Simultaneous passenger train routing and timetabling using an efficient train-based Lagrangian relaxation decomposition

Wenliang Zhou and Hualiang Teng

Transportation Research Part B: Methodological, 2016, vol. 94, issue C, 409-439

Abstract: This paper focuses on the simultaneous passenger train routing and timetabling problem on the rail network consisting of both unidirectional and bidirectional tracks using an efficient train-based Lagrangian relaxation decomposition. We first build an integer linear programming model with many 0–1 binary and non-negative integer decision variables, after then reformulate it as a train path-choice model for providing an easier train-based Lagrangian relaxation decomposition mechanism based on the construction of space-time discretized network extending from node-cell-based rail network. Moreover, through reformulating safety usage interval restrictions with a smaller number of constraints in this reformulated model, the train-based decomposition needs fewer Lagrangian multipliers to relax these constraints. On the basis of this decomposition, a solving framework including a heuristic algorithm is proposed to simultaneously optimize both the dual and feasible solutions. A set of numerical experiments demonstrate the proposed Lagrangian relaxation decomposition approach has better performances in terms of minimizing both train travel time and computational times.

Keywords: Train; Routing; Timetabling; Lagrangian relaxation; Decomposition (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (16)

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DOI: 10.1016/j.trb.2016.10.010

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