A Simple and Fast Algorithm for Restricted Shortest Path Problem

The restricted shortest path problem (RSP) is considered as one of the key components of the Quality of Service (QoS) routing. It is well-known that this problem is NP-hard. A simple and fast algorithm for solving RSP is presented in this paper. The idea is to include complicating constraints in the objective function with the "penalty" term, optimizes the resulting Lagrangian relaxation problem. A simple technique of updating multiplies based on penalty method is also applied in the iterative process. The motivation behind the algorithm is that relaxation problem can be solved rapidly and updating of Lagrangian multipliers are calculated easily in the iterative process. The numerical results show that the algorithm presented in this paper is simple and fast.