A Numerical Optimization Technique for Scheduling Non-uniform Metro Trains under Time-varying Passenger Demands

Abstract

Urban rail transit is costly and often overloaded. Thus, the motivation of this paper is to develop specific operating strategies to reduce cost and improve service level. This paper proposed a numerical optimization technique to optimize non-uniform metro train timetables with time-varying passenger demands, where the total monetary cost of time and energy is minimized. The problem was formulated with a constrained, non-smooth, nonlinear programming model, and transformed into an unconstrained one by the proposed Augmented Lagrangian (AL) algorithm. Then, the Pattern Search (PS) algorithm was designed to search for an optimal solution in each iteration step of AL. The case study shows that the proposed technique is effective to obtain non-uniform timetables that significantly outperform uniform ones reducing cost at most 34.92%, and provides decision-making support.