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Solving the Large Scale Next Release Problem with a Backbone-Based multilevel algorithm

IEEE TRANSACTIONS ON SOFTWARE ENGINEERING 2012年第5期38卷 1195-1212页

作者： Xuan, Jifeng Jiang, He Ren, Zhilei Luo, Zhongxuan Dalian Univ Technol Sch Software Dalian 116621 Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116621 Peoples R China

The Next Release Problem (NRP) aims to optimize customer profits and requirements selection for the software releases. The research on the NRP is restricted by the growing scale of requirements. In this paper, we propose a Backbone-based multilevel algorithm (BMA) to address the large scale NRP. In contrast to direct solving approaches, the BMA employs multilevel reductions to downgrade the problem scale and multilevel refinements to construct the final optimal set of customers. In both reductions and refinements, the backbone is built to fix the common part of the optimal customers. Since it is intractable to extract the backbone in practice, the approximate backbone is employed for the instance reduction while the soft backbone is proposed to augment the backbone application. In the experiments, to cope with the lack of open large requirements databases, we propose a method to extract instances from open bug repositories. Experimental results on 15 classic instances and 24 realistic instances demonstrate that the BMA can achieve better solutions on the large scale NRP instances than direct solving approaches. Our work provides a reduction approach for solving large scale problems in search-based requirements engineering.

关键词： The next release problem backbone soft backbone multilevel algorithm requirements instance generation search-based requirements engineering

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A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations in two space dimensions

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 1999年第4期20卷 1214-1228页

作者： Banoczi, JM Kelley, CT N Carolina State Univ Ctr Res Sci Computat Raleigh NC 27695 USA N Carolina State Univ Dept Math Raleigh NC 27695 USA

In this paper we describe a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer in two space dimensions. This extends our previous work in one space dimension. We formulate the equations as a compact fixed point problem with the temperature as the unknown. The fixed point map requires both a Poisson solve and a transport solve for its evaluation. As a solver for both the transport problem and the full system we apply the Atkinson-Brakhage algorithm, using Newton-GMRES as the solver on the coarse mesh. We compare our solver choices with Newton-GMRES. Under modest stability and convergence assumptions on the transport solver, we prove convergence of the multilevel method for the complete system.

关键词： conductive-radiative heat transfer multilevel algorithm compact fixed point problems

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A multilevel algorithm for large-eddy simulation of turbulent compressible flows

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JOURNAL OF COMPUTATIONAL PHYSICS 2001年第2期167卷 439-474页

作者： Terracol, M Sagaut, P Basdevant, C Off Natl Etud & Rech Aerosp F-92322 Chatillon France Univ Paris 13 LAGA UMR 7539 F-93430 Villetaneuse France

A multilevel method for large-eddy simulation of turbulent compressible flows is proposed. The method relies on the splitting of the turbulent flowfield into several frequency bands in space and time, each band being associated to a specific computational grid in physical space. This allows to take into account in a deterministic way the information contained on finer grids. A subgrid model adapted to such a decomposition-based on a generalization of the Germane's identity to multilevel decomposition-is also introduced. The approach is validated by several multilevel simulations in a subsonic plane channel flow configuration for a low and a high value of the Reynolds number, while reductions of the CPU times up to 80% are obtained. (C) 2001 Academic Press.

关键词： large-eddy simulation multilevel algorithm subgrid-scale modeling turbulence

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A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 1998年第1期19卷 266-279页

作者： Banoczi, JM Kelley, CT N Carolina State Univ Ctr Res Sci Computat Raleigh NC 27695 USA N Carolina State Univ Dept Math Raleigh NC 27695 USA

In this paper we describe and analyze a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer. This system of equations for radiative intensity and temperature can be formulated as a compact fixed point problem in temperature alone with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We obtain an efficient evaluation of the fixed point map by coupling a finite element diffusion solver with a fast transport solver developed by the second author. As a solver we apply a modification of the Atkinson-Brakhage method, with Newton-GMRES as the coarse mesh solver, to the full nonlinear system. We compare our discretization/solver pair with Newton-GMRES and the classical Atkinson-Brakhage algorithm.

关键词： conductive-radiative heat transfer multilevel algorithm compact fixed point problems

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A multilevel algorithm for large eddy simulation of turbulent compressible flows

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II FASCICULE...

