On a class of bilevel linear mixed-integer programs in adversarial settings

M. Hosein Zare (), Osman Y. Özaltın () and Oleg A. Prokopyev ()
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M. Hosein Zare: University of Pittsburgh
Osman Y. Özaltın: North Carolina State University
Oleg A. Prokopyev: University of Pittsburgh

Journal of Global Optimization, 2018, vol. 71, issue 1, No 7, 113 pages

Abstract: Abstract We consider a class of bilevel linear mixed-integer programs (BMIPs), where the follower’s optimization problem is a linear program. A typical assumption in the literature for BMIPs is that the follower responds to the leader optimally, i.e., the lower-level problem is solved to optimality for a given leader’s decision. However, this assumption may be violated in adversarial settings, where the follower may be willing to give up a portion of his/her optimal objective function value, and thus select a suboptimal solution, in order to inflict more damage to the leader. To handle such adversarial settings we consider a modeling approach referred to as $$\alpha $$ α -pessimistic BMIPs. The proposed method naturally encompasses as its special classes pessimistic BMIPs and max–min (or min–max) problems. Furthermore, we extend this new modeling approach by considering strong-weak bilevel programs, where the leader is not certain if the follower is collaborative or adversarial, and thus attempts to make a decision by taking into account both cases via a convex combination of the corresponding objective function values. We study basic properties of the proposed models and provide numerical examples with a class of the defender–attacker problems to illustrate the derived results. We also consider some related computational complexity issues, in particular, with respect to optimistic and pessimistic bilevel linear programs.

Keywords: Bilevel linear mixed-integer programs; Bilevel linear programs; Computational complexity; Strong–weak approach; Pessimistic bilevel programs (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-017-0549-2

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