Optimization Algorithms For a Class of Engineering Design Problems

一类工程设计问题的优化算法

• 批准号: 9900985
• 负责人: Elijah Polak
• 金额: $ 15万
• 依托单位: University of California-Berkeley
• 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: 1999-08-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9900985&HistoricalAwards=false
• 关键词: Optimization; Algorithms; Class; Engineering; Design

This proposal is for the continuation of long standing efforts in developing special purpose algoritluns for the solution of important engineering optimization problems that are not tractable by standard mathematical programming or optimal control algorithms. The problems include design centering, tolerancing and post manufacture tuning, robot and vehicle path planning in the presence of obstacles with coners, described by max-min type inequalities, optimal control and pursuit-evasion problems arising in air-traffic control, various shape optimization problems, and problems of seismic resistant structural design subject reliability constraints. These problems are invariably characterized by nonsmoothness and infinite dimensionality of either variables or constraints or both, and often involve ordinary or partial differential equations. The proposed research will exploit several tools developed, such as (i) the theory of consistent approximations, (ii) reformulation techniques for converting seemingly intractable problems into tractable forms.The framework of consistent approximations ensures the convergence of local and global minimizers and stationary points of approximating problems to those of the original problem. Also, it provides master algorithm models with discretization adjustment procedures, which can be used in conjunction with highly polished, mathematical programming libraries. Furthermore, these algorithms can be made to converge superlinearly by calling superlinearly converging mathematical programming subroutines from the master algorithms. By contrast, the problem reformulation techniques that we envisage must be developed on an ad hoc basis, as we have already done for some path planning and reliability constrained problems.The chances for success of the proposal research will be considerably enhanced by the fact that we have already obtained some results on which we can build and the multidisciplinary setting provided by the ongoing interactions and collaborations of the principal investigator and others.

这一建议是为了继续长期以来在开发特殊目的算法方面的努力，以解决无法通过标准数学规划或最优控制算法处理的重要工程优化问题。这些问题包括设计定心、公差和制造后的调整，机器人和车辆在有角障碍物的情况下的路径规划，用极大极小型不等式描述，空中交通管制中出现的最优控制和追逃问题，各种形状优化问题，以及抗震结构设计主体可靠性约束问题。这些问题总是以非光滑和无限维度为特征，要么是变量，要么是约束，要么是两者兼而有之，通常涉及常微分方程或偏微分方程。拟议的研究将利用几种开发的工具，例如(i)一致近似理论，（ii）将看似棘手的问题转化为易于处理的形式的重新表述技术。一致逼近框架保证了逼近问题的局部极小值和全局极小值及平稳点收敛于原问题的平稳点。此外，它还提供了带有离散化调整程序的主算法模型，可以与高度完善的数学编程库一起使用。此外，这些算法可以通过调用主算法中的超线性收敛数学规划子程序来实现超线性收敛。相比之下，我们设想的问题重新表述技术必须在特别的基础上开发，正如我们已经为一些路径规划和可靠性约束问题所做的那样。提案研究成功的机会将大大增加，因为我们已经获得了一些我们可以建立的结果，以及主要研究者和其他人正在进行的互动和合作所提供的多学科环境。