Safety-oriented train timetabling and stop planning with time-varying and elastic demand on overcrowded commuter metro lines

In some megacities, commuter metro lines that connect suburbs and downtown areas always suffer from serious non-equilibrium passenger congestion at stations during rush hours, bringing huge operation risks. To balance the non-equilibrium passenger congestion on overcrowded metro lines, this study aims to jointly optimize the train timetable and stop plan from the perspective of transportation safety in which some effective skip-stop patterns are adopted to allocate necessary train capacities to overcrowded stations with consideration to time-varying and elastic demand. We formulate the problem of interest as an integer linear programming model where the total passenger gathering risk, passenger waiting time, passenger riding time, and loss of ticket income are all included in the objective function. An efficient iterated local search (ILS) algorithm is designed for the convenience of solving large-scale models. Numerical experiments for a series of small-scale and real-world case studies are conducted to test the performance of the proposed methods. The computational results show that the designed algorithm can obtain high-quality train operation schemes in a much shorter time, which can greatly improve transportation safety by balancing the number of stranded passengers at any station.