Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome … Read more
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and … Read more
To improve quality and delivery of care, operations need to be coordinated and optimized across all services in real-time. We propose a multi-stage adaptive robust optimization approach combined with machine learning techniques to achieve this goal. Informed by data and predictions, our framework unifies the bed assignment process across the entire hospital and accounts for … Read more
In this paper we present novel data-driven optimization models for Support Vector Machines (SVM), with the aim of linearly separating two sets of points that have non-disjoint convex closures. Traditional classi cation algorithms assume that the training data points are always known exactly. However, real-life data are often subject to noise. To handle such uncertainty, we … Read more
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary classification trees with univariate splits. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality … Read more
Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed-integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes … Read more
We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex ambiguity sets, including sets based on integral probability metrics and finite-order moment bounds. This perspective unifies multiple existing robust and stochastic optimization … Read more
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained … Read more
Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, … Read more
We introduce a learning based algorithm to solve the drone routing problem with recharging stops that arises in many applications such as precision agriculture, search and rescue and military surveillance. The heuristic algorithm, namely Learn and Fly (L\&F), learns from the features of high quality solutions to optimize recharging visits, starting from a given Hamiltonian … Read more