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hierarchical algorithms of functional modelling for solution of optimal operation problems in electrical power systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2008年第6-7期30卷 415-427页

作者： Makeechev, V. A. Soukhanov, O. A. Sharov, Y. V. Energy Syst Inst Moscow 125040 Russia Ind Power Co Moscow 123610 Russia Moscow Power Engn Inst Moscow 111250 Russia

This paper presents foundations of the optimization method intended for solution of power systems operation problems and based oil the principles of functional modeling (FM). This paper also presents several types of hierarchical FM algorithms for economic dispatch in these systems derived from this method. According to the FM method a power system is represented by hierarchical model consisting of systems of equations of lower (subsystem) levels and higher level system of connection equations (SCE), in which only boundary variables of subsystems are present. Solution of optimization problem in accordance with the FM method consists of the following operations: (1) solution of optimization problem for each subsystem (values of boundary variables for subsystems should be determined on the higher level of model);(2) calculation of functional characteristic (FC) of each subsystem, pertaining to state of subsystem on current iteration (these two steps are carried out on the lower level of the model);(3) formation and solution of the higher level system of equations (SCE), which gives values of boundary and supplementary boundary variables on current iteration. The key elements in the general structure of the FM method are FCs of subsystems, which represent them on the higher level of the model as "black boxes". Important advantage of hierarchical FM algorithms is that results obtained with them oil each iteration are identical to those of corresponding basic one level algorithms. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： optimization hierarchical algorithms functional modeling distributed processing economic dispatch optimal power flow

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LOW-RANK FACTORIZATIONS IN DATA SPARSE hierarchical algorithms FOR PRECONDITIONING SYMMETRIC POSITIVE DEFINITE MATRICES

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2018年第4期39卷 1701-1725页

作者： Agullo, Emmanuel Darve, Eric Giraud, Luc Harness, Yuval Inria Bordeaux F-34405 Talence France Stanford Univ Mech Engn Stanford CA 94305 USA Tel Aviv Univ Dept Appl Math Sch Math Sci IL-69978 Tel Aviv Israel

We consider the problem of choosing low-rank factorizations in data sparse matrix approximations for preconditioning large-scale symmetric positive definite (SPD) matrices. These approximations are memory-efficient schemes that rely on hierarchical matrix partitioning and compression of certain sub-blocks of the matrix. Typically, these matrix approximations can be constructed very fast, and their matrix product can be applied rapidly as well. The common practice is to express the compressed sub-blocks by low-rank factorizations, and the main contribution of this work is the numerical and spectral analysis of SPD preconditioning schemes represented by 2 x 2 block matrices, whose off-diagonal sub-blocks are low-rank approximations of the original matrix off-diagonal sub-blocks. We propose an optimal choice of low-rank approximations which minimizes the condition number of the preconditioned system, and demonstrate that the analysis can be applied to the class of hierarchically off-diagonal low-rank matrix approximations. Spectral estimates that take into account the error propagation through levels of the hierarchy which quantify the impact of the choice of low-rank compression on the global condition number are provided. The numerical results indicate that the properties of the preconditioning scheme using proper low-rank compression are superior to employing standard choices for low-rank compression. A major goal of this work is to provide an insight into how proper reweighted prior to low-rank compression influences the condition number for a simple case, which would lead to an extended analysis for more general and more efficient hierarchical matrix approximation techniques.

关键词： preconditioning symmetric positive definite data sparse hierarchical algorithms low-rank factorization minimal condition number

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ON THE hierarchical algorithms FOR NON-LINEAR SYSTEMS WITH BOUNDED CONTROL

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OPTIMAL CONTROL APPLICATIONS & METHODS 1984年第4期5卷 275-288页

作者： MAHMOUD, MS FAWSY, AS MIL TECH COLL DEPT COMP & CONTROLCAIROEGYPT

hierarchical algorithms for the dynamic optimization of non-linear systems with control bound inequality, constraints are considered. Three different computational schemes are developed, based on the costate prediction co-ordination. Each scheme consists of four levels; of which the second level manipulates the control constraints in an explicit way. Digital simulation of the developed algorithms on a typical power control system is presented.

