As a widely existing form of public transit fare structures, zone fare system is traditionally designed in a separate way, which may lead to suboptimal results. This paper aims to concurrently address the zone division and fare calculation issues of the zone fare system design in a rail transit line. It is necessary to consider passengers as well as operators to find an impartial zone fare system. A fair zone fare system is one where the zone fares are as close as possible to the distance-based fares, for the fares of the distance-based fare system are highly correlated with the actual distance of trips. Thus, the fare deviations for the trips between the zone fare system and the distance-based fare system are utilized as the evaluation metric of fairness. To achieve the goal of minimizing fare deviations for all trips, we introduce three indexes: average absolute deviation, average squared deviation, and maximum mileage fare deviation. With the three indexes as the objective functions, we develop a joint optimization algorithm where a novel zone boundary adjustment scheme is proposed as the key technique. Numerical results show that the proposed algorithm can effectively provide a joint optimal scheme and the optimal number of planned zones is 5 for Changsha Metro Line 2. The proposed algorithm can provide guidance for the practical design and adjustment of the zone fare system.

中文翻译：

---

轨道交通专线收费系统设计

作为一种广泛存在的公交票价结构形式，区域票价系统传统上是通过单独的方式设计的，这可能会导致效果不理想。本文旨在同时解决轨道交通线区域票价系统设计中的区域划分和票价计算问题。有必要考虑乘客和运营商以找到公正的区域票价系统。公平区域票价系统是一种区域票价尽可能接近基于距离的票价的系统，因为基于距离的票价系统的票价与行程的实际距离高度相关。因此，区域票价系统和基于距离的票价系统之间的行程票价偏差被用作公平性的评估指标。为了实现使所有行程的票价偏差最小化的目标，我们引入了三个指标：平均绝对偏差，平均平方偏差和最大里程票价偏差。以这三个指标为目标函数，我们开发了一种联合优化算法，其中提出了一种新的区域边界调整方案作为关键技术。数值结果表明，该算法可以有效地提供联合最优方案，长沙地铁2号线的最佳规划区域数为5。该算法可以为区域票价系统的实际设计和调整提供指导。