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Sökning: WFRF:(Nou Andreas)

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1.
  • Brännlund, Ulf, et al. (författare)
  • Railway Timetabling Using Lagrangian Relaxation
  • 1998
  • Ingår i: Transportation Science. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0041-1655 .- 1526-5447. ; 32:4, s. 358-369
  • Tidskriftsartikel (refereegranskat)abstract
    • We present a novel optimization approach for the timetabling problem of a railway company, i.e., scheduling of a set of trains to obtain a profit maximizing timetable, while not violating track capacity constraints. The scheduling decisions are based on estimates of the value of running different types of service at specified times. We model the problem as a very large integer programming problem. The model is flexible in that if allows for general cost functions. We have used a Lagrangian relaxation solution approach, in which the track capacity constraints are relaxed and assigned prices, so that the problem separates into one dynamic program for each physical train. The number of dual variables is very large. However, it turns out that only a small fraction of these are nonzero, wh ich one may take advantage of in the dual updating schemes. The approach has been, tested on a realistic example suggested by the Swedish National Railway Administration. This example contains 18 passenger trains and 8 freight trains to be scheduled during a day on a stretch of single track, consisting of 17 stations. The computation times are rather modest and the obtained timetables are within a few percent of optimality.
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2.
  • Kiwiel, Krzysztof C, et al. (författare)
  • Bregman proximal relaxation of large-scale 0-1 problems
  • 2000
  • Ingår i: Computational optimization and applications. - 0926-6003 .- 1573-2894. ; 15:1, s. 33-44
  • Tidskriftsartikel (refereegranskat)abstract
    • We apply a recent extension of the Bregman proximal method for convex programming to LP relaxations of 0-1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successively to retain global convergence. Our framework is applied to relaxations of large-scale set covering problems that arise in airline crew scheduling. Approximate relaxed solutions are used to construct primal feasible solutions via a randomized heuristic. Encouraging preliminary experience is reported.
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