Since 0.9.0 OpenMDAO has had a new derivatives system that can handle really large design spaces. What does really large mean? We’ve tested the capability (in fact, we developed the capability around) a 25,000-design-variable problem. You can read all about the details in the online docs, which include some interactive data visualization with Google Earth. The docs tell you how to install and run the this test problem for yourself.
We worked closely with the University of Michigan MDO lab to implement their problem for a small satellite design. This problem achieves its large design space because the optimizer is being given control over the attitude and power distribution to subsystems for the entire mission. So this is a big optimal control problem, with some traditional design optimization thrown into the mix.
When John Hwang did the original work, he was able to converge this problem in about 100 hours. However, about 90% of that time was used calculating derivatives. The huge derivative cost was a function of the way he got derivatives – by solving a linear system that included all the variables in the whole system each time. When we implemented this problem in OpenMDAO, we were able to get the computational cost down to about 6 hours. This pickup was due to our using the data dependency graph to figure out which variables were needed for a given derivative calculation (almost always much less then the full set of variables for the whole problem). Since we shrank the size of the linear system for the derivatives solved by quite a bit, we became a lot more efficient.