Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from slow runtimes, due to weak linear programming (LP) relaxations. In this paper, we first propose a … Read more
Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental problems in short-term electric power systems planning that are traditionally solved sequentially. The state-of-the-art mostly uses a direct current flow approximation of the power flow equations in the UC-level and the generator commitments obtained are sent as input to the OPF-level. However, such an … Read more
We consider combinatorial optimization problems with interval uncertainty in the cost vector. Recently a new approach was developed to deal with such uncertainties: instead of a single one absolute robust solution, obtained by solving a min max problem, a set of cardinality predefined and minimal absolute regret, obtained by solving a min max min problem, … Read more
We present a trilevel interdiction model for optimally segmenting the Supervisory Control and Data Acquisition (SCADA) network controlling an electric power grid. In this formulation, we decide how to partition nodes of the SCADA network in order to minimize the shedding of load from a worst-case cyberattack, assuming that the grid operator has the opportunity … Read more
We consider nonlinear optimization problems that involve surrogate models represented by neural net-works. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific … Read more
Developing solution methods for discrete bilevel problems is known to be a challenging task – even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty. We study discrete min-max problems with a follower who faces uncertainties regarding the parameters of the lower-level problem. Adopting a … Read more
Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks with binary activation functions and continuous or integer weights (BDNN). We show that the BDNN can be reformulated as a … Read more
Second-order cone programming problems are a tractable subclass of convex optimization problems and there are known polynomial algorithms for solving them. Stochastic second-order cone programming problems have also been studied in the past decade and efficient algorithms for solving them exist. A new class of interest to optimization community and practitioners is the mixed-integer version … Read more
We consider the problem of learning an optimal prescriptive tree (i.e., an interpretable treatment assignment policy in the form of a binary tree) of moderate depth, from observational data. This problem arises in numerous socially important domains such as public health and personalized medicine, where interpretable and data-driven interventions are sought based on data gathered … Read more
This paper studies optimal criteria for the appointment scheduling of outpatients in a medical imaging center. The main goal of this study is to coordinate the assignments of radiopharmaceuticals and the scheduling of outpatients on imaging scanners. We study a special case of a molecular imaging center that offers services for various diagnostic procedures for … Read more