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FTCSEM—A FORTRAN-based parallelized 1D CSEM forward and inversion program for arbitrary source-receiver geometry 认领 引用
1
作者 Wei-ying Chen Si-xu Han +2 位作者 Wan-ting Song Yu-lian Zhu Zheng Liu 《Applied Geophysics》 SCIE CSCD 2026年第2期693-709,870,共17页
This study introduces FTCSEM,a FORTRAN-based,parallelized one-dimensional controlledsource electromagnetic(CSEM)forward modeling and inversion software capable of accommodating arbitrary source-receiver confi guration... This study introduces FTCSEM,a FORTRAN-based,parallelized one-dimensional controlledsource electromagnetic(CSEM)forward modeling and inversion software capable of accommodating arbitrary source-receiver confi gurations.In comparison to existing one-dimensional CSEM tools,FTCSEM incorporates several signifi cant enhancements:it supports transmitters of diverse shapes,quantities,and spatial locations;permits receivers to be positioned flexibly on the surface,subsurface,or in the atmosphere;facilitates simulations and inversions in both frequency and time domains;integrates an adaptive regularized inversion algorithm with multiple model constraints;and leverages GPU-accelerated parallel computing to attain high computational efficiency.Validation through numerical experiments and field data inversion confirms the program’s accuracy and practical applicability.The findings indicate that FTCSEM performs robustly in complex geoelectric environments,multi-source and multi-receiver arrangements,as well as multi-component joint inversion scenarios,thereby offering a versatile and powerful tool for advancing CSEM research and applications. 展开更多
关键词 CSEM forward modeling regularized inversion parallel computing program
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PDP:Parallel Dynamic Programming 认领 引用 被引量：41
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作者 Fei-Yue Wang Jie Zhang +2 位作者 Qinglai Wei Xinhu Zheng Li Li 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2017年第1期1-5,共5页
Deep reinforcement learning is a focus research area in artificial intelligence.The principle of optimality in dynamic programming is a key to the success of reinforcement learning methods.The principle of adaptive dy... Deep reinforcement learning is a focus research area in artificial intelligence.The principle of optimality in dynamic programming is a key to the success of reinforcement learning methods.The principle of adaptive dynamic programming ADP is first presented instead of direct dynamic programming DP,and the inherent relationship between ADP and deep reinforcement learning is developed.Next,analytics intelligence,as the necessary requirement,for the real reinforcement learning,is discussed.Finally,the principle of the parallel dynamic programming,which integrates dynamic programming and analytics intelligence,is presented as the future computational intelligence.©2014 Chinese Association of Automation. 展开更多
关键词 Parallel dynamic programming Dynamic programming Adaptive dynamic programming Reinforcement learning Deep learning Neural networks Artificial intelligence
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Parallel Control for Optimal Tracking via Adaptive Dynamic Programming 认领 引用 被引量：31
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作者 Jingwei Lu Qinglai Wei Fei-Yue Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第6期1662-1674,共13页
This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is int... This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is introduced into the feedback system.However,due to the introduction of control input into the feedback system,the optimal state feedback control methods can not be applied directly.To address this problem,an augmented system and an augmented performance index function are proposed firstly.Thus,the general nonlinear system is transformed into an affine nonlinear system.The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically.It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function.Moreover,an adaptive dynamic programming(ADP)technique is utilized to implement the optimal parallel tracking control using a critic neural network(NN)to approximate the value function online.The stability analysis of the closed-loop system is performed using the Lyapunov theory,and the tracking error and NN weights errors are uniformly ultimately bounded(UUB).Also,the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals.Finally,the effectiveness of the developed optimal parallel control method is verified in two cases. 展开更多
