68,749 research outputs found
Decomposition Algorithms in Stochastic Integer Programming: Applications and Computations.
In this dissertation we focus on two main topics. Under the first topic, we develop a new framework for stochastic network interdiction problem to address ambiguity in the defender risk preferences. The second topic is dedicated to computational studies of two-stage stochastic integer programs. More specifically, we consider two cases. First, we develop some solution methods for two-stage stochastic integer programs with continuous recourse; second, we study some computational strategies for two-stage stochastic integer programs with integer recourse. We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects in the network. We take a decision-analytic perspective in addressing probabilistic risk over network parameters, assuming that the defender\u27s risk preferences over exogenously given probabilities can be summarized by the expected utility theory. Although the exact form of the utility function is ambiguous to the defender, we assume that a set of historical data on some pairwise comparisons made by the defender is available, which can be used to restrict the shape of the utility function. We use two different approaches to tackle this problem. The first approach conducts utility estimation and optimization separately, by first finding the best fit for a piecewise linear concave utility function according to the available data, and then optimizing the expected utility. The second approach integrates utility estimation and optimization, by modeling the utility ambiguity under a robust optimization framework following \cite{armbruster2015decision} and \cite{Hu}. We conduct extensive computational experiments to evaluate the performances of these approaches on the stochastic shortest path network interdiction problem. In third chapter, we propose partition-based decomposition algorithms for solving two-stage stochastic integer program with continuous recourse. The partition-based decomposition method enhance the classical decomposition methods (such as Benders decomposition) by utilizing the inexact cuts (coarse cuts) induced by a scenario partition. Coarse cut generation can be much less expensive than the standard Benders cuts, when the partition size is relatively small compared to the total number of scenarios. We conduct an extensive computational study to illustrate the advantage of the proposed partition-based decomposition algorithms compared with the state-of-the-art approaches. In chapter four, we concentrate on computational methods for two-stage stochastic integer program with integer recourse. We consider the partition-based relaxation framework integrated with a scenario decomposition algorithm in order to develop strategies which provide a better lower bound on the optimal objective value, within a tight time limit
On the relationship between Gaussian stochastic blockmodels and label propagation algorithms
The problem of community detection receives great attention in recent years.
Many methods have been proposed to discover communities in networks. In this
paper, we propose a Gaussian stochastic blockmodel that uses Gaussian
distributions to fit weight of edges in networks for non-overlapping community
detection. The maximum likelihood estimation of this model has the same
objective function as general label propagation with node preference. The node
preference of a specific vertex turns out to be a value proportional to the
intra-community eigenvector centrality (the corresponding entry in principal
eigenvector of the adjacency matrix of the subgraph inside that vertex's
community) under maximum likelihood estimation. Additionally, the maximum
likelihood estimation of a constrained version of our model is highly related
to another extension of label propagation algorithm, namely, the label
propagation algorithm under constraint. Experiments show that the proposed
Gaussian stochastic blockmodel performs well on various benchmark networks.Comment: 22 pages, 17 figure
A Nonstochastic Information Theory for Communication and State Estimation
In communications, unknown variables are usually modelled as random
variables, and concepts such as independence, entropy and information are
defined in terms of the underlying probability distributions. In contrast,
control theory often treats uncertainties and disturbances as bounded unknowns
having no statistical structure. The area of networked control combines both
fields, raising the question of whether it is possible to construct meaningful
analogues of stochastic concepts such as independence, Markovness, entropy and
information without assuming a probability space. This paper introduces a
framework for doing so, leading to the construction of a maximin information
functional for nonstochastic variables. It is shown that the largest maximin
information rate through a memoryless, error-prone channel in this framework
coincides with the block-coding zero-error capacity of the channel. Maximin
information is then used to derive tight conditions for uniformly estimating
the state of a linear time-invariant system over such a channel, paralleling
recent results of Matveev and Savkin
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