Enhanced bi-directional dynamic programming algorithm for the resource constrained shortest path problem

In this paper we propose an enhanced bi-directional dynamic programming algorithm for the Resource Constrained Shortest Path, Righini and Salani (2006). In particular we study the join procedure, one of the time consuming components of the algorithm, and propose a dominance based join that uses binary search and Pareto frontier exploration. The proposed method can be used in both node-join and arc-join procedures. The computational experiments are performed on two classes of problems both describing complete graphs with negative cost cycles. On the first set, with a single resource consumption, the proposed procedure slightly improves the overall computational time with savings up to 8.4% for the B class and just 0.4% for the most time consuming class M. On the second set, with multiple resources consumption, the proposed procedure exhibits a remarkable improvement with an average speedup of 39.2%.