Multidisciplinary design optimization under uncertainty

多学科设计优化（MDO）是解决许多现实工程问题中设计问题的新工具，如可再生能源系统、交通系统、生物医学系统等。它处理的挑战是：从不同的学科建模系统，处理不同类型的优化问题（线性，非线性，全局，整数等）与多目标，并处理非常大的计算需求。MDO需要使用合适的优化方法来解决不同学科的问题，例如，线性但规模极大的问题可能需要稀疏线性规划类型的模型或使用大型迭代稀疏求解器的方法，其他问题可能涉及需要全局优化方法的高度非光滑函数，大多数问题需要对概率依赖性进行建模，等等。******已经提出了许多MDO方法，其一般原则是将问题分解为求解一系列子问题，其中一些方法根据子学科进行分解。方法有多学科可行、个别学科可行、同时分析设计、协同优化、替代优化等。虽然这些方法考虑了大规模问题，但不确定性问题仍然是一个主要挑战。不确定性给这些问题带来了更大的复杂性，是MDO问题中的一个重要问题。新的基于copula（特别是Vine copula）的概率不确定性模型适用于这类分解问题。在本研究中，我们提出将现有的确定性多学科优化方法与可靠性和基于copula的模型相结合，以解决现实世界中不确定条件下的多学科优化问题。**

Multidisciplinary design optimization (MDO) is a new tool in solving design problems in many real-world engineering problems, such as, renewable energy systems, transportation systems, biomedical systems, among others. The challenges it tackles are: modelling systems from various disciplines, dealing with different kinds of optimization problems (linear, nonlinear, global, integer, etc) with multiobjectives, and dealing with the very large computational needs. MDO needs to use suitable optimization methods to solve problems in different disciplines, for example, problems that are linear but are extremely large scale might require sparse linear programming type models or methods that use large iterative sparse solvers, others may involve highly nonsmooth functions requiring global optimization methods, and most problems require modelling of probabilistic dependence, and so on. ******There have been many MDO methods suggested with the general principle of decomposing the problem into solving a sequence of sub problems and some of these methods decompose according to sub disciplines. There are many methods such as multidisciplinary feasible, individual discipline feasible, simultaneous analysis and design, collaborative, surrogate optimization, among others. While the issue of large scale is considered in these methods, the issue of uncertainty is still a major challenge. Uncertainty brings an order of complexity more to these problems and is an important issue in MDO problems. New probabilistic uncertainty models based on copulas (especially the Vine copulas) are suitable for such decomposed problems. In this proposal we propose to combine existing deterministic MDO methods with reliability and copula based models to solve real world multidisciplinary optimization problems under uncertainty. **