Train service design in an urban rail transit line incorporating multiple service routes and multiple train compositions

•We address a train service design problem with multiple service routes and multiple train compositions.•We formulate the problem as a mixed integer linear programming model by utilizing a novel linearization method.•We extend the optimal strategy to capture the extra waiting time of passengers due to capacity constraint.•A local search algorithm is developed to find (near-) optimal solutions in acceptable computation time.•The proposed approaches are validated by different size of instances from real urban rail transit lines. This paper focuses on the train service design problem within a given period in an urban rail transit line, where multiple either full-length or short-turn service routes can be operated, and each service route can utilize one of several different train compositions. The problem lies on determining the turn-back stations, train composition and frequency of each service route operated on the line. Considering the interests of operators and passengers, we decompose the problem as two subproblems namely train service configuration and passenger assignment. The first subproblem is formulated as an integer linear programming model with the objective of minimizing operators’ cost. Given a train service scheme, the second subproblem is modelled as a capacitated continuous multi-commodity flow model to minimize passengers’ waiting time cost and transfer cost. The optimal strategy is extended to determine the behaviour of passengers and capture the extra waiting time of passengers under capacity constraint. The two sub-models are weighted and integrated into a mixed integer nonlinear programming model, which is further transformed into a mixed integer linear programming model using a novel linearization method. By exploiting the special characteristics of the model, a tailored and easy to implement local search algorithm is developed to solve large-scale instances. Starting from the operator-optimum solution which can be easily obtained, the algorithm solves the two sub-models iteratively to search better solutions within a precalculated search range which is smaller than the complete feasible domain. Finally, different sizes of instances constructed from two urban rail transit lines are utilized to demonstrate the performance and practicability of the proposed approaches.