A Fast and Efficient Adaptive Large Neighborhood Search Heuristic for the Passenger Train Timetabling Problem with Dynamic Demand

The railway planning process is a complex activity which is usually decomposed into a succession of stages, traditionally network design, line design, timetabling, rolling stock, and personnel planning. In this paper, we study the design and optimization of train timetables adapted to a dynamic demand environment. The objective is to minimize passenger waiting times at the stations. We first describe an integer linear programming formulation which generalizes the non-periodic train timetabling problem under a dynamic demand pattern. We then introduce a fast adaptive large neighborhood search (ALNS) heuristic in order to deal with larger instances and to solve the problem efficiently within short computational times. The algorithm provides timetables that may not be regular or periodic, but adjusted to a dynamic demand behavior. Through extensive computational experiments on artificial and real-world based instances, we demonstrate the computational superiority of ALNS compared with a truncated branch-and-cut algorithm. The average reduction on passenger waiting times is 26%, while the computational time of our ALNS algorithm is less than 1% of that required by the alternative algorithm. Out of 120 open instances, we obtain 84 new best known solutions and we reach the optimum on 10 out of 14 instances with known optimal solutions.