关键词 Adaptive dynamic programming(ADP) nonlinear optimal control parallel controller parallel control theory parallel system tracking control neural network(NN)
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Scheduling Step-Deteriorating Jobs on Parallel Machines by Mixed Integer Programming 认领 引用 被引量：5
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作者 郭鹏 程文明 +1 位作者 曾鸣 梁剑 《Journal of Donghua University(English Edition)》 EI CAS 2015年第5期709-714,719,共6页
Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical... Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time. 展开更多
关键词 parallel machine step-deterioration mixed integer programming(MIP) scheduling models total completion time
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Programming for scientific computing on peta-scale heterogeneous parallel systems 认领 引用 被引量：1
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作者 杨灿群 吴强 +2 位作者 唐滔 王锋 薛京灵 《Journal of Central South University》 SCIE EI CAS 2013年第5期1189-1203,共15页
Peta-scale high-perfomlance computing systems are increasingly built with heterogeneous CPU and GPU nodes to achieve higher power efficiency and computation throughput. While providing unprecedented capabilities to co... Peta-scale high-perfomlance computing systems are increasingly built with heterogeneous CPU and GPU nodes to achieve higher power efficiency and computation throughput. While providing unprecedented capabilities to conduct computational experiments of historic significance, these systems are presently difficult to program. The users, who are domain experts rather than computer experts, prefer to use programming models closer to their domains （e.g., physics and biology） rather than MPI and OpenME This has led the development of domain-specific programming that provides domain-specific programming interfaces but abstracts away some performance-critical architecture details. Based on experience in designing large-scale computing systems, a hybrid programming framework for scientific computing on heterogeneous architectures is proposed in this work. Its design philosophy is to provide a collaborative mechanism for domain experts and computer experts so that both domain-specific knowledge and performance-critical architecture details can be adequately exploited. Two real-world scientific applications have been evaluated on TH-IA, a peta-scale CPU-GPU heterogeneous system that is currently the 5th fastest supercomputer in the world. The experimental results show that the proposed framework is well suited for developing large-scale scientific computing applications on peta-scale heterogeneous CPU/GPU systems. 展开更多
关键词 heterogeneous parallel system programming framework scientific computing GPU computing molecular dynamic
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PARALLEL MULTIPLICATIVE ITERATIVE METHODS FOR CONVEX PROGRAMMING 认领 引用 被引量：1
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作者 Chen zhong Fei Pusheng 《Acta Mathematica Scientia》 SCIE 1997年第2期205-210,共6页
In this paper,we present two parallel multiplicative algorithms for convex programming.If the objective function has compact level sets and has a locally Lipschitz continuous gradient,we discuss convergence of the alg... In this paper,we present two parallel multiplicative algorithms for convex programming.If the objective function has compact level sets and has a locally Lipschitz continuous gradient,we discuss convergence of the algorithms.The proofs are essentially based on the results of sequential methods shown by Eggermontt[1]. 展开更多
关键词 parallel algorithm convex programming
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Grid Service Framework: Supporting Multi-Models Parallel Grid Programming 认领 引用
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作者 邓倩妮 陆鑫达 《Journal of Shanghai Jiaotong university(Science)》 2004年第1期56-59,共4页
Web service is a grid computing technology that promises greater ease-of-use and interoperability than previous distributed computing technologies. This paper proposed Group Service Framework, a grid computing platfor... Web service is a grid computing technology that promises greater ease-of-use and interoperability than previous distributed computing technologies. This paper proposed Group Service Framework, a grid computing platform based on Microsoft. NET that use web service to: (1) locate and harness volunteer computing resources for different applications, and (2) support multi-models such as Master/Slave, Divide and Conquer, Phase Parallel and so forth parallel programming paradigms in Grid environment, (3) allocate data and balance load dynamically and transparently for grid computing application. The Grid Service Framework based on Microsoft. NET was used to implement several simple parallel computing applications. The results show that the proposed Group Service Framework is suitable for generic parallel numerical computing. 展开更多
