A New Paradigm for Large-Scale System Design Optimization

设计优化是对受约束的目标最小化或最大化的设计变量值的计算，其中目标函数和约束函数是工程模型的输出。将涉及多达数千个设计变量的大规模优化应用到工程设计中是具有挑战性的，因为高效的导数计算对可扩展性的要求与系统级建模的多学科耦合的要求相互冲突。然而，最先进的基于梯度的优化器，结合PI最近在开发多学科导数计算的统一理论方面的工作，使得仅通过数百次模型评估就可以解决大规模设计优化(LSDO)问题成为可能。该项目的目标是与最先进的方法相比，将大规模系统设计优化算法加速一个数量级。这一改进将通过范式转换来实现，从而实现一种新的优化算法，该算法使用缩减空间和全空间优化的混合。本项目将研究一种新的侵入式范式，其中模型的内部组件暴露给优化器。一种侵入式范例使得能够实现一种新颖的优化算法，如果这两种公式能够统一，则该算法将实现简化空间公式的稳健性和全空间公式的效率。这两种公式的不同之处在于，全空间模型将模型的状态视为设计变量。这项研究将对LSDO中最常见的优化方法序列二次规划(SQP)做出理论和算法上的贡献。该研究项目将把统一扩展到一般的SQP算法，并利用基于伴随的误差估计和不精确牛顿方法来确定自适应地选择缩减空间和完整空间的混合方法。由此产生的算法将通过开放源码许可提供，允许效率提高，使学生、研究人员和从业者受益。此外，混合算法消除了实践者在缩减空间和全空间问题公式之间进行选择的需要；因此，LSDO所需的工作和专业知识将更少。最大的影响将是在工业上，效率和可用性的改进将显著降低使用LSDO帮助设计复杂工程系统的进入门槛，这将在通用原子航空系统公司的合作中得到证明。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Design optimization is the computation of design variable values that minimize or maximizean objective subject to constraints, where the objective and constraint functions are the outputs of an engineering model. Applying large-scale optimization - which involves up to thousands of design variables - to engineering design is challenging, because of the conflicting requirements of efficient derivative computation for scalability and coupling multiple disciplines for system-level modeling. However, state-of-the-art gradient-based optimizers, combined with the PI's recent work in developing a unified theory for multidisciplinary derivative computation, have made it feasible to solve large-scale design optimization (LSDO) problems in only hundreds of model evaluations. The objective of this project is to accelerate large-scale system design optimization algorithms by an order of magnitude compared to the state-of-the-art approach. This improvement will be achieved through a paradigm shift enabling a novel optimization algorithm that uses a hybrid of reduced-space and full-space optimization.This project will investigate a new, intrusive paradigm in which the internal components of the model are exposed to the optimizer. An intrusive paradigm enables a novel optimization algorithm that would achieve the robustness of a reduced-space formulation and the efficiency of a full-space formulation if the two formulations can be unified. The difference between the two formulations is that full-space treats the model's states as design variables. This research will result in theoretical and algorithmic contributions to sequential quadratic programming (SQP), which is the most common optimization approach in LSDO. The research project will broaden the unification to general SQP algorithms and leverage adjoint-based error estimation and inexact Newton methods to determine methods for adaptively selecting the hybrid of reduced and full space. The resulting algorithms will be made available through open-source licensing, allowing the efficiency improvements to benefit students, researchers, and practitioners. Moreover, the hybrid algorithm removes the need for practitioners to choose between reduced and full space problem formulation; therefore, less effort and expertise will be required for LSDO. The largest impact will be on industry, where the efficiency and usability improvements will significantly lower the barrier-to-entry for using LSDO to help design complex engineered systems, which will be demonstrated in collaboration with General Atomics Aeronautical Systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.