Optimal Paths with Impact on a Constraint System: An Application to the 1-Request Insertion for the Pickup and Delivery Problem with Transfers

In this paper, we deal with the Pickup and Delivery Problem with Transfers, and focus on the way a new request can be inserted into a current solution. This problem may be viewed as the search for a specific collection of constraints related to the nodes of a Time Expanded Network. It has most often been addressed in a very empirical way, and our goal here is to formalize it and handle it in an exact way through an adaptation of the A* algorithm that involves constraint propagation. We also present an empirical Dijkstra algorithm that computes tentative solutions whose consistence is then checked through constraint propagation. We conclude by comparing the behavior and performance of those algorithms.