234,010 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
Robust Geotechnical Design - Methodology and Applications
This dissertation is aimed at developing a novel robust geotechnical design methodology and demonstrating this methodology for the design of geotechnical systems. The goal of a robust design is to make the response of a system insensitive to, or robust against, the variation of uncertain geotechnical parameters (termed noise factors in the context of robust design) by carefully adjusting design parameters (those that can be controlled by the designer such as geometry of the design). Through an extensive investigation, a robust geotechnical design methodology that considers explicitly safety, robustness, and cost is developed. Various robustness measures are considered in this study, and the developed methodology is implemented with a multi-objective optimization scheme, in which safety is considered as a constraint and cost and robustness are treated as the objectives. Because the cost and the robustness are conflicting objectives, the robust design optimization does not yield a single best solution. Rather, a Pareto front is obtained, which is a collection of non-dominated optimal designs. The Pareto front reveals a trade-off relationship between cost and robustness, which enables the engineer to make an informed design decision according to a target level of cost or robustness. The significance and versatility of the new design methodology are illustrated with multiple geotechnical applications, including the design of drilled shafts, shallow foundations, and braced excavations
Robust Principal Component Analysis?
This paper is about a curious phenomenon. Suppose we have a data matrix,
which is the superposition of a low-rank component and a sparse component. Can
we recover each component individually? We prove that under some suitable
assumptions, it is possible to recover both the low-rank and the sparse
components exactly by solving a very convenient convex program called Principal
Component Pursuit; among all feasible decompositions, simply minimize a
weighted combination of the nuclear norm and of the L1 norm. This suggests the
possibility of a principled approach to robust principal component analysis
since our methodology and results assert that one can recover the principal
components of a data matrix even though a positive fraction of its entries are
arbitrarily corrupted. This extends to the situation where a fraction of the
entries are missing as well. We discuss an algorithm for solving this
optimization problem, and present applications in the area of video
surveillance, where our methodology allows for the detection of objects in a
cluttered background, and in the area of face recognition, where it offers a
principled way of removing shadows and specularities in images of faces
Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center
The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed
A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA
Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algorithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical examples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications
Likelihood-Based Inference for Discretely Observed Birth-Death-Shift Processes, with Applications to Evolution of Mobile Genetic Elements
Continuous-time birth-death-shift (BDS) processes are frequently used in
stochastic modeling, with many applications in ecology and epidemiology. In
particular, such processes can model evolutionary dynamics of transposable
elements - important genetic markers in molecular epidemiology. Estimation of
the effects of individual covariates on the birth, death, and shift rates of
the process can be accomplished by analyzing patient data, but inferring these
rates in a discretely and unevenly observed setting presents computational
challenges. We propose a mutli-type branching process approximation to BDS
processes and develop a corresponding expectation maximization (EM) algorithm,
where we use spectral techniques to reduce calculation of expected sufficient
statistics to low dimensional integration. These techniques yield an efficient
and robust optimization routine for inferring the rates of the BDS process, and
apply more broadly to multi-type branching processes where rates can depend on
many covariates. After rigorously testing our methodology in simulation
studies, we apply our method to study intrapatient time evolution of IS6110
transposable element, a frequently used element during estimation of
epidemiological clusters of Mycobacterium tuberculosis infections.Comment: 31 pages, 7 figures, 1 tabl
Non-Convex Rank Minimization via an Empirical Bayesian Approach
In many applications that require matrix solutions of minimal rank, the
underlying cost function is non-convex leading to an intractable, NP-hard
optimization problem. Consequently, the convex nuclear norm is frequently used
as a surrogate penalty term for matrix rank. The problem is that in many
practical scenarios there is no longer any guarantee that we can correctly
estimate generative low-rank matrices of interest, theoretical special cases
notwithstanding. Consequently, this paper proposes an alternative empirical
Bayesian procedure build upon a variational approximation that, unlike the
nuclear norm, retains the same globally minimizing point estimate as the rank
function under many useful constraints. However, locally minimizing solutions
are largely smoothed away via marginalization, allowing the algorithm to
succeed when standard convex relaxations completely fail. While the proposed
methodology is generally applicable to a wide range of low-rank applications,
we focus our attention on the robust principal component analysis problem
(RPCA), which involves estimating an unknown low-rank matrix with unknown
sparse corruptions. Theoretical and empirical evidence are presented to show
that our method is potentially superior to related MAP-based approaches, for
which the convex principle component pursuit (PCP) algorithm (Candes et al.,
2011) can be viewed as a special case.Comment: 10 pages, 6 figures, UAI 2012 pape
On the Selection of Tuning Methodology of FOPID Controllers for the Control of Higher Order Processes
In this paper, a comparative study is done on the time and frequency domain
tuning strategies for fractional order (FO) PID controllers to handle higher
order processes. A new fractional order template for reduced parameter modeling
of stable minimum/non-minimum phase higher order processes is introduced and
its advantage in frequency domain tuning of FOPID controllers is also
presented. The time domain optimal tuning of FOPID controllers have also been
carried out to handle these higher order processes by performing optimization
with various integral performance indices. The paper highlights on the
practical control system implementation issues like flexibility of online
autotuning, reduced control signal and actuator size, capability of measurement
noise filtration, load disturbance suppression, robustness against parameter
uncertainties etc. in light of the above tuning methodologies.Comment: 27 pages, 10 figure
Features for Exploiting Black-Box Optimization Problem Structure.
Abell T, Malitsky Y, Tierney K. Features for Exploiting Black-Box Optimization Problem Structure. In: Nicosia G, Pardalos P, eds. Learning and Intelligent Optimization: 7th International Conference, LION 7, Catania, Italy, January 7-11, 2013, Revised Selected Papers. Lecture Notes in Computer Science. Vol 7997. Berlin, Heidelberg: Springer Berlin Heidelberg; 2013: 30-36.Black-box optimization (BBO) problems arise in numerous scientific and engineering applications and are characterized by computationally intensive objective functions, which severely limit the number of evaluations that can be performed. We present a robust set of features that analyze the fitness landscape of BBO problems and show how an algorithm portfolio approach can exploit these general, problem independent, features and outperform the utilization of any single minimization search strategy. We test our methodology on data from the GECCO Workshop on BBO Benchmarking 2012, which contains 21 state-of-the-art solvers run on 24 well-established functions
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