I'm a prof. The easy solution is to give very little weight to homework. The assignments should be designed to teach concepts. Concepts that are then tested in a controlled environment, where cheating is not possible.
Remove the incentive to cheat, and save yourself the time trying to catch it (and punish it, despite an uncooperative administration).
Remove the incentive to cheat, and save yourself the time trying to catch it (and punish it, despite an uncooperative administration).