Global Dynamic Optimization

全局动态优化

• 批准号: 0521962
• 负责人: Paul Barton
• 金额: --
• 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: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0521962&HistoricalAwards=false
• 关键词: Global; Dynamic; Optimization

ABSTRACTPI: Paul I. Barton Institution: Massachusetts Institute of TechnologyProposal Number: 0521962Title: Global Dynamic OptimizationDynamic optimization determines values for input/control profiles, real valued parameters, initial conditions and/or boundary conditions of a dynamic system that optimize its performance over some period of time according to a specified metric. Dynamic optimization problems appear in almost every aspect of modern chemical engineering. The dynamic optimization problems encountered in chemical engineering often exhibit multiple suboptimal local minima. Conventional approaches for the solution of dynamic optimization problems can only guarantee locating local minima, which may be suboptimal. Suboptimality can have direct economic, safety and environmental impacts if a suboptimal solution is implemented on a real system. This project will develop theory, numerical methods and software that can guarantee locating a global solution of a dynamic optimization problem within a finite number of iterations.Intellectual Merit Previous research by the PI supported by the NSF has created global optimization theory and algorithms for optimization problems embedding linear time varying ordinary differential equations (ODEs) and nonlinear ODEs. The approach has been demonstrated for relatively small dynamic systems and up to about ten degrees of freedom in the optimization problem. The purpose of this research is to develop the theory and algorithms further so that optimization problems involving large-scale dynamic systems (possibly 1,000s-10,000s of state variables) and tens of degrees of freedom can be solved to guaranteed global optimality. This would bring a majority of the dynamic optimization problems in chemical engineering within the scope of global optimization methods. A key theoretical and practical issue in this extension is the computation of tight estimates of the image of a parameter set under the solution of nonquasi-monotone differential equations (most chemical engineering applications are nonquasi-monotone). Theory and algorithms based on extensions of classical results in differential inequalities will be used to address this issue. Moreover, many dynamic optimization problems in chemical engineering also have differential-algebraic equations (DAEs) and/or partial differential equations (PDEs) embedded. Theory and algorithms extending the global optimization approach to DAE and PDE embedded systems are planned.An application of global dynamic optimization is formal safety verification; deterministic global optimization provides a constructive proof that a dynamic system is safe, or guarantees location of a counterexample. However, formal verification is always with respect to a model and does not take into account the fact that there is always a discrepancy between the predictions of a model and the behavior of the corresponding physical system. This is commonly referred to as model uncertainty. Previous research has not considered the issue of model uncertainty in formal safety verification, but this is a potentially critical issue in guaranteeing the safety of a physical system. An approach based on a semi-infinite program with differential equations embedded is proposed to address model uncertainty in safety verification.Broader Impacts: The growing capability to solve dynamic optimization problems to guaranteed global optimality could have broad practical implications. For example, in the area of process operations there is hope for solving problems such as formal safety verification under uncertainty, the synthesis of integrated batch processes, and the design of major process transients such as start-up and shut-down procedures, using detailed dynamic models. The results of this work will be broadly disseminated through journal articles, publicly distributed software, course curricula and a textbook on global optimization currently being prepared by the PI. Moreover, the software developed through this project will be freely distributed via the Web to academic researchers. The project should provide students many opportunities for multidisciplinary education and research. The large number of female undergraduate and graduate students in the department should help in attracting some of them t o work on this project.

[摘要]pi: Paul I. Barton机构：麻省理工学院提案号：0521962标题：全局动态优化动态优化确定输入/控制轮廓，实值参数，初始条件和/或边界条件的值，动态系统根据指定的度量在一段时间内优化其性能。动态优化问题几乎出现在现代化工的各个方面。化工动态优化问题往往存在多个次优局部最小值。求解动态优化问题的传统方法只能保证找到局部极小值，而这可能是次优的。如果在实际系统中实现次优解决方案，则次优性会对经济、安全和环境产生直接影响。该项目将开发理论、数值方法和软件，以保证在有限次数的迭代中找到动态优化问题的全局解。由国家科学基金会资助的PI先前的研究已经为嵌入线性时变常微分方程和非线性常微分方程的优化问题创建了全局优化理论和算法。该方法已在相对较小的动态系统和高达约十个自由度的优化问题中得到证明。本研究的目的是进一步发展理论和算法，以便解决涉及大规模动态系统（可能有1,000 -10,000个状态变量）和数十个自由度的优化问题，以保证全局最优性。这将把大多数化工动态优化问题纳入全局优化方法的范畴。在这个扩展中，一个关键的理论和实践问题是在非拟单调微分方程（大多数化学工程应用是非拟单调的）解下参数集像的紧估计的计算。基于微分不等式经典结果扩展的理论和算法将用于解决这个问题。此外，化学工程中的许多动态优化问题还包含微分代数方程（DAEs）和/或偏微分方程（PDEs）。规划了将全局优化方法扩展到DAE和PDE嵌入式系统的理论和算法。全局动态优化的一个应用是形式安全验证；确定性全局优化提供了一个建设性的证据，证明一个动态系统是安全的，或者保证反例的位置。然而，形式验证总是针对模型，而没有考虑到模型的预测与相应物理系统的行为之间总是存在差异这一事实。这通常被称为模型不确定性。以前的研究没有考虑到形式安全验证中的模型不确定性问题，但这是保证物理系统安全的潜在关键问题。提出了一种基于嵌入微分方程的半无限规划方法来解决安全验证中的模型不确定性问题。更广泛的影响：解决动态优化问题以保证全局最优性的能力日益增长，可能具有广泛的实际意义。例如，在工艺操作领域，利用详细的动态模型，有希望解决不确定条件下的正式安全验证、集成批量工艺的综合以及启动和关闭程序等主要工艺瞬态的设计等问题。这项工作的成果将通过期刊文章、公开分发的软件、课程和PI目前正在编写的关于全球优化的教科书广泛传播。此外，通过该项目开发的软件将通过网络免费分发给学术研究人员。该项目应为学生提供多学科教育和研究的机会。该系大量的女性本科生和研究生应该有助于吸引她们中的一些人参与这个项目。