This article presents a specific filtering algorithm for the Frequency Assignment Problem with Polarisation, which combines arc-consistency and path-inverse-consistency adapted to the specificities of the constraints. The effectiveness of this filtering algorithm enabled us to improve the Tabu Search on a Consistent Neighbourhood (CN-Tabu) using two different approaches. So, after a short recall of this general methodology and a presentation of its obtained results on the FAPP, we propose a behavioural study of the two approaches by comparing the results.