Train schedule optimization for commuter-metro networks

The interconnection and synchronization among different transport modes have been more and more attractive as the modern transportation system is moving towards Mobility-as-a Service. In this study, we address the train scheduling problem for "commuter rail-metro"systems, where the trains from commuter rail lines can go directly into metro systems to provide seamless services for passengers. To optimize the schedule of trains for both commuter rail lines and metro lines, we propose a job shop scheduling model where precedence constraints from commuter-metro networks are taken into account and develop a mixed-integer programming (MIP) model with quadratic constraints. Our model considers the orders of different types of trains and the safety constraints, due to different types of signalling equipment in commuter and metro systems. Since these constraints involve a set of IF-THEN rules, we prove that these constraints can be equivalently reformulated as linear inequalities, without adding new variables. To solve the proposed model efficiently, we design an iterative solution framework, which generates a feasible solution using dynamic programming, next solves a MIP model, then calculates the train speed profiles, and if train speed profiles violate the safety constraints, re optimizes the MIP model with modified alternative constraints. To verify the effectiveness of the proposed approaches, numerical experiments are performed on small and real-world instances based on the Beijing metro Line 1 and the Batong Line operational data.