OpenMDAO

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OpenMDAO in a nutshell

OpenMDAO is an open source framework written in Python to faciliate the coupling of multiple models to perform multidisciplinary analysis and design optimization. One of the unique features of OpenMDAO is the use of derivatives to accelerate the solution of the coupled system and to provide gradients for gradient-based optimization algorithms. As a result, OpenMDAO can solver problems with tens of thousands of variables and a similar number of constraints.

The development of OpenMDAO started in 2008, when developers at NASA identified the need for a new design optimization framework to address complex aircraft design optimization problems. More recently, OpenMDAO was re-written to use the modular analsysis and unified derivatives (MAUD) architecture, enabling the efficient computation of coupled derivatives. Follow the links to the websites and papers below for more details.

Links

• OpenMDAO site
• OpenMDAO documentation
• OpenMDAO source GitHub

References

• This is the main paper that describes the latest version of OpenMDAO 1. For a quick overview of what OpenMDAO is and what it does, read the introduction, the overview of applications (Sec. 7, especially Table 13), and the conclusions (Sec. 8). Potential OpenMDAO users should also read Sec. 3, which explains the basic usage and features through a simple example. The rest of the paper provides a background on MDO frameworks and the history of OpenMDAO development (Sec. 2), the theory behind OpenMDAO (Sec. 4), and the details of the major new contributions in OpenMDAO V2 in terms of multidisciplinary solvers (Sec. 5) and coupled derivative computation (Sec. 6).
• This paper on MAUD describes the core algorithms and data structures that are implemented in OpenMDAO 2.
• This paper on the unified derivatives equation (UDE) contains the theory that MAUD is built on. It explains all the methods for computing derivatives (finite differences, complex step, automatic differentiation, direct, and adjoint), including the derivatives of coupled multidisciplinary systems, and unifies the various methods using a single equations.

