Related papers: A Decision Rule Approach for Two-Stage Data-Driven…
Multi-stage problems with uncertain parameters and integer decisions variables are among the most difficult applications of robust optimization (RO). The challenge in these problems is to find optimal here-and-now decisions, taking into…
Mixed integer sets have a strong modeling capacity to describe practical systems. Nevertheless, incorporating a mixed integer set often renders an optimization formulation drastically more challenging to compute. In this paper, we study how…
This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage…
Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…
We study iterative methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. We propose a machine-learning-based heuristic to determine starting scenarios that provide strong lower bounds. To this end, we…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
This paper proposes a novel method to co-optimize distribution system operation and repair crew routing for outage restoration after extreme weather events. A two-stage stochastic mixed integer linear program is developed. The first stage…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large.…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…
Edge computing has emerged as a key technology to reduce network traffic, improve user experience, and enable various Internet of Things applications. From the perspective of a service provider (SP), how to jointly optimize the service…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Distributionally robust optimization (DRO) has shown lot of promise in providing robustness in learning as well as sample based optimization problems. We endeavor to provide DRO solutions for a class of sum of fractionals, non-convex…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…