, J.W., Kristjansson, B., Saltzman, M.J. (eds) Operations Research and Cyber-Infrastructure. Operations Research/Computer Science Interfaces, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-88843-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-88843-9_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-88842-2

  • Online ISBN: 978-0-387-88843-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation