Need help designing a multi-threaded solver

[4Dummies]

There's no code, because I haven't selected the tools yet. That's the question: choose among or between threading, multiprocessing, subprocess, pyzmq, and anything else, and give advice about how to put the pieces together. I'm in a quandary for having too many choices, each of which has its own learning curve, and I may not even know about the best possible tools for the job.