@article{SchienleMaristanydelasCasasBlanco, author = {Schienle, Adam and Maristany de las Casas, Pedro and Blanco, Marco}, title = {A Priori Search Space Pruning in the Flight Planning Problem}, issn = {1438-0064}, doi = {https://doi.org/10.4230/OASIcs.ATMOS.2019.8}, abstract = {We study the Flight Planning Problem for a single aircraft, where we look for a minimum cost path in the airway network, a directed graph. Arc evaluation, such as weather computation, is computationally expensive due to non-linear functions, but required for exactness. We propose several pruning methods to thin out the search space for Dijkstra's algorithm before the query commences. We do so by using innate problem characteristics such as an aircraft's tank capacity, lower and upper bounds on the total costs, and in particular, we present a method to reduce the search space even in the presence of regional crossing costs. We test all pruning methods on real-world instances, and show that incorporating crossing costs into the pruning process can reduce the number of nodes by 90\\% in our setting.}, language = {en} } @misc{BlancoBorndoerferHoangetal., author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Maristany de las Casas, Pedro and Schlechte, Thomas and Schlobach, Swen}, title = {Cost Projection Methods for the Shortest Path Problem with Crossing Costs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64817}, abstract = {Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that approximates crossing costs by shadow costs on individual arcs, thus reducing the SPPCC to a standard shortest path problem. We evaluate all algorithms' performance on real-world flight trajectory optimization instances, obtaining very good {\`a} posteriori error bounds.}, language = {en} }