This paper considers a line planning problem in an urban rail transit (URT) network with passenger path assignment. The line planning problem involves both line configuration and frequency setting for the optimization of a combination of operator-oriented objective (minimization of operating costs or maximization of profits) and passenger-oriented objective (minimization of total travel times). The interplay between the line planning and the passenger assignment is explicitly taken into account and the problem is formulated as a mixed-integer non-linear programming (MINLP) model with linear constraints. In order to take advantage of existing commercial mix-integer linear programming (MILP) solvers, we propose an outer approximation method to linearize the objective. Finally, the model and solution algorithm are illustrated with a simplified version of the Hong Kong Mass Transit Railway (MTR) network.

本文考虑了带有旅客路径分配的城市轨道交通（URT）网络中的线路规划问题。线路规划问题涉及线路配置和频率设置，以优化以运营商为导向的目标（运营成本的最小化或利润的最大化）和以旅客为导向的目标（总行程时间的最小化）的组合。明确考虑了线路规划和乘客分配之间的相互作用，并将问题表述为具有线性约束的混合整数非线性规划（MINLP）模型。为了利用现有的商业混合整数线性规划（MILP）求解器，我们提出了一种外部逼近方法来线性化目标。最后，