关键词 web service volunteer computing grid computing parallel programming garadigm
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Implementable Strategy Research of Brake Energy Recovery Based on Dynamic Programming Algorithm for a Parallel Hydraulic Hybrid Bus 认领 引用 被引量：6
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作者 Zhong-Liang Zhang Jie Chen 《International Journal of Automation and computing》 CSCD 2014年第3期249-255,共7页
The purpose of this paper is to develop an implementable strategy of brake energy recovery for a parallel hydraulic hybrid bus. Based on brake process analysis, a dynamic programming algorithm of brake energy recovery... The purpose of this paper is to develop an implementable strategy of brake energy recovery for a parallel hydraulic hybrid bus. Based on brake process analysis, a dynamic programming algorithm of brake energy recovery is established. And then an implementable strategy of brake energy recovery is proposed by the constraint variable trajectories analysis of the dynamic programming algorithm in the typical urban bus cycle. The simulation results indicate the brake energy recovery efficiency of the accumulator can reach 60% in the dynamic programming algorithm. And the hydraulic hybrid system can output braking torque as much as possible.Moreover, the accumulator has almost equal efficiency of brake energy recovery between the implementable strategy and the dynamic programming algorithm. Therefore, the implementable strategy is very effective in improving the efficiency of brake energy recovery.The road tests show the fuel economy of the hydraulic hybrid bus improves by 22.6% compared with the conventional bus. 展开更多
关键词 Implementable strategy brake energy recovery dynamic programming parallel hydraulic hybrid bus shifting schedule pump/motor displacement.
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VulSCP: Automated Code Vulnerability Detection via Sequential Convolution and Parallel Attention Mechanism 认领 引用
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作者 Zhe Wang Yu Yan +3 位作者 Junqi Tong Yijun Lin Dechun Yin Xiaoliang Zhao 《Computers, Materials & Continua》 SCIE EI 2026年第8期1057-1081,共25页
As software applications grow increasingly large and complex,traditional code vulnerability detection methods struggle with performance and efficiency.Although code visualization-based algorithms have demonstrated eff... As software applications grow increasingly large and complex,traditional code vulnerability detection methods struggle with performance and efficiency.Although code visualization-based algorithms have demonstrated effectiveness in capturing sparse features and complex workflows in large-scale source code,their capacity to extract global semantic information and intricate long-range dependencies remains limited.Recent large language model(LLM)-based approaches have shown promising accuracy by leveraging rich contextual information,but their high computational cost often limits practical efficiency.To address these challenges,we propose VulSCP,a new framework that integrates sequential convolution with a parallel attention mechanism.Specifically,VulSCP first constructs a semantically weighted graph from the source code,then employs sequential convolution to extract local vulnerability-related features,and finally enhances the global feature representation through parallel attention.Experimental results on large-scale C/C++function-level datasets show that VulSCP achieves an accuracy of 85.14%and a false positive rate of 17.25%,outperforming the best baseline in accuracy by 1.73 percentage points and reducing the false positive rate by 3.38 percentage points.Moreover,while maintaining high detection accuracy,VulSCP achieves a low average inference time of 1.89 s per sample,showing favorable efficiency compared with the evaluated LLM-based methods.These results suggest that VulSCP is a promising approach for vulnerability detection in large and complex software systems,offering a favorable balance between accuracy and efficiency.The source code of VulSCP is publicly available at http://gffzz188fe103f8f1460asnnk0fxv5kwov69pf.ffgz.tsg.suse.edu.cn/Hwzx-ZeL/VulSCP. 展开更多
