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Two-stage stochastic unit commitment (2S-SUC) problems have been widely adopted to manage the uncertainties introduced by high penetrations of intermittent renewable energy resources. While decomposition-based algorithms such as…
In the (binary) Distinct Vectors problem we are given a binary matrix A with pairwise different rows and want to select at most k columns such that, restricting the matrix to these columns, all rows are still pairwise different. A result by…
Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
Catastrophic tornadoes cause severe damage and are a threat to human wellbeing, making it critical to determine mitigation strategies to reduce their impact. One such strategy, following recent research, is to retrofit existing structures.…
Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…
We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…
This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time…
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery…
In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…