38,459 research outputs found
An efficient method for multiobjective optimal control and optimal control subject to integral constraints
We introduce a new and efficient numerical method for multicriterion optimal
control and single criterion optimal control under integral constraints. The
approach is based on extending the state space to include information on a
"budget" remaining to satisfy each constraint; the augmented
Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our
approach hinges on the causality in that PDE, i.e., the monotonicity of
characteristic curves in one of the newly added dimensions. A semi-Lagrangian
"marching" method is used to approximate the discontinuous viscosity solution
efficiently. We compare this to a recently introduced "weighted sum" based
algorithm for the same problem. We illustrate our method using examples from
flight path planning and robotic navigation in the presence of friendly and
adversarial observers.Comment: The final version accepted by J. Comp. Math. : 41 pages, 14 figures.
Since the previous version: typos fixed, formatting improved, one mistake in
bibliography correcte
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
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Chippe : a system for constraint driven behavioral synthesis
This report describes the Chippe system, gives some background previous work and describes several sample design runs of the system. Also presented are the sources of the design tradeoffs used by Chippe, and overview of the internal design model, and experiences using the system
Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks
We study the problem of computing shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing techniques follow a two-phase approach: In a preprocessing step, an index is built. The index depends on the road network and the traffic patterns but not on the path start and end. The latter are the input of the query phase, in which shortest paths are computed. All existing techniques have either large index size, slow query running times, or may compute suboptimal paths. In this work, we introduce CATCHUp (Customizable Approximated Time-dependent Contraction Hierarchies through Unpacking), the first algorithm that simultaneously achieves all three objectives. The core idea of CATCHUp is to store paths instead of travel times at shortcuts. Shortcut travel times are derived lazily from the stored paths. We perform an experimental study on a set of real world instances and compare our approach with state-of-the-art techniques. Our approach achieves the fastest preprocessing, competitive query running times and up to 30 times smaller indexes than competing approaches
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