We consider the price-optimal earliest arrival problem in public transit (POEAP) in which we aim to calculate the Pareto-front 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.

翻译：我们认为公共交通(POEAP)中的价格最理想的最早抵达问题,我们试图在公共交通网络中计算票价和抵达时间,在公共交通网络中计算Pareto行程前端的票价和抵达时间,公共过境票价结构往往是各种票价战略的组合,例如远程票价、区价票价或平价票价等,决定实际票价的规则往往非常复杂。因此,票价结构的模型非常困难,因为通常不足以简单地在路由图中为Arcs分配费用。对POEAP的研究很少,通常依赖超额票价,或只是考虑限制性票价模式,这些模式太有限,无法涵盖大多数现实世界应用程序的全部范围。因此,我们引入了有条件的远价网络,这是代表大量真实世界远价结构的第一个框架。我们表明,通过放松标签控制标准,CFNFS可以进一步用作制定标签的多目标最短路径算法的建筑块块。基于其广泛建模能力的性质,在低于C-MAR标准值上最优化的C-RBA值,但通过降低C-RA-RMA标准,而降低C-RBRBRAFA值的标准是降低C-RM的10级标准。