Abstract network optimization with application to vehicular routing

In this paper, the authors present a method for determining the optimum path within a network of two-way streets or roads. This approach builds on the principle of dynamic programming, but is distinct from it in that it is iterative and more straightforward in its formulation. In the process of determining the optimal solution, at the first iteration any node whose previous remaining cost is unknown is assigned an artificial, very large value. As the iterations proceed, these artificial values are replaced by their correct values once they are computed. The iterations stop when there is no further improvement. This will depend on the number of "backward" links in the optimal solution which of course is unknown a priori; however, it can never exceed N-3 where N is the total number of nodes. The user is required only to specify the origin node and destination node as well as the cost (both ways) between all pairs of nodes which have connecting links. Ordering of the intermediate nodes is arbitrary; however, the use of good judgment in choosing this ordering can reduce the number of iterations required. Bounds are presented on the total number of calculations required and examples are presented which demonstrate the effectiveness of the methods.