A Robust Optimization Framework for Wildfire Fuel Management
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Oleg A. Prokopyev
Dimensionality Reduction in Bilevel Linear Programming
We consider bilevel programs that involve a leader, who first commits to a mixed-integer decision, and a follower, who observes this decision and then responds rationally by solving a linear program (LP). Standard approaches often reformulate these bilevel optimization problems as single-level mixed-integer programs by exploiting the follower’s LP optimality conditions. These reformulations introduce either … Read more
On Local Search in Bilevel Mixed-Integer Linear Programming
Two-level hierarchical decision-making problems, where a leader’s choice influences a follower’s action, arise across key business and public-sector domains, from market design and pricing to defense. These problems are typically modeled as bilevel programs and are known to be notoriously hard to solve at scale. In single-level combinatorial optimization, especially for challenging instances, local search … Read more
On the Complexity of Finding Locally Optimal Solutions in Bilevel Linear Optimization
We consider the theoretical computational complexity of finding locally optimal solutions to bilevel linear optimization problems (BLPs), from the leader’s perspective. We show that, for any constant \(c > 0\), the problem of finding a leader’s solution that is within Euclidean distance \(c^n\) of any locally optimal leader’s solution, where \(n\) is the total number … Read more
Finding Groups with Maximum Betweenness Centrality via Integer Programming with Random Path Sampling
One popular approach to access the importance/influence of a group of nodes in a network is based on the notion of centrality. For a given group, its group betweenness centrality is computed, first, by evaluating a ratio of shortest paths between each node pair in a network that are “covered” by at least one node … Read more
Mixed Integer Bilevel Optimization with k-optimal Follower: A Hierarchy of Bounds
We consider mixed integer bilevel linear optimization problems in which the decision variables of the lower-level (follower’s) problem are all binary. We propose a general modeling and solution framework motivated by the practical reality that in a Stackelberg game, the follower does not always solve their optimization problem to optimality. They may instead implement a … Read more
Analysis of Process Flexibility Designs under Disruptions
Most of the previous studies of process flexibility designs have focused on expected sales and demand uncertainty. In this paper, we examine the worst-case performance of flexibility designs in the case of demand and supply uncertainties, where the latter can be in the form of either plant or arc disruptions. We define the Plant Cover … Read more
On robust fractional 0-1 programming
We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide-range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator, and the latter accounts for different forms of inter-relatedness between them. First, we demonstrate that, unlike the … Read more
A mixed-integer fractional optimization approach to best subset selection
We consider the best subset selection problem in linear regression, i.e., finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We show that, for a broad range of criteria used in the statistics literature, the best subset selection problem can be modeled as … Read more
Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function
We introduce a generalized value function of a mixed-integer program, which is simultaneously parameterized by its objective and right-hand side. We describe its fundamental properties, which we exploit through three algorithms to calculate it. We then show how this generalized value function can be used to reformulate two classes of mixed-integer optimization problems: two-stage stochastic … Read more