Journal of Global Optimization

, Volume 61, Issue 2, pp 291–310 | Cite as

Exact solution approach for a class of nonlinear bilevel knapsack problems

  • Behdad Beheshti
  • Osman Y. Özaltın
  • M. Hosein Zare
  • Oleg A. Prokopyev


We study a class of nonlinear bilevel knapsack problems. The upper-level objective is a nonlinear integer function of both the leader’s and the follower’s decision variables. At the lower level the follower solves a linear binary knapsack problem, where the right-hand side of the knapsack constraint depends on the resource allocated by the leader. After discussing computational complexity issues, we propose an exact solution approach using an equivalent single-level value function reformulation. Extensive computational experiments are performed with quadratic and fractional binary objective functions.


Bilevel programming Integer programming Value functions  Knapsack problem 



O.Y. Özaltın was supported by Natural Sciences and Engineering Research Council of Canada. The other three authors were partially supported by AFOSR Grant FA9550-08-1-0268, NSF Grant CMMI-0825993 and DoD DURIP Grant FA2386-12-1-3032. O.A. Prokopyev was also supported by US Air Force Summer Faculty Fellowship. In addition, we are grateful to Gabriel L. Zenarosa, Austin L. Buchanan and two anonymous reviewers for their helpful comments.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Behdad Beheshti
    • 1
  • Osman Y. Özaltın
    • 2
  • M. Hosein Zare
    • 1
  • Oleg A. Prokopyev
    • 1
  1. 1.Department of Industrial EngineeringUniversity of PittsburghPittsburghUSA
  2. 2.Edward P. Fitts Department of Industrial and Systems EngineeringNorth Carolina State UniversityRaleighUSA

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