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 βF βx = partial derivative of a function F with respect to a variable x
This paper presents a framework under development for enabling large-scale multi-fidelity modeling and optimization of electric vertical takeoff and landing concepts (eVTOL). The key features of the framework are a geometry-centric approach to multidisciplinary design
Large-scale system design optimization has recently started being used in many fields as a tool in the design of new concepts. This has exposed many of its limitations, especially in regard to its usability and computational efficiency. State-of-the-art optimization algorithms can solve problems with tens of thousands of design variables in just hundreds of model evaluations. However, this can be computationally expensive for complex systems with costly simulations. A new, hybrid algorithm called SURF, which unifies the full-space and reduced-space architectures, can accelerate optimization of computational models of engineering systems involving large numbers of implicitly defined state variables. However, the theory and numerical results for SURF were restricted to equality-constrained problems solved using the method of Newton-Lagrange. This paper investigates the extension of SURF to the inequality-constrained optimization setting. We first extend the theory of SURF to bring sequential quadratic programming under the scope of SURF. Based on this extended theory, we propose an implementation of the SURF algorithm for inequality-constrained problems. We then test the hypothesis that this algorithm unifies the full-space and reduced-space algorithms, using a nonlinear topology optimization problem. Finally, we measure the improvement provided by SURF over the reduced-space method, using the same optimization problem. The results from the investigation suggest that the proposed new algorithm unifies the full-space and reduced-space methods for any constrained optimization setting. We also observe a reduction in the total number of linear system solutions required in solving the nonlinear systems within the model. However, we expect an actual improvement in the overall optimization time only with an industrial quality sequential quadratic programming optimizer implemented with SURF since the optimizer used in this study did not scale well with the number of design variables thus inherently favoring the reduced-space approach. Nomenclature= partial derivative of a function F with respect to a variable x d d = total derivative of a function F with respect to a variable x β ( ) = gradient of a function F with respect to a variable x
The optimization of large-scale and multidisciplinary engineering systems is now prevalent in many fields, exemplified in areas such as aircraft, satellite, and wind turbine design. The rise of advanced modeling frameworks has expanded the scope of large-scale optimization techniques across various research domains. However, novel applications have emerged that pose efficiency-related computational challenges to the existing methods employed in large-scale, gradient-based optimization. The authors previously proposed a new paradigm for accelerating the optimization of large-scale and complex-engineered systems, laying the groundwork for a new approach. The new paradigm is based on a hybrid optimization architecture called SURF which stands for strong unification of reduced-space and full-space. SURF has the potential to expedite optimization of models with state variables that are iteratively computed by solving nonlinear systems. This paper extends the existing paradigm by providing new theoretical results that unify the reduced-space and full-space algorithms in a practical optimization setting that considers line searches and quasi-Newton methods. We also present a practical, SQP-based SURF algorithm that can be applied to general, inequality-constrained problems. The new algorithm also includes an adaptive hybrid selection strategy for robust convergence and faster solutions. We test the new algorithm on a low-fidelity motor optimization problem and a wind farm layout optimization problem to validate the optimization results, and to demonstrate its computational benefits. In one of the problems, SURF was able to speed up the traditional optimization by approximately 25 percent. In the other problem, SURF was able to converge to a better optimal solution. I. Nomenclature ππΉ ππ₯= partial derivative of a function πΉ with respect to a variable π₯ d π dπ₯ = total derivative of a function πΉ with respect to a variable π₯
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