We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more
Distributionally robust optimization (DRO) has been successful in addressing decision-making problems under uncertainty when the underlying distribution is unknown. Existing data-driven DRO frameworks, however, often impose restrictive assumptions on the data-generating process. We propose a new DRO framework based on targeted integral probability metrics. The ambiguity set is defined directly through the loss functions induced … Read more
We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This … Read more
Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an … Read more
We study the k-delete recoverable robust 0–1 problem in which a decision-maker solves a combinatorial optimization problem subject to objective uncertainty. The model follows a two-stage robust setup. The decision-maker first commits to an initial plan and may then revoke up to k components of this decision after the uncertainty is revealed. The underlying uncertainty … Read more
We study optimistic robust bilevel problems with uncertainty in the follower’s problem, where the follower adopts a so-called wait-and-see approach. In this setting, the leader decides without knowledge of the specific realization of the uncertainty. Then, the uncertainty realizes in a worst-case manner, and afterward the follower makes her own decisions. For this challenging problem … Read more
We study asymptotic consistency of data-driven distributionally robust optimization with shrinking ambiguity sets. The analysis separates reference-distribution convergence from ambiguity-set shrinkage on a prescribed test-function class. Under compactness and continuity assumptions, this yields uniform convergence of robust objectives, optimal-value convergence, and outer convergence of minimizers. For constrained DRO, the same mechanism gives uniform convergence of … Read more
With the high penetration of distributed energy resources in active distribution networks(ADNs), forecast errors from renewables and loads pose significant risks of bilateral violations, including overvoltage/undervoltage and line overloads. To address this challenge, this paper proposes a KDE-DRCCO model that integrates kernel density estimation (KDE) with distributionally robust chance-constrained optimization (DRCCO). Leveraging the radial topology … Read more
Abstract—Renewable-driven direct-current optimal load shedding (DC-OLS) requires a model that is interpretable to operators, data driven under continuous forecast errors, sensitive to severe security failures, and computationally tractable. This paper develops a budgeted KDE-ϕ-HMCR-RS-OLS framework for that purpose. Robust satisficing (RS) replaces ambiguity-radius tuning with an admissible shedding budget. A one-dimensional KDE reference family with … Read more
Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often … Read more