An Alternative Formulation of Collaborative Optimization Based on Geometric Analysis
An Alternative Formulation of Collaborative Optimization Based on Geometric Analysis
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DOI：
10.1115/1.4003919
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发表时间：
2011-05
影响因子：
3.3
通讯作者：
Xiang Li;Chang’an Liu;Weiji Li;Teng Long
中科院分区：
文献类型：
--
作者：
Xiang Li;Chang’an Liu;Weiji Li;Teng Long
协同优化（CO）是一种具有双层计算结构的多学科设计优化（MDO）方法，它将原优化问题分解为一个系统级问题和多个子系统问题。协同设计中的分解策略是解决大型工程设计问题的有效途径。然而，系统级一致性等式约束所带来的计算困难阻碍了协同优化的发展。本文基于协同优化的几何分析，提出了协同优化的一种新形式--协同优化与线性近似组合（CLA-CO），它比以往的代数分析更直观、更直接。在CLA-CO中，一致性等式约束在CO中被替换为子系统响应的线性近似。随着迭代过程的进行，更多的线性近似被添加到系统级。因此，这些线性近似的组合使得系统级问题逐渐逼近原始问题。在CLA-CO中，保持了分解策略的优点，同时避免了传统CO的计算困难。然而，仍然有困难的应用CLA-CO的非凸约束的问题。CLA-CO的应用程序的三个优化问题，数值试验问题，复合梁设计问题，齿轮减速器的设计问题，说明了CLA-CO的能力和局限性。
Collaborative optimization (CO) is a multidisciplinary design optimization (MDO) method with bilevel computational structure, which decomposes the original optimization problem into one system-level problem and several subsystem problems. The strategy of decomposition in CO is a useful way for solving large engineering design problems. However, the computational difficulties caused by the system-level consistency equality constraints hinder the development of CO. In this paper, an alternative formulation of CO called CO with combination of linear approximations (CLA-CO) is presented based on the geometric analysis of CO, which is more intuitive and direct than the previous algebraic analysis. In CLA-CO, the consistency equality constraints in CO are replaced by linear approximations to the subsystem responses. As the iterative process goes on, more linear approximations are added into the system level. Consequently, the combination of these linear approximations makes the system-level problem gradually approximate the original problem. In CLA-CO, the advantages of the decomposition strategy are maintained while the computational difficulties of the conventional CO are avoided. However, there are still difficulties in applying the presented CLA-CO to problems with nonconvex constraints. The application of CLA-CO to three optimization problems, a numerical test problem, a composite beam design problem, and a gear reducer design problem, illustrates the capabilities and limitations of CLA-CO.