17,234 research outputs found
Shortest Path versus Multi-Hub Routing in Networks with Uncertain Demand
We study a class of robust network design problems motivated by the need to
scale core networks to meet increasingly dynamic capacity demands. Past work
has focused on designing the network to support all hose matrices (all matrices
not exceeding marginal bounds at the nodes). This model may be too conservative
if additional information on traffic patterns is available. Another extreme is
the fixed demand model, where one designs the network to support peak
point-to-point demands. We introduce a capped hose model to explore a broader
range of traffic matrices which includes the above two as special cases. It is
known that optimal designs for the hose model are always determined by
single-hub routing, and for the fixed- demand model are based on shortest-path
routing. We shed light on the wider space of capped hose matrices in order to
see which traffic models are more shortest path-like as opposed to hub-like. To
address the space in between, we use hierarchical multi-hub routing templates,
a generalization of hub and tree routing. In particular, we show that by adding
peak capacities into the hose model, the single-hub tree-routing template is no
longer cost-effective. This initiates the study of a class of robust network
design (RND) problems restricted to these templates. Our empirical analysis is
based on a heuristic for this new hierarchical RND problem. We also propose
that it is possible to define a routing indicator that accounts for the
strengths of the marginals and peak demands and use this information to choose
the appropriate routing template. We benchmark our approach against other
well-known routing templates, using representative carrier networks and a
variety of different capped hose traffic demands, parameterized by the relative
importance of their marginals as opposed to their point-to-point peak demands
Optimistic Robust Optimization With Applications To Machine Learning
Robust Optimization has traditionally taken a pessimistic, or worst-case
viewpoint of uncertainty which is motivated by a desire to find sets of optimal
policies that maintain feasibility under a variety of operating conditions. In
this paper, we explore an optimistic, or best-case view of uncertainty and show
that it can be a fruitful approach. We show that these techniques can be used
to address a wide variety of problems. First, we apply our methods in the
context of robust linear programming, providing a method for reducing
conservatism in intuitive ways that encode economically realistic modeling
assumptions. Second, we look at problems in machine learning and find that this
approach is strongly connected to the existing literature. Specifically, we
provide a new interpretation for popular sparsity inducing non-convex
regularization schemes. Additionally, we show that successful approaches for
dealing with outliers and noise can be interpreted as optimistic robust
optimization problems. Although many of the problems resulting from our
approach are non-convex, we find that DCA or DCA-like optimization approaches
can be intuitive and efficient
A note on hierarchical hubbing for a generalization of the VPN problem
Robust network design refers to a class of optimization problems that occur
when designing networks to efficiently handle variable demands. The notion of
"hierarchical hubbing" was introduced (in the narrow context of a specific
robust network design question), by Olver and Shepherd [2010]. Hierarchical
hubbing allows for routings with a multiplicity of "hubs" which are connected
to the terminals and to each other in a treelike fashion. Recently, Fr\'echette
et al. [2013] explored this notion much more generally, focusing on its
applicability to an extension of the well-studied hose model that allows for
upper bounds on individual point-to-point demands. In this paper, we consider
hierarchical hubbing in the context of a previously studied (and extremely
natural) generalization of the hose model, and prove that the optimal
hierarchical hubbing solution can be found efficiently. This result is relevant
to a recently proposed generalization of the "VPN Conjecture".Comment: 14 pages, 1 figur
Data-Driven Computing in Dynamics
We formulate extensions to Data Driven Computing for both distance minimizing
and entropy maximizing schemes to incorporate time integration. Previous works
focused on formulating both types of solvers in the presence of static
equilibrium constraints. Here formulations assign data points a variable
relevance depending on distance to the solution and on maximum-entropy
weighting, with distance minimizing schemes discussed as a special case. The
resulting schemes consist of the minimization of a suitably-defined free energy
over phase space subject to compatibility and a time-discretized momentum
conservation constraint. The present selected numerical tests that establish
the convergence properties of both types of Data Driven solvers and solutions.Comment: arXiv admin note: substantial text overlap with arXiv:1702.0157
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