The OpenVSP-in-the-loop process that they describe includes the parametric variation of an OpenVSP geometry to produce a new shape while exporting the base mesh to TCAE. If you zoom in on the mesh setup (looks like polyhedral mesh generation from tris, quads, pents, and hexes) they are reading STL files from a directory and the software is building on that. It doesn't look like they used OpenVSP's intersection algorithms to do this. Just read a raw STL export.
You would read in a VSP3 file as Rob described, manipulate your parameters to change the shape, export the resulting mesh as STL (I assume), and repeat until converged on your solution. This can be performed in any of the API languages but would commonly be used in the native VSPSCRIPT or Python API options. It all depends on what your optimizer loops are written in. If TOPT can speak directly to the VSP API, then it would be handled within the TCAE/TOPT software, otherwise there is an established connection between the tools that tells the TOPT parameters 1-4 to change and reimport the VSP model.
