We study a single-commodity Robust Network Design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of … Read more
We present a robust optimization approach to 0-1 linear programming with uncertain objective coefficients based on a safe tractable approximation of chance constraints, when only the first two moments and the support of the random parameters is known. We obtain nonlinear problems with only one additional (continuous) variable, for which we discuss solution techniques. The … Read more
This article studies a multi-period capacitated fixed-charge location-transportation problem in which, while the location and capacity of each facility need to be determined immediately, the determination of final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, … Read more
We present a new partition-and-bound method for multistage adaptive mixed integer optimization (AMIO) problems that extends previous work on finite adaptability. The approach analyzes the optimal solution to a static (non-adaptive) version of an AMIO problem to gain insight into which regions of the uncertainty set are restricting the objective function value. We use this … Read more
The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, … Read more
We study the robust constrained shortest path problem under resource uncertainty. After proving that the problem is \NPhard in the strong sense for arbitrary uncertainty sets, we focus on budgeted uncertainty sets introduced by Bertsimas and Sim (2003) and their extension to variable uncertainty by Poss (2013). We apply classical techniques to show that the … Read more
In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period … Read more
Abstract— The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the Unit Commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that prevent or restrict their … Read more
We consider a problem where an investment manager must allocate an available budget among a set of fund managers, whose asset allocations are not precisely known to the investment manager. In this paper, we propose a robust framework that takes into account the uncertainty stemming from the fund managers’ allocation, as well as the more … Read more
Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We provide an overview on robust optimization criteria … Read more