8,229 research outputs found
A global optimization approach to solve multi-aircraft routing problems
"This chapter appears in Computational Models, Software Engineering and Advanced Technologies in Air Transportation edited by Dr. Li Weigang and Dr. Alexandre G. de Barros. Chap.12 pp.237-259. Copyright 2009. Posted by permission of the publisher."This paper describes the formulation and solution of a multi-aircraft routing problem which is posed as a global optimization calculation. The paper extends previous work (involving a single aircraft using two dimensions) which established that the algorithm DIRECT is a suitable solution technique. The present work considers a number of ways of dealing with multiple routes using different problem decompositions. A further enhancement is the introduction of altitude to the problems so that full three-dimensional routes can be produced. Illustrative numerical results are presented involving up to three aircraft and including examples which feature routes over real-life terrain data
Transverse electric scattering on inhomogeneous objects: spectrum of integral operator and preconditioning
The domain integral equation method with its FFT-based matrix-vector products
is a viable alternative to local methods in free-space scattering problems.
However, it often suffers from the extremely slow convergence of iterative
methods, especially in the transverse electric (TE) case with large or negative
permittivity. We identify the nontrivial essential spectrum of the pertaining
integral operator as partly responsible for this behavior, and the main reason
why a normally efficient deflating preconditioner does not work. We solve this
problem by applying an explicit multiplicative regularizing operator, which
transforms the system to the form `identity plus compact', yet allows the
resulting matrix-vector products to be carried out at the FFT speed. Such a
regularized system is then further preconditioned by deflating an apparently
stable set of eigenvalues with largest magnitudes, which results in a robust
acceleration of the restarted GMRES under constraint memory conditions.Comment: 20 pages, 8 figure
Improving Performance of Iterative Methods by Lossy Checkponting
Iterative methods are commonly used approaches to solve large, sparse linear
systems, which are fundamental operations for many modern scientific
simulations. When the large-scale iterative methods are running with a large
number of ranks in parallel, they have to checkpoint the dynamic variables
periodically in case of unavoidable fail-stop errors, requiring fast I/O
systems and large storage space. To this end, significantly reducing the
checkpointing overhead is critical to improving the overall performance of
iterative methods. Our contribution is fourfold. (1) We propose a novel lossy
checkpointing scheme that can significantly improve the checkpointing
performance of iterative methods by leveraging lossy compressors. (2) We
formulate a lossy checkpointing performance model and derive theoretically an
upper bound for the extra number of iterations caused by the distortion of data
in lossy checkpoints, in order to guarantee the performance improvement under
the lossy checkpointing scheme. (3) We analyze the impact of lossy
checkpointing (i.e., extra number of iterations caused by lossy checkpointing
files) for multiple types of iterative methods. (4)We evaluate the lossy
checkpointing scheme with optimal checkpointing intervals on a high-performance
computing environment with 2,048 cores, using a well-known scientific
computation package PETSc and a state-of-the-art checkpoint/restart toolkit.
Experiments show that our optimized lossy checkpointing scheme can
significantly reduce the fault tolerance overhead for iterative methods by
23%~70% compared with traditional checkpointing and 20%~58% compared with
lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1
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