A New Resource-Constrained Multicommodity Flow Model for Conflict-Free Train Routing and Scheduling

G. Caimi (), F. Chudak (), M. Fuchsberger (), M. Laumanns () and R. Zenklusen ()
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G. Caimi: Institute for Operations Research, ETH Zurich, 8092 Zurich, Switzerland
F. Chudak: D-Wave Systems Inc., Burnaby, British Columbia V5C 6G9, Canada
M. Fuchsberger: Institute for Operations Research, ETH Zurich, 8092 Zurich, Switzerland
M. Laumanns: Institute for Operations Research, ETH Zurich, 8092 Zurich, Switzerland
R. Zenklusen: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Transportation Science, 2011, vol. 45, issue 2, 212-227

Abstract: This paper addresses the problem of generating conflict-free train schedules on a microscopic model of the railway infrastructure. Conflicts arise if two or more trains are scheduled to block the same track section at the same time. A standard model for this problem is the so-called conflict graph, where each considered train path corresponds to a vertex, and edges represent pairwise conflicts so that a conflict-free schedule corresponds to a maximum independent set. Because the linear programming relaxation of the conflict graph formulation is typically very weak, we develop an alternative model using the sequence of resources that each train path passes, encoded in a resource tree. For each resource, we can efficiently determine the maximal conflict cliques by scanning through the blocking times of all train paths and use these cliques as strong cutting planes in an integer linear programming formulation. We show that the number of maximal conflict cliques is linear in the number of train paths, so the ILP formulation uses much fewer but stronger constraints compared to the conflict graph model. In tests with real-world data from the Swiss Federal Railways, the new Resource Tree Conflict Graph model generates for major stations within seconds, even though the underlying model contains about half a million binary variables. This corresponds to a reduction of the computation time of roughly two orders of magnitude when compared to previous approaches and thus allows us to tackle considerable larger problem instances.

Keywords: train scheduling; blocking times; multicommodity flow; train routing; conflict graph; conflict cliques; integer linear programming (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (25)

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