Permutation Inversion Question

For solving a quadratic assignment problem (QAP) I use a heuristic and for comparison reasons I use the inversion table of the permutation (see: http://clarkgrubb.wordpress.com/2005/08/14/iterating-through-permutations/) to represent the solutions.
To evaluate the cost function I always have to reconstruct the permutation from the inversion.
Since these are isomorph there has to be a possibility to evaluate the cost from the invertion table too.

I've no idea how to manage it. Any help is welcome!
Thanks,
Markus
.