I'm trying to understand what my options are for optimizing a black-box simulation (output from a commercial, closed source finite element solver).
An example problem is the following. We have a building composed of a large number of beams. The size of each beam comes from a discrete set of choices (depending on what is available from the manufacturer). We would like to minimize the weight under some constraints, for example the internal force in each beam needs to be lower than its maximum force capacity.
At the moment we simply start with the lowest-weight solution, and iteratively increase the sizes until the constraints are satisfied, but this can result in cycles (increasing the size of one beam and increase the load in an another). We are looking for something that is a bit more robust.
I think what I'm looking for is surrogate optimization. But ideally I would like to work with hundreds if not thousands of variables and I think methods like Bayesian optimization are limited to low dimensional problems. I'm happy with just finding 'good-enough' solutions instead of a global optimal.