Given an undirected graph G(V, E) with each edge e is associated with k weight functions where ωl(e) > 0, ∀ e ∈ E and 1 ≤ l ≤ k. A constants vector c = (c1, c2, …, ck). A multi-constrained QoS routing problem consists in finding a path p between a source s and destination d, so that, ωl(p) ≤ cl, where 1 ≤ l ≤ k.