Integrated line configuration and frequency determination with passenger path assignment in urban rail transit networks

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.