Multidisciplinary design optimization (MDO) is concerned with solving design problems involving coupled numerical models of complex engineering systems. While various MDO software frameworks exist, none of them take full advantage of state-of-the-art algorithms to solve coupled models efficiently. Furthermore, there is a need to facilitate the computation of the derivatives of these coupled models for use with gradient-based optimization algorithms to enable design with respect to large numbers of variables. In this paper, we present the theory and architecture of OpenMDAO, an open-source MDO framework that uses Newton-type algorithms to solve coupled systems and exploits problem structure through new hierarchical strategies to achieve high computational efficiency. OpenMDAO also provides a framework for computing coupled derivatives efficiently and in a way that exploits problem sparsity. We demonstrate the framework's efficiency by benchmarking scalable test problems. We also summarize a number of OpenMDAO applications previously reported in the literature, which include trajectory optimization, wing design, and structural topology optimization, demonstrating that the framework is effective in both coupling existing models and developing new multidisciplinary models from the ground up. Given the potential of the OpenMDAO framework, we expect the number of users and developers to continue growing, enabling even more diverse applications in engineering analysis and design.
This paper describes the progress made in the development of OpenMDAO, an open source framework for performing Multidisciplinary Analysis and Optimization (MDAO). NASA intends to use OpenMDAO to aid in the design of unconventional aircraft, but the general structure and methods may be applied to solve any number of engineering-related design problems. The framework currently supports data passing capabilities, and several example problems have been executed with it. Recent work has focused on enabling the creation of more complex MDAO strategies, such as collaborative optimization and surrogate modeling techniques. An example is presented that demonstrates an implementation of the surrogate model generation using Kriging surrogate models augmented with the expected improvement method.
The optimization of multidisciplinary systems with respect to large numbers of design variables is best pursued using a gradient-based optimization together with a method that efficiently evaluates coupled derivatives, such as the coupled adjoint method. However, implementing such a method in a problem with more than a few disciplines is time consuming and error prone. To address this issue, we develop an automated procedure for assembling and solving the coupled derivative equations that takes into account the disciplinary couplings using the interdisciplinary dependency graph of the problem. The coupled derivatives can be computed completely analytically, if analytic derivatives are available for all disciplines; otherwise, the coupled derivatives are computed semi-analytically. The procedure determines the disciplinary analyses execution order, detects iterative cycles, and uses this information to converge the coupled analysis, and evaluate the coupled derivatives as efficiently as possible by exploiting sparsity. Sparsity can occur at two levels within a multidisciplinary problem: between disciplines, when certain analyses do not affect all outputs, and within a discipline when, the Jacobian of that discipline is sparse. The numerical procedures are implemented in NASA's OpenMDAO framework, providing a flexible API for declaring discipline-level derivatives that can handle sparsity within a discipline. The tool is demonstrated in two MDO problems: the design of a small satellite and its operation with the objective of maximizing downloaded data to a ground station, and the design of a horizontal-axis wind turbine with the objective of minimizing the cost of energy. In both cases, the method demonstrated improved efficiency by taking advantage of analytic gradients considering sparsity. This new capability in OpenMDAO greatly facilitates the implementation of system-level direct and adjoint coupled derivative evaluations, and is applicable for general problems.
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