LegalFarePlan: A Label-Setting Framework for Fare-Transparent Urban Rail Route Planning under Non-Additive Fare Rules

Urban rail fare systems may be non-additive: the fare of a single paid journey from an origin to a destination can differ from the sum of fares over multiple legally separated journey legs. This paper presents LegalFarePlan, a fare-transparent route-planning framework that models legal exit-and-reentry operations as explicit, auditable constraints. Given a transit network, fare function, transfer rules, station-level exit/re-entry costs, an extra-time budget, and a split limit, the planner computes explainable route plans over paid journey segments. The artifact implements Dijkstra shortest-time and direct route-planner baselines, a greedy split heuristic, bounded exact label-setting, and Pareto-frontier search. Evaluation uses controlled synthetic data and a 57-station semi-synthetic benchmark with 360 OD pairs. On the semi-synthetic benchmark, bounded exact search identifies positive modeled fare reductions for 71.11% of OD pairs, with mean reduction 3.78 and maximum reduction 9.0 synthetic fare units under a 45-minute extra-time budget. These results demonstrate method behavior and reproducibility; they are not empirical conclusions about MTR or any transit operator.