关键词 Code vulnerability detection sequential convolution parallel attention program dependency graph semantic graph representation
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Optimization Techniques for GPU-Based Parallel Programming Models in High-Performance Computing 认领 引用
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作者 Shuntao Tang Wei Chen 《信息工程期刊（中英文版）》 2024年第1期7-11,共5页
This study embarks on a comprehensive examination of optimization techniques within GPU-based parallel programming models,pivotal for advancing high-performance computing(HPC).Emphasizing the transition of GPUs from g... This study embarks on a comprehensive examination of optimization techniques within GPU-based parallel programming models,pivotal for advancing high-performance computing(HPC).Emphasizing the transition of GPUs from graphic-centric processors to versatile computing units,it delves into the nuanced optimization of memory access,thread management,algorithmic design,and data structures.These optimizations are critical for exploiting the parallel processing capabilities of GPUs,addressingboth the theoretical frameworks and practical implementations.By integrating advanced strategies such as memory coalescing,dynamic scheduling,and parallel algorithmic transformations,this research aims to significantly elevate computational efficiency and throughput.The findings underscore the potential of optimized GPU programming to revolutionize computational tasks across various domains,highlighting a pathway towards achieving unparalleled processing power and efficiency in HPC environments.The paper not only contributes to the academic discourse on GPU optimization but also provides actionable insights for developers,fostering advancements in computational sciences and technology. 展开更多
关键词 Optimization Techniques GPU-Based Parallel Programming Models High-Performance Computing
Stochastic Programming Model for Discrete Lotsizing and Scheduling Problem on Parallel Machines 认领 引用
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作者 Kensuke Ishiwata Jun Imaizumi +1 位作者 Takayuki Shiina Susumu Morito 《American Journal of Operations Research》 2012年第3期374-381,共8页
In recent years, it has been difficult for manufactures and suppliers to forecast demand from a market for a given product precisely. Therefore, it has become important for them to cope with fluctuations in demand. Fr... In recent years, it has been difficult for manufactures and suppliers to forecast demand from a market for a given product precisely. Therefore, it has become important for them to cope with fluctuations in demand. From this viewpoint, the problem of planning or scheduling in production systems can be regarded as a mathematical problem with stochastic elements. However, in many previous studies, such problems are formulated without stochastic factors, treating stochastic elements as deterministic variables or parameters. Stochastic programming incorporates such factors into the mathematical formulation. In the present paper, we consider a multi-product, discrete, lotsizing and scheduling problem on parallel machines with stochastic demands. Under certain assumptions, this problem can be formulated as a stochastic integer programming problem. We attempt to solve this problem by a scenario aggregation method proposed by Rockafellar and Wets. The results from computational experiments suggest that our approach is able to solve large-scale problems, and that, under the condition of uncertainty, incorporating stochastic elements into the model gives better results than formulating the problem as a deterministic model. 展开更多
关键词 Stochastic Programming Lotsizing and Scheduling Parallel Machines Scenario Aggregation Method
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Research and Review on the Java Multi-thread Programming and Its Further Development Tendency 认领 引用
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作者 Jiangtao Geng 《International Journal of Technology Management》 2016年第5期4-6,共3页
