Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Merve Bodur (), Timothy C. Y. Chan () and Ian Yihang Zhu ()
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Merve Bodur: Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada
Timothy C. Y. Chan: Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada
Ian Yihang Zhu: Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada

INFORMS Journal on Computing, 2022, vol. 34, issue 3, 1471-1488

Abstract: Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

Keywords: inverse optimization; mixed integer programming; cutting planes algorithms; decomposition methods • bilevel optimization (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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