Related papers: Constructing Representative Scenarios to Approxima…
We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Considering widely dispersed uncertain renewable energy sources (RESs), scenario-based stochastic optimization is an effective method for the economic dispatch of renewables-rich power systems. However, on classic computers, to simulate RES…
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
We treat the so-called scenario approach, a popular probabilistic approximation method for robust minmax optimization problems via independent and indentically distributed (i.i.d) sampling from the uncertainty set, from various…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
In this paper new complexity and approximation results on the robust versions of the representatives selection problem, under the scenario uncertainty representation, are provided, which extend the results obtained in the recent papers by…
Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…