Related papers: Algorithm for solving optimization problems with I…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
An interval transportation problem represents a model for a transportation problem in which the values of supply, demand, and transportation costs are affected by uncertainty and can vary independently within given interval ranges. One of…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we…
Interval-valued computing is a relatively new computing paradigm. It uses finitely many interval segments over the unit interval in a computation as data structure. The satisfiability of Quantified Boolean formulae and other hard problems,…
This paper is concerned with portfolio optimization models for creating high-quality lists of recommended items to balance the accuracy and diversity of recommendations. However, the statistics (i.e., expectation and covariance of ratings)…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic…
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables…
The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…