Robust Optimization (RO) is an approach to tackle uncertainties in the parameters of an optimization problem. Constructing an uncertainty set is crucial for RO, as it determines the quality and the conservativeness of the solutions. In this paper, we introduce an approach for constructing a data-driven uncertainty set through volume-based clustering, which we call Minimum-Volume … Read more
Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more
Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO to large-scale decision problems. In this paper, we devise a first-order algorithm for solving RO based on a novel max-min-max perspective. … Read more
Factored Markov decision processes (MDPs) are a prominent paradigm within the artificial intelligence community for modeling and solving large-scale MDPs whose rewards and dynamics decompose into smaller, loosely interacting components. Through the use of dynamic Bayesian networks and context-specific independence, factored MDPs can achieve an exponential reduction in the state space of an MDP and … Read more
Problem definition: Drone delivery has recently garnered significant attention due to its potential for faster delivery at a lower cost than other delivery options. When scheduling drones from a depot for delivery to various destinations, the dispatcher must take into account the uncertain wind conditions, which affect the delivery times of drones to their destinations, … Read more
We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). … Read more
Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for adaptive robust binary optimization (ARBO) problems with objective uncertainty. Without loss of generality, we focus on ARBO problems with “selective adaptability”, a … Read more
We study network design problems for nonlinear and nonconvex flow models under demand uncertainties. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, demand scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear … Read more
Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future … Read more
Sample average approximation-based stochastic dynamic programming and model predictive control are two different methods of approaching multistage stochastic optimization. Model predictive control—despite a lack of theoretical backing—is often used instead of stochastic dynamic programming due to computational necessity. For settings where the stage reward is a convex function of the random terms, the stage dynamics … Read more