Tight Feasibility Constraints in Engineering Design

本研究将评估一种新方法的潜力，该方法通过分段线性函数紧密夹持非线性函数，有效地找到具有严格可行性约束的优化问题的解决方案。工程设计中的一类常见问题需要找到并优化函数，这些函数在一个区间内适合于严格分离的下限和上限之间。一个典型的例子考虑的是承载梁或线的组件，其必须装配到两个现有表面之间的狭窄空间中，并且在刚度方面进行优化。目前，此类问题需要大量且昂贵的试错人工干预。新的理论和软件工具将使搜索自动化，并使公差和计算预算之间的权衡变得明确。该方法可用于时间敏感的情况下，如交互式几何设计工具，并预计将释放计算周期的额外的工程目标，如刚度，热传导，不确定性，成本或进度。 在更广泛的范围内，新工具将有效地将现有的计算几何技术扩展到弯曲的路径和表面。 表格、工具和教程示例将作为开放源码SubLiME软件库的一部分分发。教育举措将侧重于调整本科数值计算的教学大纲，以提高对优化问题的认识;并教授如何制定和解决这些问题。 将通过两个以工程分析为特色的展览向公众传达研究的各个方面。

This research will assess the potential of a new method that tightly sandwiches nonlinear functions by piecewise linear functions, for efficiently finding solutions to optimization problems with tight feasibility constraints. A common class of problems in engineering design requires finding and optimizing functions that, over an interval, fit between narrowly separated lower and upper bounds. One typical example considers the components of a load-bearing beam or wire that has to fit into a narrow space between two existing surfaces and is to be optimized with respect to stiffness. Currently, such problems require extensive and expensive trial-and-error human intervention. The new theory and software tools will automate the search and make the trade-off between tolerances and computational budget explicit. The approach can be used in time-sensitive scenarios, such as interactive geometric design tools, and is expected to free computational cycles for the additional engineering objectives such as stiffness, heat conduction, uncertainty, cost or schedule. On a broader scale, the new tools will effectively extend existing computational geometry techniques to curved paths and surfaces. Tables, tools and tutorial examples will be disseminate as a part of the open-source SubLiME software library. The educational initiative will focus on adjusting the syllabus of undergraduate numerical computing to increase awareness of optimization problems; and to teach how to formulate and solve such problems. Aspects of the research to the general public will be communicated via two exhibitions featuring engineering analysis.