Unifying Monolithic Architectures for Large-Scale System Design Optimization

Abstract

Large-scale system design optimization is a numerical technique used in solving system design problems that involve a large number of design variables. These systems are often multidisciplinary, with many disciplines interacting with each other. The scale of these problems demands a gradient-based approach for efficient solutions, and it is often implemented by coupling an engineering model with an optimizer. A recently developed theory on multidisciplinary derivative computation has made it feasible to solve large-scale system design optimization problems in only hundreds of model evaluations. This has led to an increase in the number of applications for large-scale system design optimization with new applications still emerging. This paper presents a new optimization formulation that can further reduce the required number of model evaluations by unifying two widely used optimization architectures, namely, multidisciplinary feasible, and simultaneous analysis and design. Complex engineering systems that require solutions of large nonlinear systems can potentially benefit from this new formulation, and the optimized solutions can be reached in just tens of equivalent model evaluations. We demonstrate this order of magnitude improvement using a bar design problem. The paper also provides details on the practical implementation of this new formulation in an equality-constrained optimization setting.Nomenclature df dx = total derivative of a variable f with respect to a variable x ∂F ∂x = partial derivative of a function F with respect to a variable x

An SQP algorithm based on a hybrid architecture for accelerating optimization of large-scale systems

“…Here we describe the modified full-space (MFS) method proposed in [1] for an equality-constrained setting. The MFS method is derived from the conventional FS method by incorporating two updates.…”

“…Since the standard MFS method is equivalent to the RS method, we can get any hybrids of the FS and RS by applying inexact tolerances on the two solvers in the MFS method. The SURF (strong unification of reduced-space and full-space) architecture proposed in [1] results from the introduction of this inexactness into the MFS architecture. Therefore, SURF provides a complete theoretical unification of the RS and FS architectures as we can now select one of the two architectures or any of its hybrids by just varying the inexact solver tolerances.…”

“…Joshy and Hwang [1] had earlier proposed a hybrid architecture that has the potential to reduce overall optimization times for large-scale systems with expensive nonlinear systems by utilizing an intrusive paradigm combining modeling and optimization. Based on this intrusive paradigm, a new algorithm called SURF (strong unification of reducedspace and full-space) was shown to accelerate the optimization by an order of magnitude for an equality-constrained optimization problem.…”

“…Fig. 2 Reduced-space versus full-space formulation for a model containing implicit state variables [1].…”

“…From Eq. ( 9) for the merit function, we can exactly measure the error in the terms 𝜓 𝑇 R (𝑥, 𝑦) and 1 2 𝜌R (𝑥, 𝑦) 𝑇 R (𝑥, 𝑦) as respectively 𝜓 𝑇 𝜖 𝑟 and 1 2 𝜌𝜖 𝑇 𝑟 𝜖 𝑟 , where 𝜖 𝑟 = R (𝑥, 𝑦) is the tolerance on the nonlinear solvers. We now approximate 𝜖 𝜙 using adjoint-based error estimation for the remaining three terms as…”