关键词： Optimal control Non-linear systems hierarchical algorithms Costate co-ordination Computational schemes Power systems

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Quasi-periodic boundary conditions for hierarchical algorithms used for the calculation of inter-particle electrostatic interactions

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年 472卷

作者： Boutsikakis, Athanasios Fede, Pascal Simonin, Olivier Univ Toulouse Inst Mecan Fluides Toulouse IMFT CNRS Toulouse France

In the present work, a simplified way to apply tri-periodic Boundary Conditions (BCs) in hierarchical algorithms has been devised. The application of these BCs is demonstrated using an in-house algorithm that is used for the calculation of electrostatic interactions in a system of charged particles. The proposed quasi-periodic BCs entail a truncation of the infinite periodic domain with a reasonable cut-off error. For a correct representation of the physics, two properties have to be ensured: the convergence of the electrostatic forces and the isotropy of the electric field. The developed algorithm allows for a rather efficient and precise calculation of the former in a tri-periodic computational domain by separating them in short-and long-range parts, which are calculated exactly and approximately, respectively. The approximation error, computational cost and performance of the proposed algorithm are documented and thoroughly analyzed. Then, an application of the method is presented for dry mono-charged (all particles bear equal charge) particle flows where the fundamentals physics of particle-particle electrostatic interactions are investigated via characteristic length and time scales. It is shown that the underlying mechanism of these interactions is the Coulomb collision, a concept that allows to interpret these interactions in a rather intuitive way. In addition, an attempt is made to provide analytical estimations for several statistical quantities via dimensional analysis based on measured simulation data. Finally, the particle-induced electric field is presented and its characteristics are related to particle motion.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Particle flows Charged particles Electrostatic interaction hierarchical algorithms Periodic boundary conditions

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Tapas: An Implicitly Parallel Programming Framework For hierarchical N-body algorithms 22

Tapas: An Implicitly Parallel Programming Framework For Hier...

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22nd IEEE International Conference on Parallel and Distributed Systems (ICPADS)

作者： Fukuda, Keisuke Matsuda, Motohiko Maruyama, Naoya Yokota, Rio Taura, Kenjiro Matsuoka, Satoshi RIKEN Adv Inst Computat Sci Kobe Hyogo Japan Tokyo Inst Technol Tokyo Japan Univ Tokyo Tokyo Japan

ISBN: (纸本)9781509044573

Tapas is our new C++ programming framework for hierarchical algorithms such as N-body, on large scale heterogeneous supercomputers. Although N-body and their variants are widely used in scientific applications, their correct implementations are often difficult on such modern machines, as the algorithms are irregular, complex, and involve explicit task parallel programming over distributed nodes. Encapsulating the complexities in a library or a framework has been challenging due to irregular data access over massively distributed memory. Tapas solves this by converting the users clean implicit-style parallel program into an inspector-executor style code on heterogeneous multi-core, multi-node environment solely by the use of C++ template metaprogramming. A prototype implementation of the Fast Multipole Method on Tapas demonstrates a comparable performance and scaling as ExaFMM, the fastest hand-tuned implementation of FMM, as well as efficient usage of hundreds of GPUs. Specifically, the serial performance is 95% of ExaFMM, whereas the distributed-memory strong-scaling evaluation using up to 1500 CPU cores demonstrates 64% to 81% of the ExaFMM performance. The multi-GPU version of the Tapas-based FMM achieves a 5.15x speedup when executed on 100 nodes of TSUBAME2.5 with 300 GPUs.

关键词： Fast Multipole Method GPGPU hierarchical algorithms N-body algorithms Programming Framework

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BIOLOGICALLY PLAUSIBLE BSDT RECOGNITION OF COMPLEX IMAGES: THE CASE OF HUMAN FACES

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INTERNATIONAL JOURNAL OF NEURAL SYSTEMS 2008年第6期18卷 527-545页

作者： Gopych, Petro Univ Power Syst USA Ukraine LLC UA-61012 Kharkov Ukraine

On the basis of recent binary signal detection theory (BSDT), optimal recognition algorithms for complex images are constructed and their optimal performance are calculated. A methodology for comparing BSDT predictions and measured human performance is developed and applied to explaining particular face recognition experiment. The BSDT makes possible computer codes with recognition performance better than that in humans, its fundamental discreteness is consistent with the experiment. Related neurobiological and behavioral effects are briefly discussed.

关键词： Neural networks predictive coding hierarchical algorithms psychometric functions Neyman-Pearson objective decision confidence face recognition human errors

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Periodic hierarchical load balancing for large supercomputers

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INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2011年第4期25卷 371-385页

作者： Zheng, Gengbin Bhatele, Abhinav Meneses, Esteban Kale, Laxmikant V. Univ Illinois Dept Comp Sci Urbana IL 61801 USA Univ Illinois Parallel Programming Lab Urbana IL 61801 USA

