Tree decomposition introduced by Robertson and Seymour aims to decompose a problem into clusters constituting an acyclic graph. There are works exploiting tree decomposition for complete search methods. In this paper, we show how tree decomposition can be used to efficiently guide the exploration of local search methods that use large neighborhoods like VNS. We introduce tightness dependant tree decomposition which allows to take advantage of both the structure of the problem and the constraints tightness. Experiments performed on random instances (GRAPH) and real life instances (CELAR and SPOT5) show the appropriateness and the efficiency of our approach.