Publications from the MDO Lab that used OpenMDAO

1. Aircraft Ducted Heat Exchanger Aerodynamic Shape and Thermal Optimization

   E. J. Adler, A. H. R. Lamkin, and J. R. R. A. Martins

   ASME Journal of Heat and Mass Transfer, 147(1):011902, 2025

   doi:10.1115/1.4066438

   Details

2. Robust Schur-Complement Solvers and Large-Scale Multidisciplinary Design Optimization

   M. A. S. Abdul-Kaiyoom, A. Yildirim, , and R. R. A. M. Joaquim

   34th Congress of the International Council of the Aeronautical Sciences, 2024

   Details

3. Coupled Aeropropulsive Design Optimization of an Over-Wing Nacelle Configuration

   M. A. S. Abdul-Kaiyoom, A. Yildirim, , and R. R. A. M. Joaquim

   Journal of Aircraft, 2024

   Details

4. Blended wing body configuration for hydrogen-powered aviation

   E. J. Adler, and J. R. R. A. Martins

   Journal of Aircraft, 61(3), 2024

   doi:10.2514/1.C037582

   Details

5. A Proposed Benchmark Model for Practical Aerostructural Optimization of Aircraft Wings

   A. C. Gray, and J. R. R. A. Martins

   AIAA SciTech Forum, 2024

   doi:10.2514/6.2024-2775

   Details

6. Rapid Aerostructural Optimization of Wing-Propeller Systems

   J. Exalto, B. Pacini, S. Kaneko, J. R. R. A. Martins, and M. Hoogreef

   AIAA SciTech Forum, 2024

   doi:10.2514/6.2024-0374

   Details

7. Aerodynamic shape optimization of filleted intersections with surface mesh deformation

   H. M. Hajdik, A. Yildirim, and J. R. R. A. Martins

   34th Congress of the International Council of the Aeronautical Sciences, 2024

   Details

8. MDO Formulations for Simultaneous Design and Trajectory Optimization

   S. Kaneko, and J. R. R. A. Martins

   AIAA SciTech Forum, 2024

   doi:10.2514/6.2024-2231

   Details

9. Simultaneous optimization of design and takeoff trajectory for an eVTOL aircraft

   S. Kaneko, and J. R. R. A. Martins

   Aerospace Science and Technology, 155109617, 2024

   doi:10.1016/j.ast.2024.109617

   Details

10. Coupled Aeropropulsive Design Optimization of an Over-Wing Nacelle Configuration

    M. A. S. Abdul-Kaiyoom, A. Yildirim, , and R. R. A. M. Joaquim

    AIAA SciTech Forum, 2023

    doi:10.2514/6.2023-0327

    Details

11. RANS-Based Multipoint Aeropropulsive Design Optimization of an Over-Wing Nacelle Configuration

    M. A. S. Abdul-Kaiyoom, A. Yildirim, and J. R. R. A. Martins

    AIAA Aviation Forum, 2023

    doi:10.2514/6.2023-3588

    Details

12. Blended wing body configuration for hydrogen-powered aviation

    E. J. Adler, and J. R. R. A. Martins

    AIAA Aviation 2023 Forum, 2023

    doi:10.2514/6.2023-4020

    Details

13. Efficient Aerostructural Wing Optimization Considering Mission Analysis

    E. J. Adler, and J. R. R. A. Martins

    Journal of Aircraft, 60(3), 2023

    doi:10.2514/1.c037096

    Details

14. Geometrically Nonlinear High-fidelity Aerostructural Optimization Including Geometric Design Variables

    A. C. Gray, G. J. Kennedy, and J. R. R. A. Martins

    AIAA Aviation Forum, 2023

    doi:10.2514/6.2023-3316

    Details

15. Comparing Hydrogen and Jet-A for an N+3 Turbofan with Water Recirculation using Gradient-Based Optimization

    P. N. Atma, A. H. R. Lamkin, and J. R. R. A. Martins

    AIAA Aviation Forum, 2023

    doi:10.2514/6.2023-4018

    Details

16. Advancing Modularity and Framework Integration Level for Scalable High-Fidelity MDO

    T. Backhaus, M. A. S. Abdul-Kaiyoom, A. Yildirim, A. Stueck, and J. R. R. A. Martins

    AIAA AVIATION Forum, 2023

    doi:10.2514/6.2023-3315

    Details

17. Combined systems packaging and aerodynamic shape optimization of a full aircraft configuration

    H. M. Hajdik, B. Pacini, A. Yildirim, B. J. Brelje, and J. R. R. A. Martins

    AIAA Aviation Forum, 2023

    doi:10.2514/6.2023-3589

    Details

18. Simultaneous Optimization of Conceptual Design and Takeoff Trajectory of a Lift-Plus-Cruise UAV

    S. Kaneko, and J. R. R. A. Martins

    10th Autonomous VTOL Technical Meeting, 2023

    Details

19. Advancements in Coupled Aeropropulsive Design Optimization for High-Bypass Turbofan Engines

    A. H. R. Lamkin, A. Yildirim, J. R. R. A. Martins, and N. A. Wukie

    AIAA Aviation Forum, 2023

    doi:10.2514/6.2023-3591

    Details

20. Minimum Trim Drag for a Three-Surface Supersonic Transport Aircraft

    S. Seraj, and J. R. R. A. Martins

    AIAA Aviation Forum, 2023

    doi:10.2514/6.2023-3472

    Details

21. Aerostructural wing design optimization considering full mission analysis

    E. J. Adler, and J. R. R. A. Martins

    AIAA SciTech Forum, 2022

    doi:10.2514/6.2022-0382

    Details

22. Thermal Management System Optimization for a Parallel Hybrid Aircraft Considering Mission Fuel Burn

    E. J. Adler, B. J. Brelje, and J. R. R. A. Martins

    Aerospace, 9(5), 2022

    doi:10.3390/aerospace9050243

    Details

23. Automated Hybrid Propulsion Model Construction for Conceptual Aircraft Design and Optimization

    M. Fouda, E. J. Adler, J. H. Bussemaker, J. R. R. A. Martins, D. F. Kurtulus, L. Boggero, and B. Nagel

    33rd Congress of the International Council of the Aeronautical Sciences, 2022

    Details

24. Fleet Design Optimization of Package Delivery UAVs Considering Operations

    S. Kaneko, and J. R. R. A. Martins

    AIAA SciTech Forum, 2022

    doi:10.2514/6.2022-1503

    Details

25. Boundary Layer Ingestion Benefit for the STARC-ABL Concept

    A. Yildirim, J. S. Gray, C. A. Mader, and J. R. R. A. Martins

    Journal of Aircraft, 59(4):896–911, 2022

    doi:10.2514/1.C036103

    Details

26. A Nonlinear Schur Complement Solver for CFD-Based Multidisciplinary Models

    A. Yildirim, J. S. Gray, and J. R. R. A. Martins

    Eleventh International Conference on Computational Fluid Dynamics, 2022

    Details

27. Performance Analysis of Optimized STARC-ABL Designs Across the Entire Mission Profile

    A. Yildirim, J. S. Gray, C. A. Mader, and J. R. R. A. Martins

    Proceedings of the AIAA SciTech Forum, 2021

    doi:10.2514/6.2021-0891

    Details

28. Coupled Aeropropulsive Design Optimization of a Podded Electric Propulsor

    A. Yildirim, J. S. Gray, C. A. Mader, and J. R. R. A. Martins

    AIAA Aviation Forum, 2021

    doi:10.2514/6.2021-3032

    Details

29. Large-Scale Path-Dependent Optimization of Supersonic Aircraft

    J. Jasa, B. Brelje, J. Gray, C. A. Mader, and J. R. R. A. Martins

    Aerospace, 7(152), 2020

    doi:10.3390/aerospace7100152

    Details

30. Development of a Conceptual-Level Thermal Management System Design Capability in OpenConcept

    B. J. Brelje, J. P. Jasa, J. R. R. A. Martins, and J. S. Gray

    NATO Research Symposium on Hybrid/Electric Aero-Propulsion Systems for Military Applications (AVT-RSY-323), 2019

