Optimization for Systems Under Uncertainty: Modeling, Asymptotic Analysis, and Recursive Algorithms

不确定性下的系统优化：建模、渐近分析和递归算法

• 批准号: 9877090
• 负责人: Gang George Yin
• 金额: $ 12万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-01 至 2003-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9877090&HistoricalAwards=false
• 关键词: Optimization; Systems; Under; Uncertainty; Modeling

Proposal Title: Optimization for Systems under Uncertainty: Modeling, Asymptotic Analysis, and Recursive AlgorithmsProposal Number: DMS-9877090PI: G. George YinAffl.: Department of Mathematics, Wayne State University, Detroit, MI 48202 Tel. [phone], Fax [phone], Email: [e-mail] Description:Focusing on modeling and optimization for systems under uncertainty, thisproposal consists of four parts. Part I proposes two types of algorithms. Thefirst one is an approximation of an analog diffusion machine; the secondone also takes measurement errors into consideration. Our goal is to developasymptotic properties of such algorithms. By using weak convergence methods,suitably scaled sequences will be shown to converge to appropriate diffusions.Part II treats a class of hybrid models. Approximation schemes forsystems involving singularly perturbed Markov chains with weak and stronginteractions will be developed, which are useful for natural time-scaleseparation and reduction of complexity for large-scale systems.Part III investigates asymptotic properties of solutions of Cauchy problemsarising from null-recurrent diffusions. Our focus is on obtaining convergenceand rate of convergence of the solutions. One of the primary motivations comesfrom the investigation of singularly perturbed systems. The results will beuseful to the ever expanding applications in optimization, controlled Markovsystems, hierarchical decision making, production planning, telecommunication,queueing networks, and system reliability.Part IV models single-machine scheduling problems under random processing time, and/or under random machine breakdownsand repairs, and/or subject to random compression of processing times.Our objectives are to develop feasible models and to obtain optimalscheduling policies for the underlying systems. These results will allow usto design scheduling models and strategies for more complex jobshops byconsidering integrated processes as single-machine systems.Nontechnical explanation:To bridge the gap between theory and applications, this research projectincludes three components: modeling, asymptotic analysis, and simulation.The ultimate goals are to provide useful models, to investigate their basicproperties, and to develop sound and feasible algorithms.Part 1 proposes two classes of algorithms with applications to machinelearning,image segmentation, and various global optimization tasks.To meet the increasing demand on robust design and control of systems inspeechand pattern recognition, signal processing, telecommunications, andmanufacturing, Part 2 aims to reduce the complexity of a large-scalesystem of complex structure by using a simple system via approximationschemes.The origin of the planned work for Part 3 stems from the effort of modelinguncertainties due to random influence such as demands for a product in amanufacturing system or fluctuation in the stock market. To controlthe underlying system, it is imperative to understand the system's long-termbehavior, which is our primary goal.In production planning, it is vital to provide good strategyin sequencing the parts to be processed by the machines. Part 4 proposessingle-machine scheduling models in uncertain environment.The proposed work aims to develop optimal scheduling policies.The overall planned work represents a continuation of the PI's recent preliminary exploration in these areas. It is expected that the results will be applicable in the further improvements of optimization methods.

提案标题：对不确定性下的系统的优化：建模，渐近分析和递归算法质量编号：DMS-987709090PI：G。George Yinaffl。：MI 48202 TEL。 313-577-2496，传真313-577-7596，电子邮件：[e-mail]说明：专注于在不确定性下对系统建模和优化，此质量包括四个部分。第一部分提出了两种类型的算法。第一个是模拟扩散机的近似值。第二个系统还考虑了测量误差。我们的目标是开发此类算法的性质。通过使用弱收敛方法，将显示适当的缩放序列可以收敛到适当的扩散。第二部分处理一类混合模型。将开发出涉及具有弱和强相互作用的奇异扰动的马尔可夫链的近似方案的结构系统，这对于大规模系统的自然时间范围内养成和降低复杂性很有用。我们的重点是获得解决方案收敛速率的收敛速度。主要动机之一来自对奇异扰动系统的研究。结果将使在优化，受控的马尔可足系统，等级决策，生产计划，电信，电信，排队网络和系统可靠性方面不断扩展的应用程序。基础系统的政策。这些结果将允许USTO设计调度模型和策略，以通过将整合过程作为单播种系统来进行更复杂的工作坊。非技术性解释：为了弥合理论与应用之间的差距，这项研究指出了三个组成部分，包括三个组成部分：建模，分析和模拟的最终目标。提出两类算法，并在机械学习，图像分割和各种全球优化任务中适用。满足对系统启发性识别，信号处理，电信处理，电信处理，和制造的需求不断增长由于随机影响而导致的建模剂，例如对制造系统中产品的需求或股票市场波动。为了控制基础系统，必须了解该系统的长期行为，这是我们的主要目标。在生产计划中，必须提供良好的策略，以测序机器要处理的零件。第4部分提议的机器调度模型在不确定的环境中。拟议的工作旨在制定最佳的调度政策。整体计划的工作代表了PI在这些领域的最新初步探索的延续。预计结果将适用于优化方法的进一步改进。