A Computational Study of Bi-directional Dynamic Programming for the Traveling Salesman Problem with Time Windows

This paper presents computational studies for the traveling salesman problem with time windows by applying a bi-directional resource-bounded label correcting algorithm. Label extensions and dominance start simultaneously in both forward and backward directions: the forward direction from the starting depot and the backward direction from the terminating depot. The resultant label extension process scans much smaller the space than in single directional dynamic programming, substantially reducing the number of non-dominated labels. The labels for both the forward direction and backward direction are ultimately joined to form a complete route if all relevant feasibility conditions are satisfied. We conduct extensive computational experiments on six benchmark data sets available in the literature. Optimal solutions are reported for a number of the instances for which no optimal solutions have been previously reported. The approach developed is shown competitive for the traveling salesman problem with time windows if compared with state-of-art methods in the literature.