In this paper, we conduct research on the Java multi-thread programming and its further development tendency. Multithreading mechanisms can run several programs at the same time, make the program run effi ciency becom... In this paper, we conduct research on the Java multi-thread programming and its further development tendency. Multithreading mechanisms can run several programs at the same time, make the program run effi ciency becomes higher that also can overcome the problem of basic traditional programming language design while its design is the key to the realization of the synchronous thread. Multithreading is a mechanism that allows concurrent execution of multiple instruction stream in the program, each instruction stream is called a thread, independent from each other between each other. Thread is also known as a lightweight process, it have independent execution and process control. Our research starts from the analysis of the corresponding mechanism to enhance the performance that is innovative and meaningful. 展开更多
关键词 Review Multi-thread Development Tendency Programming Computer Science
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A Neuron-Oriented Programming System 认领 引用 被引量：4
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作者 李涛 《High Technology Letters》 EI CAS 2001年第1期70-73,共4页
A neruon-oriented programming system based on parallel neural information processing has been presented. With the neural programming system built upon 4～8 process elements(TMS C30), the system has thus provided users... A neruon-oriented programming system based on parallel neural information processing has been presented. With the neural programming system built upon 4～8 process elements(TMS C30), the system has thus provided users high speed, general purpose and large scale neural network application development platforms etc. 展开更多
关键词 Neural networks Parallel processing Programming system
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Dynamically Translating Binary Code for Multi-Threaded Programs Using Shared Code Cache 认领 引用
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作者 Chia-Lun Liu Jiunn-Yeu Chen +1 位作者 Wuu Yang Wei-Chung Hsu 《Journal of Electronic Science and Technology》 CAS 2014年第4期434-438,共5页
mc211vm is a process-level ARM-to-x86 binary translator developed in our lab in the past several years. Currently, it is able to emulate singlethreaded programs. We extend mc211vm to emulate multi-threaded programs. O... mc211vm is a process-level ARM-to-x86 binary translator developed in our lab in the past several years. Currently, it is able to emulate singlethreaded programs. We extend mc211vm to emulate multi-threaded programs. Our main task is to reconstruct its architecture for multi-threaded programs. Register mapping, code cache management, and address mapping in mc2llvm have all been modified. In addition, to further speed up the emulation, we collect hot paths, aggressively optimize and generate code for them at run time. Additional threads are used to alleviate the overhead. Thus, when the same hot path is walked through again, the corresponding optimized native code will be executed instead. In our experiments, our system is 8.8X faster than QEMU （quick emulator） on average when emulating the specified benchmarks with 8 guest threads. 展开更多
关键词 ARM binary translation hot path,mc211vm multi-threaded program QEMU （quickemulator）.
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Programming System PARCS 认领 引用
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作者 A. V. Anisimov A. V. Derevianchenko +1 位作者 P. P. Kuliabko O. M. Fedorus 《Journal of Computer and Communications》 2017年第9期129-139,共11页
PARCS (Parallel Asynchronous Recursive Control System) programming tools that allow unified add-on parallel extensions over traditional programming languages are described. The PARCS model is based on the conception o... PARCS (Parallel Asynchronous Recursive Control System) programming tools that allow unified add-on parallel extensions over traditional programming languages are described. The PARCS model is based on the conception of a control space, which is used to describe parallel interacting processes. Structurally, the control space consists of addressable “points” and “channels”. Executing modules are assigned to points and communicate through channels connecting points. Recursive embeddings of processes are allowed. The effective implementation of PARCS on cloud platforms Microsoft AZURE and Amazon EC2 is also presented. 展开更多
关键词 Parallel Computing Programming Language Control Space Cloud Computing
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中小型流域梯级水电站群机组负荷分配方法 认领 引用
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作者 龚科 江政 +2 位作者 张元元 杨立勇 邱晓松 《水电能源科学》 北大核心 2026年第7期217-221,216,共5页
