Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 66, Issue 2, Pages 225-262Publisher
SPRINGER
DOI: 10.1007/s10898-015-0274-7
Keywords
Bilevel programming; Interdiction problems; Integer programing; Algorithms
Funding
- National Science Foundation [CMMI-11000765]
- Defense Threat Reduction Agency [HDTRA1-10-1-0050]
- Air Force Office of Scientific Research [FA9550-12-1-0353]
- Office of Naval Research [N000141310036]
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In this paper, we introduce a new class of algorithms for solving the mixed-integer bilevel min-max optimization problem. This problem involves two players, a leader and a follower, who play a Stackelberg game. In particular, the leader seeks to minimize over a set of discrete variables the maximum objective that the follower can achieve. The complicating features of our problem are that a subset of the follower's decisions are restricted to be integer-valued, and that the follower's decisions are constrained by the leader's decisions. We first describe several bilevel min-max programs that can be used to obtain lower and upper bounds on the optimal objective value of the problem. We then present algorithms for this problem that finitely terminate with an optimal solution when the leader variables are restricted to take binary values. Finally, we report the results of a computational study aimed at evaluating the quality of our algorithms on two families of randomly generated problems.
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