Journal
OPERATIONS RESEARCH
Volume 65, Issue 3, Pages 768-786Publisher
INFORMS
DOI: 10.1287/opre.2017.1589
Keywords
bilevel optimization; integer programming; nonlinear programming; scheduling
Funding
- National Science Foundation [CMMI-1100765]
- Defense Threat Reduction Agency [HDTRA-10-01-0050]
- Air Force Office of Scientific Research [FA9550-12-1-0353]
- Office of Naval Research [N000141310036]
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We examine bilevel mixed-integer programs whose constraints and objective functions depend on both upper-and lower-level variables. The class of problems we consider allows for nonlinear terms to appear in both the constraints and the objective functions, requires all upper-level variables to be integer, and allows a subset of the lower-level variables to be integer. This class of bilevel problems is difficult to solve because the upper-level feasible region is defined in part by optimality conditions governing the lower-level variables, which are difficult to characterize because of the nonconvexity of the follower problem. We propose an exact finite algorithm for these problems based on an optimal-value-function reformulation. We demonstrate how this algorithm can be tailored to accommodate either optimistic or pessimistic assumptions on the follower behavior. Computational experiments demonstrate that our approach outperforms a state-of-the-art algorithm for solving bilevel mixed-integer linear programs.
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