A New Paradigm for Large-Scale System Design Optimization

设计优化是设计变量值的计算，最小化或最大化受约束的目标，其中目标和约束函数是工程模型的输出。将大规模优化（涉及多达数千个设计变量）应用于工程设计是具有挑战性的，因为可扩展性的有效导数计算和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。该项目的目标是加速大规模系统设计优化算法的数量级相比，国家的最先进的方法。这种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。该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。一个侵入式的范例，使一种新的优化算法，将实现的鲁棒性的减少空间制定和全空间制定的效率，如果这两个配方可以统一。这两种公式之间的区别在于全空间将模型的状态视为设计变量。这项研究将导致理论和算法的贡献，序列二次规划（SQP），这是最常见的优化方法在LSDO。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选择缩减空间和全空间混合的方法。由此产生的算法将通过开源许可提供，从而提高效率，使学生，研究人员和从业人员受益。此外，混合算法消除了从业者之间选择减少和全空间问题制定的需要，因此，更少的努力和专业知识将需要LSDO。最大的影响将是在工业领域，效率和可用性的改进将大大降低使用LSDO帮助设计复杂工程系统的门槛，这将在与通用原子航空系统公司的合作中得到证明。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值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.