Serial and Parallel Algorithms for Large-Scale Nonlinear Network Flow Problems (Engineering)

大规模非线性网络流问题的串行和并行算法（工程）

• 批准号: 8800361
• 负责人: Anna Nagurney
• 金额: $ 13.88万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800361&HistoricalAwards=false
• 关键词: Serial; Parallel; Algorithms; Large; Scale

Many problems in engineering can be modeled and studied as nonlinear network flow problems. Examples include such large- scale systems as congested transportation networks, telecommuni- cation and computer systems, and resource distribution networks. Since such applications require timely solution, network algorithms must be designed for efficient computation and, hence, take advantage of any special problem structure and high- performance computer architectures. In this project, several serial and parallel equilibration algorithms will be developed for pure and generalized nonlinear network flow problems, with and without capacities. The node-link formulation of the problems, rather than the path, will be used for both fixed and elastic demand problems to substantially reduce the computer storage requirements of such algorithms. First, equilibration algorithms will be derived for quadratic networks, and then for more highly nonlinear networks, and convergence conditions established. Network topologies will then be defined to construct specialized algorithms. All algorithms will be computationally tested on different architectures using real- world data arising from a variety of applications, to demonstrate empirically their performance. Dr. Nagurney will develop and teach a course for upper-level undergraduates and graduate students on network equilibrium taught from the standpoint of competitive equilibrium problems and variational inequalities, in the spring 1989. She will conduct a series of lectures to faculty and students about her research on equilibrium algorithms for nonlinear network flow problems. In addition, Dr. Nagurney will organize a distinguished lecture series in which senior female scholars will be invited to M.I.T. to relate their experiences as female researchers. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.

工程中的许多问题都可以建模和研究， 非线性网络流问题 例如，大- 规模系统作为拥挤的交通网络， 阳离子和计算机系统以及资源分配网络。 由于此类应用需要及时解决，网络 算法必须被设计用于有效的计算，因此， 利用任何特殊问题结构和高- 性能计算机体系结构。 在这个项目中，几个 将开发串行和并行平衡算法 对于纯和广义非线性网络流问题， 没有能力。 的节点链接公式 问题，而不是路径，将用于固定和 弹性需求的问题，以大大减少计算机 这类算法的存储需求。 第一，平衡 算法将推导出二次网络，然后为 更高的非线性网络和收敛条件 确立了习 然后，将网络拓扑定义为 构建专门的算法。 所有算法都将 使用真实的- 世界数据所产生的各种应用，以证明 凭经验他们的表现。 Nagurney博士将开发和教授一门课程， 大学生和研究生的网络均衡 从竞争均衡问题的观点出发 和变分不等式，在1989年春天。 她将 为教师和学生举办一系列关于她的讲座 非线性网络流平衡算法研究 问题 此外，Nagurney博士将组织一次 杰出的系列讲座，资深女学者将 被麻省理工学院邀请把她们作为女性的经历 研究人员 本项目进一步促进了VPW计划的目标，即（1） 为妇女提供机会， 工程和科学的学科由NSF支持 （2）鼓励妇女从事科学事业， 通过提高女科学家的知名度， 以及受雇于工业、政府和学术界的工程师 机构职能体系 通过鼓励妇女参与 这是对国家未来的宝贵投资。 科学生命力