A pattern-based timetabling strategy for a short-turning metro line

The planning of metro lines is typically done through a strictly hierarchical approach, which is effective but somewhat inflexible. In this paper, we propose a flexible semiperiodic timetabling strategy using short-turning; thus, allowing trains to turn before reaching the terminal station of a line. Our strategy produces timetables that are periodic with respect to a group of short-turning destinations. This is denoted by the term service pattern. We introduce the service pattern timetabling problem (SPTP). Given a service pattern, the SPTP optimizes the train timetable considering capacity restrictions. The SPTP is modeled as a constraint program. We develop a framework for producing a large set of diverse and high-quality timetables for a metro line. This is achieved by repeatedly solving the SPTP with different patterns. Then we select a restricted list of non-dominated solutions with respect to three objectives: (1) the average passenger waiting time, (2) the maximum load factor achieved by the trains, and (3) the number of transfers induced by short-turning. We evaluate the proposed framework on a number of test instances. Through our computational experiments, we demonstrate the effectiveness of the developed strategy.