An optimization method for uncertain structures is suggested based on convex model and a satisfaction degree of interval. In the investigated problem, the uncertainty only exists in constraints. Convex model is used to describe the uncertainty in which the intervals of the uncertain parameters are only needed, not necessarily to know the precise probability distributions. A satisfaction degree ...

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on φ-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization ...

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization problems with expected value objectives and constraints where the underlying probability distributions are observed via limited data. This approach relies o...

Based on the recent approach of Bertsimas and Sim (2004, 2003) to robust optimization in the presence of data uncertainty, we prove an easily computable and simple bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty.We exploit the binary nat...

Many real-world engineering design problems are naturally cast in the form of optimization programs with uncertainty-contaminated data. In this context, a reliable design must be able to cope in some way with the presence of uncertainty. In this paper, we consider two standard philosophies for finding optimal solutions for uncertain convex optimization problems. In the first approach, classical...

The theory of risk provides a systematic approach to handling uncertainty with well-defined risk and deviation measures. As the model-based economic optimization of the water-flooding process in oil reservoirs suffers from high levels of uncertainty, the concepts from the theory of risk are highly relevant. In this paper, the main focus is to offer an asymmetric risk management, i.e., to maximi...

This research focuses on the methods and application of optimization under uncertainty to radiation therapy planning, where it is natural and useful to model the uncertainty of the problem directly. In particular, we present methods for optimization under uncertainty in radiation therapy of tumors and compare their results. Two themes are developed in this study: (1) the modeling of inherent un...

Decision-making under uncertainty is particularly challenging in the case of multidisciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical s...

Many existing works for handling uncertainty in problem-solving rely on some form of a priori knowledge of the uncertainty structure. However, in reality, one may not always possess the necessary expertise or sufficient knowledge to identify suitable bounds of the uncertainty involved. Rather, it is more likely that specifications of the realistic performance desired are derived, which may be b...