## Railway Track Allocation by Rapid Branching

Please always quote using this URN: urn:nbn:de:0297-zib-11864
• The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for difficult instances of the benchmark library TTPLIB are reported.

Author: Ralf Borndörfer, Thomas Schlechte, Steffen Weider ZIB-Report Ganzzahlige Programmierung ; Proximale Bündelmethode; Rapid-Branching-Heuristik ; Trassenallokationsproblem Bundle Method ; Optimization ; Railway Track Allocation ; Rapid Branching 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B06 Transportation, logistics 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C27 Combinatorial optimization Zuse Institut Berlin 2010/08/24 ZIB-Report (10-22) 1438-0064

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