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With increasing share of renewables in power generation mix, system operators would need to run Optimal Power Flow (OPF) problems closer to real-time to better manage uncertainty. Given that OPF is an expensive optimization problem to…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
Most combinatorial optimization problems can be formulated as mixed integer linear programming (MILP), in which branch-and-bound (B\&B) is a general and widely used method. Recently, learning to branch has become a hot research topic in the…
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then…
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem…
In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming (MIP) relaxations.…
We study an incremental network design problem, where in each time period of the planning horizon an arc can be added to the network and a maximum flow problem is solved, and where the objective is to maximize the cumulative flow over the…
The goal to decarbonize the energy sector has led to increased research in modeling and optimizing multi-energy systems. One of the most promising techniques for modeling (multi-)energy optimization problems is mixed-integer programming…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
We propose a meta-learning method for positive and unlabeled (PU) classification, which improves the performance of binary classifiers obtained from only PU data in unseen target tasks. PU learning is an important problem since PU data…
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…
Efficient algorithms and solvers are required to provide optimal or near-optimal solutions quickly and enable organizations to react promptly to dynamic situations such as supply chain disruptions or changing customer demands.…
Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
Finding approximate occurrences of a pattern in a text using a full-text index is a central problem in bioinformatics and has been extensively researched. Bidirectional indices have opened new possibilities in this regard allowing the…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…