Time-dependent route planning with generalized objective functions

Abstract

We consider the problem of finding routes in road networks that optimize a combination of travel time and additional time-invariant costs. These could be an approximation of energy consumption, distance, tolls, or other penalties. The resulting problem is NP-hard, but if the additional cost is proportional to driving distance we can solve it optimally on the German road network within 2.3 s using a multi-label A*search. A generalization of time-dependent contraction hierarchies to the problem yields approximations with negligible errors using running times below 5 ms which makes the model feasible for high-throughput web services. By introducing tolls we get considerably harder instances, but still we have running times below 41 ms and very small errors. © 2012 Springer-Verlag.