Possibly Mankind on the runMankind on the run (1956) by Gordon R. Dickson. I haven't read it and don't have a copy handy to check, but the title seemed promising, and this quote from someone at the Goodreads site is intriguing:
A hypothetical future where the world's problems have been solved by setting humans into castes and where no one gets to stay in one place for more than six months.