Approximate dynamic programming approach to efficient metro train timetabling and passenger flow control strategy with stop-skipping

Urban metro systems continuously face high travel demand during rush hours, which brings excessive energy waste and high risk to passengers. In order to alleviate passenger congestion, improve train service levels and reduce energy consumption, a nonlinear dynamic programming (DP) model of efficient metro train timetabling and passenger flow control strategy with stop-skipping is presented, which consists of state transition equations concerning train traffic and passenger load. To overcome the curse of dimensionality, the formulated nonlinear DP problem is transformed into a discrete Markov decision process, and a novel approximate dynamic programming (ADP) approach is designed based on the lookahead policy and linear parametric value function approximation. Finally, the effectiveness of this method is verified by three groups of numerical experiments. Compared with Particle Swarm Optimization (PSO) and Simulated Annealing (SA), the designed ADP approach could obtain high-quality solutions quickly, which makes it applicable to the practical implementation of metro operations.