If your polymer chains are open (embedded closed line segment in 3-space), then I wouldn't recommend using global knot invariants (Alexander polynomial, Jones polynomial) because they will not make any sense. Artificially closing open knots (pretending they are honest topological knots) strikes me as being bad strategy. Instead, Peter Røgen has a body of work on Gauss integral invariants (modifications of early Vassiliev invariants) which in my understanding are the best computational "invariants" ("descriptors" is the right word, because an open knot is topologically trivial) out there right now. His papers also discuss the use of early Vassiliev invariants in distinguishing closed knots.
For closed knots at least, it is my impression understanding that knot signatures and versions of covering linkage invariants (see e.g. Hartley-Murasugi and e.g. Gordon-Litherland) can be calculated in polynomial time, and are very good at distinguishing knots in practice. I don't know why biologists who study molecules which form closed loops are not using such invariants more extensively, in preference to more computationally expensive invariants; maybe somebody more knowledgeable can comment.
The best answer I can give, though, would be to e-mail Peter Røgen directly and to ask him, because this is exactly what he does for a living.