传统梯级水电站群短期调度通常先确定电站出力再分配至机组,需反复校正约束以保证水量平衡,降低了计算效率与解集质量。为此,提出一种以机组为最小单元的中小型流域梯级水电站短期调度模型。该模型包含两层:内层采用基于水位启发信息的... 传统梯级水电站群短期调度通常先确定电站出力再分配至机组,需反复校正约束以保证水量平衡,降低了计算效率与解集质量。为此,提出一种以机组为最小单元的中小型流域梯级水电站短期调度模型。该模型包含两层:内层采用基于水位启发信息的层推法确定机组启停与出力;外层是以水位经济区间上下限为决策变量,通过多核并行禁忌增量动态规划求解不同水位经济区间下的机组出力。两层交替迭代直至发电量变化满足精度要求,最终得到各电站最优水位经济运行区间及机组出力过程。某流域5座日调节电站实例表明,该方法可快速制定日发电计划,机组出力过程平稳,且能显著提升梯级总发电量,适用于中小流域梯级电站的短期调度。 展开更多
关键词 短期调度 机组负荷分配 多核并行 增量动态规划法
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基于SSA算法的C语言程序多核可扩展并行计算优化方法 认领 引用
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作者 元尼东珠 《西安文理学院学报（自然科学版）》 2026年第2期49-54,共6页
C语言程序在多核可扩展并行计算过程中,增加线程数可以显著提高程序的并行度,使更多的计算任务可以同时进行.但随着线程数的增加,线程间的同步和资源竞争问题会变得更加复杂,降低并行计算效果.对此,提出基于SSA算法的C语言程序多核可扩... C语言程序在多核可扩展并行计算过程中,增加线程数可以显著提高程序的并行度,使更多的计算任务可以同时进行.但随着线程数的增加,线程间的同步和资源竞争问题会变得更加复杂,降低并行计算效果.对此,提出基于SSA算法的C语言程序多核可扩展并行计算优化方法.通过综合考虑平衡执行时间、资源利用率、负载均衡等多个方面,将C语言程序多核可扩展并行计算优化问题建模为一个多目标优化问题.对线程数、任务划分以及负载均衡等目标进行约束,保证C语言程序的并行计算性能.结合SSA算法对约束目标进行求解,通过不断调整线程分配与任务划分策略,优化C语言程序在多核环境下的并行计算结果.在实验中,对提出的方法进行了代码运行质量的检验,测试结果表明,采用提出的方法对C语言程序进行优化后,代码覆盖率在高线程条件下依然保持较高水平,具备较为理想的优化效果. 展开更多
关键词 SSA算法 C语言程序 多核可扩展 并行计算 程序优化
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Parallel Dispatch:A New Paradigm of Electrical Power System Dispatch 认领 引用 被引量：10
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作者 Jun Jason Zhang Fei-Yue Wang +5 位作者 Qiang Wang Dazhi Hao Xiaojing Yang David Wenzhong Gao Xiangyang Zhao Yingchen Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第1期311-319,共9页
Modern power systems are evolving into sociotechnical systems with massive complexity, whose real-time operation and dispatch go beyond human capability. Thus,the need for developing and applying new intelligent power... Modern power systems are evolving into sociotechnical systems with massive complexity, whose real-time operation and dispatch go beyond human capability. Thus,the need for developing and applying new intelligent power system dispatch tools are of great practical significance. In this paper, we introduce the overall business model of power system dispatch, the top level design approach of an intelligent dispatch system, and the parallel intelligent technology with its dispatch applications. We expect that a new dispatch paradigm,namely the parallel dispatch, can be established by incorporating various intelligent technologies, especially the parallel intelligent technology, to enable secure operation of complex power grids,extend system operators' capabilities, suggest optimal dispatch strategies, and to provide decision-making recommendations according to power system operational goals. 展开更多
关键词 ACP knowledge automation power dispatch parallel dynamic programming parallel intelligence paralle learning situational awareness
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The parallel 3D magnetotelluric forward modeling algorithm 认领 引用 被引量：34
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作者 Tan Handong Tong Tuo Lin Changhong 《Applied Geophysics》 2006年第4期197-202,共6页
The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the dat... The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the data in the frequency domain, which is very suitable for parallel computation. With the advantage of MPI and based on an analysis of the flow of the 3D magnetotelluric serial forward algorithm, we suggest the idea of parallel computation and apply it. Three theoretical models are tested and the execution efficiency is compared in different situations. The results indicate that the parallel 3D forward modeling computation is correct and the efficiency is greatly improved. This method is suitable for large size geophysical computations. 展开更多
关键词 Magnetotelluric 3D forward modeling MPI parallel programming design 3D staggered-grid finite difference method parallel algorithm.
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Scheduling and Subcontracting under Parallel Machines 认领 引用 被引量：2
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作者 陈荣军 唐国春 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期590-597,共8页
In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.T... In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted.Furthermore,it needs to determine a production schedule for jobs to be produced in-house.We discuss five classical scheduling objectives as production costs.For each problem with different objective functions,we give optimality conditions and propose dynamic programming algorithms. 展开更多
关键词 scheduling subcontracting dynamic programming parallel machines
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