Large parallel machines with hundreds of thousands of processors are becoming more prevalent. Ensuring good load balance is critical for scaling certain classes of parallel applications on even thousands of processors. Centralized load balancing algorithms suffer from scalability problems, especially on machines with a relatively small amount of memory. Fully distributed load balancing algorithms, on the other hand, tend to take longer to arrive at good solutions. In this paper, we present an automatic dynamic hierarchical load balancing method that overcomes the scalability challenges of centralized schemes and longer running times of traditional distributed schemes. Our solution overcomes these issues by creating multiple levels of load balancing domains which form a tree. This hierarchical method is demonstrated within a measurement-based load balancing framework in CHARM++. We discuss techniques to deal with scalability challenges of load balancing at very large scale. We present performance data of the hierarchical load balancing method on up to 16,384 cores of Ranger (at the Texas Advanced Computing Center) and 65,536 cores of Intrepid (the Blue Gene/P at Argonne National Laboratory) for a synthetic benchmark. We also demonstrate the successful deployment of the method in a scientific application, NAMD, with results on Intrepid.

关键词： hierarchical algorithms load balancing parallel applications performance study scalability

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A tuned and scalable fast multipole method as a preeminent algorithm for exascale systems

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INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2012年第4期26卷 337-346页

作者： Yokota, Rio Barba, Lorena A. Boston Univ Dept Mech Engn Boston MA 02215 USA

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes of the order of billions of unknowns. That work led to an extremely parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This paper reports on a campaign of performance tuning and scalability studies using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were parallelized using OpenMP, and a test using 10(7) particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using single instruction multiple data (SIMD) instructions resulted in 4 x speed-up of the overall algorithm on single-core tests with 10(3)-10(7) particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 10(8) particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2 x faster). The weak scaling test used 10(6) particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that FMM is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape. The code is open for unrestricted use under the MIT license.

关键词： fast multipole method FMM hierarchical algorithms exascale performance tuning OpenMP MPI

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Robotic path planning in static environment using hierarchical multi-neuron heuristic search and probability based fitness

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NEUROCOMPUTING 2011年第14-15期74卷 2314-2335页

作者： Kala, Rahul Shukla, Anupam Tiwari, Ritu Indian Inst Informat Technol & Management Gwalior Soft Comp & Expert Syst Lab Gwalior Madhya Pradesh India

Path Planning is a classical problem in the field of robotics. The problem is to find a path of the robot given the various obstacles. The problem has attracted the attention of numerous researchers due to the associated complexities, uncertainties and real time nature. In this paper we propose a new algorithm for solving the problem of path planning in a static environment. The algorithm makes use of an algorithm developed earlier by the authors called Multi-Neuron Heuristic Search (MNHS). This algorithm is a modified A* algorithm that performs better than normal A* when heuristics are prone to sharp changes. This algorithm has been implemented in a hierarchical manner, where each generation of the algorithm gives a more detailed path that has a higher reaching probability. The map used for this purpose is based on a probabilistic approach where we measure the probability of collision with obstacle while traveling inside the cell. As we decompose the cells, the cell size reduces and the probability starts to touch 0 or 1 depending upon the presence or absence of obstacles in the cell. In this approach, it is not compulsory to run the entire algorithm. We may rather break after a certain degree of certainty has been achieved. We tested the algorithm in numerous situations with varying degrees of complexities. The algorithm was able to give an optimal path in all the situations given. The standard A* algorithm failed to give results within time in most of the situations presented. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Path planning Robotics Multi-neuron heuristic search A* algorithm Heuristics Probabilistic fitness hierarchical algorithms

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hierarchical Normal Space Sampling to speed up point cloud coarse matching

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PATTERN RECOGNITION LETTERS 2012年第16期33卷 2127-2133页

作者： Diez, Yago Marti, Joan Salvi, Joaquim Univ Girona Dept Arquitectura & Tecnol Computadors Girona 17071 Spain

Point cloud matching is a central problem in Object Modeling with applications in Computer Vision and Computer Graphics. Although the problem is well studied in the case when an initial estimate of the relative pose is known (fine matching), the problem becomes much more difficult when this a priori knowledge is not available (coarse matching). In this paper we introduce a novel technique to speed up coarse matching algorithms for point clouds. This new technique, called hierarchical Normal Space Sampling (HNSS), extends Normal Space Sampling by grouping points hierarchically according to the distribution of their normal vectors. This hierarchy guides the search for corresponding points while staying free of user intervention. This permits to navigate through the huge search space taking advantage of geometric information and to stop when a sufficiently good initial pose is found. This initial pose can then be used as the starting point for any fine matching algorithm. hierarchical Normal Space Sampling is adaptable to different searching strategies and shape descriptors. To illustrate HNSS, we present experiments using both synthetic and real data that show the computational complexity of the problem, the computation time reduction obtained by HNSS and the application potentials in combination with ICP. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Coarse point cloud matching Normal space sampling hierarchical algorithms Data Structures

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