94,631 research outputs found
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Optimization of Gaussian Random Fields
Many engineering systems are subject to spatially distributed uncertainty,
i.e. uncertainty that can be modeled as a random field. Altering the mean or
covariance of this uncertainty will in general change the statistical
distribution of the system outputs. We present an approach for computing the
sensitivity of the statistics of system outputs with respect to the parameters
describing the mean and covariance of the distributed uncertainty. This
sensitivity information is then incorporated into a gradient-based optimizer to
optimize the structure of the distributed uncertainty to achieve desired output
statistics. This framework is applied to perform variance optimization for a
model problem and to optimize the manufacturing tolerances of a gas turbine
compressor blade
New results about multi-band uncertainty in Robust Optimization
"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in
the development of a tractable robust counterpart of Linear Programming
Problems. However, the central modeling assumption that the deviation band of
each uncertain parameter is single may be too limitative in practice:
experience indeed suggests that the deviations distribute also internally to
the single band, so that getting a higher resolution by partitioning the band
into multiple sub-bands seems advisable. The critical aim of our work is to
close the knowledge gap about the adoption of a multi-band uncertainty set in
Robust Optimization: a general definition and intensive theoretical study of a
multi-band model are actually still missing. Our new developments have been
also strongly inspired and encouraged by our industrial partners, which have
been interested in getting a better modeling of arbitrary distributions, built
on historical data of the uncertainty affecting the considered real-world
problems. In this paper, we study the robust counterpart of a Linear
Programming Problem with uncertain coefficient matrix, when a multi-band
uncertainty set is considered. We first show that the robust counterpart
corresponds to a compact LP formulation. Then we investigate the problem of
separating cuts imposing robustness and we show that the separation can be
efficiently operated by solving a min-cost flow problem. Finally, we test the
performance of our new approach to Robust Optimization on realistic instances
of a Wireless Network Design Problem subject to uncertainty.Comment: 15 pages. The present paper is a revised version of the one appeared
in the Proceedings of SEA 201
Modeling of Phenomena and Dynamic Logic of Phenomena
Modeling of complex phenomena such as the mind presents tremendous
computational complexity challenges. Modeling field theory (MFT) addresses
these challenges in a non-traditional way. The main idea behind MFT is to match
levels of uncertainty of the model (also, problem or theory) with levels of
uncertainty of the evaluation criterion used to identify that model. When a
model becomes more certain, then the evaluation criterion is adjusted
dynamically to match that change to the model. This process is called the
Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes
of the mind and natural evolution. This paper provides a formal description of
DLP by specifying its syntax, semantics, and reasoning system. We also outline
links between DLP and other logical approaches. Computational complexity issues
that motivate this work are presented using an example of polynomial models
A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification
In this work we consider a class of uncertainty quantification problems where
the system performance or reliability is characterized by a scalar parameter
. The performance parameter is random due to the presence of various
sources of uncertainty in the system, and our goal is to estimate the
probability density function (PDF) of . We propose to use the multicanonical
Monte Carlo (MMC) method, a special type of adaptive importance sampling
algorithm, to compute the PDF of interest. Moreover, we develop an adaptive
algorithm to construct local Gaussian process surrogates to further accelerate
the MMC iterations. With numerical examples we demonstrate that the proposed
method can achieve several orders of magnitudes of speedup over the standard
Monte Carlo method
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