  We consider the price-optimal earliest arrival problem in public transit
(POEAP) in which we aim to calculate the Pareto-set of journeys with respect to
ticket price and arrival time in a public transportation network. Public
transit fare structures are often a combination of various fare strategies such
as, e.g., distance-based fares, zone-based fares or flat fares. The rules that
determine the actual ticket price are often very complex. Accordingly, fare
structures are notoriously difficult to model, as it is in general not
sufficient to simply assign costs to arcs in a routing graph. Research into
POEAP is scarce and usually either relies on heuristics or only considers
restrictive fare models that are too limited to cover the full scope of most
real-world applications. We therefore introduce conditional fare networks
(CFNs), the first framework for representing a large number of real-world fare
structures. We show that by relaxing label domination criteria, CFNs can be
used as a building block in label-setting multi-objective shortest path
algorithms. By the nature of their extensive modeling capabilities, optimizing
over CFNs is NP-hard. However, we demonstrate that adapting the multi-criteria
RAPTOR (MCRAP) algorithm for CFNs yields an algorithm capable of solving POEAP
to optimality in less than 400 ms on average on a real-world data set. By
restricting the size of the Pareto-set, running times are further reduced to
below 10 ms.
