At the time of writing, the P&R algorithms included with Rig do not make any guarantees about repeatability with the exception of the SA algorithm. It would be "nice to have" the whole process produce repeatable results given some suitable extra "seed" hint arguments and OrderedDict based vertices_resources.
Fixing up the other placement and allocation algorithms should be easy enough. The router, however, may be tricker since there's a lot of fussing around with data structures and lookups and even the shortest-path functions are (by design) non deterministic.