破解地铁票价非叠加难题，让换乘路线更省钱透明
LegalFarePlan: A Label-Setting Framework for Fare-Transparent Urban Rail Route Planning under Non-Additive Fare Rules
- 将换乘规则建模为可审计的显式约束，实现票价透明化规划
- 在57站半合成数据上，71.11%的起点终点对可节省3.78至9.0单位票价
- 适合关注公共交通经济性与算法可解释性的研究者和城市规划者
城市轨道交通票价系统可能具有非叠加性：从起点到终点的一次付费行程票价，可能不同于多个合法分段行程票价之和。本文提出LegalFarePlan，一个票价透明的路径规划框架，将合法出站再进站操作建模为显式、可审计的约束。给定交通网络、票价函数、换乘规则、站点级进出站成本、额外时间预算及拆分限制，该框架可计算出覆盖付费行程段的可解释路线方案。实现包括基于Dijkstra的最短时间基线、直接路径规划器、贪心拆分启发式、有界精确标签设置和帕累托前沿搜索。评估使用控制合成数据及包含360个起讫点对的57站半合成基准。在半合成基准上，有界精确搜索在45分钟额外时间预算下，对71.11%的起讫点对实现了正向票价降低，平均降幅3.78，最大降幅9.0合成票价单位。结果验证了方法行为与可复现性，不构成对MTR或任何公交运营商的实际结论。
原文摘要 · Abstract (English)
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.
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