A column-generation-based matheuristic for periodic train timetabling with integrated passenger routing
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In this study, the periodic train timetabling problem is formulated using a time-space graph formulation. The problem is tested on the morning rush hour period of the Regional and InterCity train network of Zealand, Denmark. The implemented solution method is based on an iterative model that applies what we define as a dive-and-cut-and-price procedure. An LP relaxed version of the problem with a subset of constraints is solved using column generation where each column corresponds to the train paths of a line. Violated constraints are added by separation and a heuristic process is applied to help to find integer solutions. The passengers are routed based on each resulting timetable allowing the method to estimate the total passenger travel time. The solution approach shows robust performance in a variety of the scenarios being able to find good quality solutions in terms of travel time and path length relatively fast. In addition, the graph formulation covers different real-life constraints and has the potential to easily be extended to accommodate more constraints.
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