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COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II FASCICULE B-MECANIQUE PHYSIQUE ASTRONOMIE 2000年第1期328卷 81-86页

作者： Terracol, M Sagaut, P Basdevant, C Off Natl Etud & Rech Aerosp F-92322 Chatillon France Univ Paris 13 LAGA UMR 7539 F-93430 Villetaneuse France

A multilevel method for Large-Eddy Simulation of turbulent unsteady compressible flows is proposed. It relies on the splitting of the turbulent flowfield into several frequency bands in space and time, each band being associated to a computational grid in physical space, allowing to take into account in a deterministic way the information contained on finer grids. A subgrid-scale model adapted to such a decomposition based on a generalization of the Germane's identity to multilevel decomposition - is also introduced. The approach is validated by a simulation in a subsonic plane channel flow configuration. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

关键词： large eddy simulation multilevel algorithm subgrid-scale modeling turbulence

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A multilevel algorithm FOR SOLVING A BOUNDARY INTEGRAL-EQUATION OF WAVE SCATTERING

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 1994年第10期7卷 466-470页

作者： LU, CC CHEW, WC Department of Electrical and Computer Engineering University of Illinois Urbana Illinois 61801

In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix-vector multiplication, requiring O(N2) floating-point operations. The fast multipole method (FMM) reduced the operation to O(N1-5). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix-vector multiplication is proportional to N (log(N))2. (C) 1994 John Wiley & Sons, Inc.

关键词： FAST MULTIPOLE algorithm multilevel algorithm WAVE SCATTERING BOUNDARY INTEGRAL EQUATION NUMERICAL METHODS

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A multilevel algorithm based on binary decision diagrams

A multilevel algorithm based on binary decision diagrams

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14th International Conference on Analytical and Stochastic Modelling Techniques and Applications

作者： Schuster, Johann Siegle, Markus Univ Buderswehr Munchen Inst Tech Informat Munich Germany

ISBN: (纸本)9780955301841

In this paper, a new variant of the multilevel algorithm for computing the steady-state solution of a continuous-time Markov chain is proposed. The method is integrated into a symbolic framework, where the CTMC is represented in a compact way using multi-terminal binary decision diagrams (MTBDD). It is shown how to represent the original CTMC and several aggregated chains within the same decision diagram, where particular attention is devoted to the question of how to deal with unreachable states. Some preliminary empirical results are provided which indicate that the method has the potential to solve very large Markov chains in an efficient manner.

关键词： markov chain numerical analysis aggregation multilevel algorithm binary decision diagram

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Numerical Calculation of Electromagnetic Scattering from Multiple Objects by Superposition Solution Combined with MoM - multilevel algorithm

Numerical Calculation of Electromagnetic Scattering from Mul...

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Conference on International Symposium on Electromagnetic Compatibility Tokyo

作者： Tanaka, Masahiro Gifu Univ Fac Engn Gifu 5011193 Japan

We have applied the superposition solution combined with the method of moments into electromagnetic scattering from multiple objects so far. In this paper, we apply the multilevel algorithm for superposition solution,... 详细信息

ISBN: (纸本)9784885522871

关键词： superposition solution multilevel algorithm method of moments integral equations

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A multilevel bilinear programming algorithm for the vertex separator problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第1期69卷 189-223页

作者： Hager, William W. Hungerford, James T. Safro, Ilya Univ Florida Dept Math POB 118105 Gainesville FL 32611 USA RaceTrac Store Support Ctr 200 Galleria Pkwy SE Atlanta GA 30339 USA Clemson Univ Sch Comp 228 McAdams Hall Clemson SC 29634 USA

The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. The Vertex Separator Problem was formulated in the paper 10.1016/***.2014.05.042 as a continuous (non-concave/non-convex) bilinear quadratic program. In this paper, we develop a more general continuous bilinear program which incorporates vertex weights, and which applies to the coarse graphs that are generated in a multilevel compression of the original Vertex Separator Problem. We develop a method for improving upon a given vertex separator by applying a Mountain Climbing algorithm to the bilinear program using an incidence vector for the separator as a starting guess. Sufficient conditions are developed under which the algorithm can improve upon the starting guess after at most two iterations. The refinement algorithm is augmented with a perturbation technique to enable escapes from local optima and is embedded in a multilevel framework for solving large scale instances of the problem. The multilevel algorithm is shown through computational experiments to perform particularly well on communication and collaboration networks.

关键词： Vertex separator Continuous formulation Graph partitioning multilevel Weighted edge contractions multilevel algorithm

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A fast multilevel domain decomposition algorithm for radar imaging

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2001年第4期49卷 666-671页

作者： Boag, A Tel Aviv Univ Dept Elect Engn Phys Elect IL-69978 Tel Aviv Israel

A novel algorithm for radar imaging is presented. The method comprises two steps. First, a decomposition of the radar data domain into subdomains and computation of pertinent low resolution images. Second, interpolation, phase correction and aggregation of the low-resolution images into the final high resolution one. A multilevel algorithm is formulated via a recursive application of the domain decomposition and image aggregation steps. The computational cost of the proposed algorithm is comparable to that of the fast Fourier transform (FFT) based techniques while it appears to he considerably more flexible than the latter.

关键词： multilevel algorithm radar imaging synthetic aperture radar

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