Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or 'instance' parameter. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization and chance-constrained optimization. Robust optimization is a deterministic paradigm where one seeks a...

The use of optimization for the propagation of mixed epistemic/aleatory uncertainties is demonstrated within the context of hypersonic flows. Specifically, this work focuses on strategies applicable for models where input parameters can be divided into a set of variables containing only aleatory uncertainties and a set with epistemic uncertainties. With the input parameters divided in this way,...

This report documents the development of several transportation optimization models under uncertainty. First, a robust evacuation transportation planning model for freeway traffic systems was developed, in which demand is uncertain. The study results provide preliminary evidence that routing traffic using such a robust, optimization-based model can improve the average objective performance. Nex...

The problem of nonlinear optimization for process design under uncertainty is addressed in this paper. A novel robust optimization framework is proposed to address general nonlinear problems under uncertainty. To address the limitation of single point linearization with respect to uncertain parameters for a large uncertainty region, an iterative algorithm is developed. The new method applies lo...

Background: Polymer gel dosimeters combined with magnetic resonance imaging (MRI) can be used for dose verification of advanced radiation therapy techniques. However, the uncertainty of dose map measured by gel dosimeter should be known. The purpose of this study is to investigate the uncertainty related to calibration curve and MRI protocol for MAGIC (Methacrylic and Ascorbic acid in Gelatin I...

The S-System formalism provides a popular, versatile and mathematically tractable representation of metabolic pathways. At steady-state, after a logarithmic transformation, the S-System representation reduces into a system of linear equations. Thus, the maximization of a particular metabolite concentration or a flux subject to physiological constraints can be expressed as a linear programming (...

Structural reliability and decomposition techniques have recently proved to be appropriate tools for solving robust uncertain mixed-integer linear programs using ellipsoidal uncertainty sets. In fact, its computational performance makes this type of problem to be an alternative method in terms of tractability with respect to robust problems based on cardinality constrained uncertainty sets. Thi...

Surrogate-based optimization proceeds in cycles. Each cycle consists of analyzing a number of designs, fitting a surrogate, performing optimization based on the surrogate, and finally analyzing a candidate solution. Algorithms that use the surrogate uncertainty estimator to guide the selection of the next sampling candidate are readily available, e.g., the efficient global optimization (EGO) al...

This article presents a brief survey on some of the most relevant developments in the field of optimization under uncertainty. In particular, the scope and the relevance of the papers included in this Special Issue are analyzed. The importance of uncertainty quantification and optimization techniques for producing improved models and designs is thoroughly discussed. The focus of the discussion ...