Is there a Python project where a commercial FEA (finite element analysis) package is used to generate input data for a freely available optimizer, such as scipy.optimize, pymoo, pyopt, pyoptsparse?
You can find one implementation of Python/ABAQUS optimization in the following paper:
DOI: 10.1016/j.advengsoft.2015.02.006
However, this is not a black box optimization since the analytical derivatives are used. You can implement the black-box optimization by presenting a Python code that presents an artificial neural network (ANN) surrogate to predict the derivatives (ANN is implemented in Python). You can also predict the objective by ANN. Then you can perform the mathematical optimization so easily (for example the implementation of MMA is available in Python). You can find such a project in the following link (a Ph.D. thesis but the codes are not available):