    doi:10.14339/STO-MP-AVT-323

    Details

31. OpenMDAO: An open-source framework for multidisciplinary design, analysis, and optimization

    J. S. Gray, J. T. Hwang, J. R. R. A. Martins, K. T. Moore, and B. A. Naylor

    Structural and Multidisciplinary Optimization, 59(4):1075–1104, 2019

    doi:10.1007/s00158-019-02211-z

    Details

32. High-fidelity design-allocation optimization of a commercial aircraft maximizing airline profit

    J. T. Hwang, J. Jasa, and J. R. R. A. Martins

    Journal of Aircraft, 56(3):1165–1178, 2019

    doi:10.2514/1.C035082

    Details

33. Coupled Design of a Supersonic Engine and Thermal System

    J. P. Jasa, B. J. Brelje, C. A. Mader, and J. R. R. A. Martins

    World Congress of Structural and Multidisciplinary Optimization, 2019

    Details

34. How Certain Physical Considerations Impact Aerostructural Wing Optimization

    J. P. Jasa, S. S. Chauhan, J. S. Gray, and J. R. R. A. Martins

    AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2019

    doi:10.2514/6.2019-3242

    Details

35. Multipoint Variable Cycle Engine Design Using Gradient-based Optimization

    J. P. Jasa, J. S. Gray, J. A. Seidel, C. A. Mader, and J. R. R. A. Martins

    57th AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, 2019, 2019

    doi:10.2514/6.2019-0172

    Details

36. Aeropropulsive Design Optimization of a Boundary Layer Ingestion System

    A. Yildirim, J. S. Gray, C. A. Mader, and J. R. R. A. Martins

    AIAA Aviation Forum, 2019

    doi:10.2514/6.2019-3455

    Details

37. Development of a Conceptual Design Model for Aircraft Electric Propulsion with Efficient Gradients

    B. J. Brelje, and J. R. R. A. Martins

    Proceedings of the AIAA/IEEE Electric Aircraft Technologies Symposium, 2018

    doi:10.2514/6.2018-4979

    Details

38. Multifidelity Optimization Under Uncertainty for a Tailless Aircraft

    A. Chaudhuri, J. Jasa, J. R. R. A. Martins, and K. Willcox

    2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference; AIAA SciTech Forum, 2018

    doi:10.2514/6.2018-1658

    Details

39. Low-Fidelity Aerostructural Optimization of Aircraft Wings with a Simplified Wingbox Model Using OpenAeroStruct

    S. S. Chauhan, and J. R. R. A. Martins

    Proceedings of the 6th International Conference on Engineering Optimization, EngOpt 2018, 418-431, 2018

    doi:10.1007/978-3-319-97773-7

    Details

40. A computational architecture for coupling heterogeneous numerical models and computing coupled derivatives

    J. T. Hwang, and J. R. R. A. Martins

    ACM Transactions on Mathematical Software, 44(4):Article 37, 2018

    doi:10.1145/3182393

    Details

41. Open-source coupled aerostructural optimization using Python

    J. P. Jasa, J. T. Hwang, and J. R. R. A. Martins

    Structural and Multidisciplinary Optimization, 57(4):1815–1827, 2018

    doi:10.1007/s00158-018-1912-8

    Details

42. Design and Trajectory Optimization of a Morphing Wing Aircraft

    J. P. Jasa, J. T. Hwang, and J. R. R. A. Martins

    2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference; AIAA SciTech Forum, 2018

    doi:10.2514/6.2018-1382

    Details

43. Trajectory Optimization of a Supersonic Air Vehicle with Thermal Fuel Management System

    J. P. Jasa, C. A. Mader, and J. R. R. A. Martins

    AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2018

    doi:10.2514/6.2018-3884

    Details

44. Next generation aircraft design considering airline operations and economics

    S. Roy, W. A. Crossley, K. T. Moore, J. S. Gray, and J. R. R. A. Martins

    AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2018

    doi:10.2514/6.2018-1647

    Details

45. Large-Scale Multidisciplinary Optimization of a Small Satellite’s Design and Operation

    J. T. Hwang, D. Y. Lee, J. W. Cutler, and J. R. R. A. Martins

    Journal of Spacecraft and Rockets, 51(5):1648–1663, 2014

    doi:10.2514/1.A32751

    Details

46. Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models

    J. R. R. A. Martins, and J. T. Hwang

    AIAA Journal, 51(11):2582–2599, 2013

    doi:10.2514/1.J052184

    Details

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