An improved solution algorithm for the constrained shortest path problem

The shortest path problem is one of the classic network problems. The objective of this problem is to identify the least cost path through a network from a pre-determined starting node to a pre-determined terminus node. It has many practical applications and can be solved optimally via efficient algorithms. Numerous modifications of the problem exist. In general, these are more difficult to solve. One of these modified versions includes an additional constraint that establishes an upper limit on the sum of some other arc cost (e.g., travel time) for the path. In this paper, a new optimal algorithm for this constrained shortest path problem is introduced. Extensive computational tests are presented which compare the algorithm to the two most commonly used algorithms to solve it. The results indicate that the new algorithm can solve optimally very large problem instances and is generally superior to the previous ones in terms of solution time and computer memory requirements. This is particularly true for the problem instances that are most difficult to solve. That is, those on large networks and/or where the additional constraint is most constraining.