57,750 research outputs found
A generalized model of equality measures in network location problems
In this paper, the concept of the ordered weighted averaging operator is applied to define a model which unifies and generalizes several inequality measures. For a location x, the value of the new objective function is the ordered weighted average of the absolute deviations from the average distance from the facilities to the location x. Several kinds of networks are studied: cyclic, tree and path networks and, for each of them, the properties of the objective function are analyzed in order to identify a finite dominating set for optimal locations. Polynomial-time algorithms are proposed for these problems, and the corresponding complexity is discussed.Future and Emerging Technologies Unit (European Commission)Ministerio de Educación y Cienci
Sensor Deployment for Network-like Environments
This paper considers the problem of optimally deploying omnidirectional
sensors, with potentially limited sensing radius, in a network-like
environment. This model provides a compact and effective description of complex
environments as well as a proper representation of road or river networks. We
present a two-step procedure based on a discrete-time gradient ascent algorithm
to find a local optimum for this problem. The first step performs a coarse
optimization where sensors are allowed to move in the plane, to vary their
sensing radius and to make use of a reduced model of the environment called
collapsed network. It is made up of a finite discrete set of points,
barycenters, produced by collapsing network edges. Sensors can be also
clustered to reduce the complexity of this phase. The sensors' positions found
in the first step are then projected on the network and used in the second
finer optimization, where sensors are constrained to move only on the network.
The second step can be performed on-line, in a distributed fashion, by sensors
moving in the real environment, and can make use of the full network as well as
of the collapsed one. The adoption of a less constrained initial optimization
has the merit of reducing the negative impact of the presence of a large number
of local optima. The effectiveness of the presented procedure is illustrated by
a simulated deployment problem in an airport environment
Optimization of stochastic lossy transport networks and applications to power grids
Motivated by developments in renewable energy and smart grids, we formulate a
stylized mathematical model of a transport network with stochastic load
fluctuations. Using an affine control rule, we explore the trade-off between
the number of controllable resources in a lossy transport network and the
performance gain they yield in terms of expected power losses. Our results are
explicit and reveal the interaction between the level of flexibility, the
intrinsic load uncertainty and the network structure.Comment: 30 pages, 10 figure
Convex Optimal Uncertainty Quantification
Optimal uncertainty quantification (OUQ) is a framework for numerical
extreme-case analysis of stochastic systems with imperfect knowledge of the
underlying probability distribution. This paper presents sufficient conditions
under which an OUQ problem can be reformulated as a finite-dimensional convex
optimization problem, for which efficient numerical solutions can be obtained.
The sufficient conditions include that the objective function is piecewise
concave and the constraints are piecewise convex. In particular, we show that
piecewise concave objective functions may appear in applications where the
objective is defined by the optimal value of a parameterized linear program.Comment: Accepted for publication in SIAM Journal on Optimizatio
Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks
In complex network-coupled dynamical systems, two questions of central
importance are how to identify the most vulnerable components and how to devise
a network making the overall system more robust to external perturbations. To
address these two questions, we investigate the response of complex networks of
coupled oscillators to local perturbations. We quantify the magnitude of the
resulting excursion away from the unperturbed synchronous state through
quadratic performance measures in the angle or frequency deviations. We find
that the most fragile oscillators in a given network are identified by
centralities constructed from network resistance distances. Further defining
the global robustness of the system from the average response over ensembles of
homogeneously distributed perturbations, we find that it is given by a family
of topological indices known as generalized Kirchhoff indices. Both resistance
centralities and Kirchhoff indices are obtained from a spectral decomposition
of the stability matrix of the unperturbed dynamics and can be expressed in
terms of resistance distances. We investigate the properties of these
topological indices in small-world and regular networks. In the case of
oscillators with homogeneous inertia and damping coefficients, we find that
inertia only has small effects on robustness of coupled oscillators. Numerical
results illustrate the validity of the theory.Comment: 11 pages, 9 figure
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