Based on time-dependent travel times for N past days, we consider the computation of robust routes according to the min-max relative regret criterion. For this method we seek a path minimizing its maximum weight in any one of the N days, normalized by the weight of an optimum for the respective day. In order to speed-up this computationally demanding approach, we observe that its output belongs to the Pareto front of the network with time-dependent multi-criteria edge weights. We adapt a well-known algorithm for computing Pareto fronts in time-dependent graphs and apply the bi-directional search technique to it. We also show how to parametrize this algorithm by a value K to compute a K-approximate Pareto front. An experimental evaluation for the cases N = 2 and N = 3 indicates a considerable speed-up of the bi-directional search over the uni-directional.
@InProceedings{mihalak_et_al:OASIcs.ATMOS.2015.82, author = {Mihal\'{a}k, Mat\'{u}\v{s} and Montanari, Sandro}, title = {{Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks}}, booktitle = {15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)}, pages = {82--94}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-99-6}, ISSN = {2190-6807}, year = {2015}, volume = {48}, editor = {Italiano, Giuseppe F. and Schmidt, Marie}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.82}, URN = {urn:nbn:de:0030-drops-54561}, doi = {10.4230/OASIcs.ATMOS.2015.82}, annote = {Keywords: shortest path, time-dependent, bi-criteria, bi-directional search, min-max relative regret} }
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